Monthly Archives: June 2024

Quantum computing will be a game-changer and could create big opportunities for some of the top quantum computing stocks.

In fact, according to McKinsey, it could take computing and the ability to solve complex problems quickly to a whole new level. They also believe it could create a $1.3 trillion opportunity by the time 2035 rolls around.

Quantum computing is a huge leap forward because complex problems that currently take the most powerful supercomputer several years could potentially be solved in seconds, said Charlie Campbell forTime.This could open hitherto unfathomable frontiers in mathematics and science, helping to solve existential challenges like climate change and food security.

It couldhelp speed up new drug treatment discoveries. It may even help speed up financing and data speed, assist with climate change issues, cybersecurity and other mind-boggling complex issues faster than a regular computer.

Even more impressive, the technology is already beingreferred to as a revolution for humanity bigger than fire, bigger than the wheel, according toHaim Israel, Head of Thematic Investing Research atBank of America.

All of which could fuel big upside for quantum computing stocks.

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Consolidating at $7.87, Id like to see shares of IonQ (NYSE:IONQ) initially run back to $10 a share.

For one, earnings have been ok.The company just posted a first-quarter loss of 19 cents, which beat expectations by six cents. Revenue of $7.6 million up 77.2% year over year beat by $600,000. Also, for the full year, revenue is expected to be between $37 million and $41 million, with estimates calling for $39.99 million.

Two, the company is quickly gaining more U.S. defense, technology and university clients. It also expects to increase its computing power from AQ 36 (a tool used to show how useful a quantum computer is at solving real problems) to AQ 64 by 2025.

Three, whats really enticing about IONQ is that were still in the early stages of growth. When quantum computing does become far bigger than it is now, it could propel this $1.74 billion company to higher highs.

Source: Bartlomiej K. Wroblewski / Shutterstock.com

Another one of the top quantum computing stocks to buy isD-Wave Quantum(NYSE:QBTS), which claims to be the worlds first commercial supplier of quantum computers.

At the moment, QBTS is sitting at double-bottom support at $1.16. From here, Id like to see it initially run to about $1.70. Then, once the quantum computing story really starts to heat up, Id like to see the stock run back to $3.20 from its current price.

Helping, QBTS has a consensus strong buy rating from four analysts, with an average price target of $3. And, the stock is set to join theRussell 3000 Index on July 1, which will give it even more exposure to investors. In addition, not long ago, analysts at Needham initiated coverage of QBTS with a buy rating and a price target of $2.50.

Even better, the company just extended its partnership with Aramco to help solve complex geophysical optimization issues with quantum technologies. All of which should draw in a good number of eyeballs to the QBTS stock.

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One of the best ways to diversify your portfolio and spend less is with an exchange-traded fund (ETF) like the Defiance Quantum ETF(NYSEARCA:QTUM).

For one, with an expense ratio of 0.40%, the QTUM ETF provides exposure to companies on the forefront of machine learning, quantum computing, cloud computing and other transformative computing technologies,according to Defiance ETFs.

Two, some of 71 holdings include MicroStrategy (NASDAQ:MSTR), Nvidia (NASDAQ:NVDA), Micron(NASDAQ:MU), Coherent (NYSE:COHR), Applied Materials(NASDAQ:AMAT) and Rigetti Computing (NASDAQ:RGTI).

Even better, I can gain access to all 71 names for less than $65 with the ETF.

Three, the ETF has been explosive. Since bottoming out around $55, its now up to $63.37. From that current price, Id like to see the QTUM ETF race to $70 a share, near term.

On the date of publication, Ian Cooper did not hold (either directly or indirectly) any positions in the securities mentioned. The opinions expressed in this article are those of the writer, subject to the InvestorPlace.comPublishing Guidelines.

Ian Cooper, a contributor to InvestorPlace.com, has been analyzing stocks and options for web-based advisories since 1999.

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3 Quantum Computing Stocks That Still Have Sky-High Potential - InvestorPlace

While the technology offers myriad innovations, investors ought to earmark the top quantum computing stocks for the speculative long-term section of their portfolio. Fundamentally, it all comes down to the projected relevance.

According to Grand View Research, the global quantum computing market size reached a valuation of $1.05 billion in 2022. Experts project that the sector could expand at a compound annual growth rate (CAGR) of 19.6% from 2023 to 2030. At the culmination of the forecast period, the segment could print revenue of $4.24 billion.

Better yet, we might be in the early stages. Per McKinsey & Company, quantum technology itself could lead to value creation worth trillions of dollars. Essentially, quantum computers represent a paradigm shift from the classical approach. These devices can generate myriad functions simultaneously, leading to explosive growth in productivity.

Granted, with every pioneering space comes high risks. If youre willing to accept the heat, these are the top quantum computing stocks to consider.

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To be sure, Honeywell (NASDAQ:HON) isnt exactly what you would call a direct player among top quantum computing stocks. Rather, the company is an industrial and applied sciences conglomerate, featuring acumen across myriad disciplines. However, Honeywell is very much relevant to the advanced computing world thanks to its investment in Quantinuum.

Earlier this year, Honeywells quantum computing enterprise reached a valuation of $5 billion following a $300 million equity funding round, per Reuters. Notably, JPMorgan Chase (NYSE:JPM) helped anchor the investment. According to the news agency, [c]ompanies are exploring ways to develop and scale quantum capabilities to solve complex problems such as designing and manufacturing hydrogen cell batteries for transportation.

Honeywell could play a big role in the applied capabilities of quantum computing, making it a worthwhile long-term investment. To be fair, its not the most exciting play in the world. Analysts rate shares a consensus moderate buy but with an average price target of $229.21. That implies about 10% upside.

Still, Honeywell isnt likely to implode either. As you build your portfolio of top quantum computing stocks, it may pay to have a reliable anchor like HON.

Source: Amin Van / Shutterstock.com

Getting into the more exciting plays among top quantum computing stocks, we have IonQ (NYSE:IONQ). Based in College Park, Maryland, IonQ mainly falls under the computer hardware space. Per its public profile, the company engages in the development of general-purpose quantum computing systems. Business-wise, IonQ sells access to quantum computers of various qubit capacities.

Analysts are quite optimistic about IONQ stock, rating shares a consensus strong buy. Further, the average price target comes in at $16.63, implying over 109% upside potential. Thats not all the most optimistic target calls for a price per share of $21. If so, we would be talking about a return of over 164%. Of course, with a relatively modest market capitalization of $1.68 billion, IONQ is a high-risk entity.

Even with the concerns, including an expansion of red ink for fiscal 2024, covering experts believe the growth narrative could overcome the anxieties. In particular, theyre targeting revenue of $39.47 million, implying 79.1% upside from last years print of $22.04 million. Whats more, fiscal 2025 sales could see a gargantuan leap to $82.38 million. Its one of the top quantum computing stocks to keep on your radar.

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Headquartered in Berkeley, California, Rigetti Computing (NASDAQ:RGTI) through its subsidiaries builds quantum computers and superconducting quantum processors. In particular, Rigetti offers a cloud-based solution under a quantum processing umbrella. It also sells access to its groundbreaking computers through a business model called Quantum Computing as a Service.

While intriguing, RGTI stock is high risk. The reality is that the enterprise features a market cap of a little over $175 million. That translates to a per-share price of two pennies over a buck. With such a diminutive profile, anything can happen. Still, its tempting because analysts rate shares a unanimous strong buy. Also, the average price target lands at $3, implying over 194% upside potential.

Whats even more enticing are the financial projections. Covering experts believe that Rigetti will post a loss per share of 41 cents. Thats an improvement over last years loss of 57 cents. Further, revenue could hit $15.3 million, up 27.4% from the prior year. And in fiscal 2025, sales could soar to $28.89 million, up nearly 89% from projected 2024 revenue.

If you can handle the heat, RGTI is one of the top quantum computing stocks to consider.

On the date of publication, Josh Enomoto did not have (either directly or indirectly) any positions in the securities mentioned in this article.The opinions expressed in this article are those of the writer, subject to the InvestorPlace.comPublishing Guidelines.

A former senior business analyst for Sony Electronics, Josh Enomoto has helped broker major contracts with Fortune Global 500 companies. Over the past several years, he has delivered unique, critical insights for the investment markets, as well as various other industries including legal, construction management, and healthcare. Tweet him at @EnomotoMedia.

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Unlock Generous Growth With These 3 Top Quantum Computing Stocks - InvestorPlace

A novel vortex phenomenon involving photon interactions was identified by scientists, potentially enhancing quantum computing. Through experiments with dense rubidium gas, they observed unique phase shifts that mimic other vortices but are distinct in their quantum implications. Credit: SciTechDaily.com

Researchers at the Weizmann Institute of Science discovered a new type of vortex formed by photon interactions, which could advance quantum computing.

Vortices are a widespread natural phenomenon, observable in the swirling formations of galaxies, tornadoes, and hurricanes, as well as in simpler settings like a stirring cup of tea or the water spiraling down a bathtub drain. Typically, vortices arise when a rapidly moving substance such as air or water meets a slower-moving area, creating a circular motion around a fixed axis. Essentially, vortices serve to reconcile the differences in flow speeds between adjoining regions.

A vortex ring and lines created by the influence of three photons on one another. The color describes the phase of the electric field, which completes a 360-degree rotation around the vortex core. Credit: Weizmann Institute of Science

A previously unknown type of vortex has now been discovered in a study, published in Science, conducted by Dr. Lee Drori, Dr. Bankim Chandra Das, Tomer Danino Zohar, and Dr. Gal Winer from Prof. Ofer Firstenbergs laboratory at the Weizmann Institute of Sciences Physics of Complex Systems Department. The researchers set out to look for an efficient way of using photons to process data in quantum computers and found something unexpected: They realized that in the rare event that two photons interact, they create vortices. Not only does this discovery add to the fundamental understanding of vortices, it may ultimately contribute to the studys original goal of improving data processing in quantum computing.

The interaction between photons light particles that also behave like waves is only possible in the presence of matter that serves as an intermediary. In their experiment, the researchers forced photons to interact by creating a unique environment: a 10-centimeter glass cell that was completely empty, save for rubidium atoms that were so tightly packed in the center of the container that they formed a small, dense gas cloud about 1 millimeter long. The researchers fired more and more photons through this cloud, examined their state after they had passed through it, and looked to see if they had influenced one another in any way.

When the gas cloud was at its densest and the photons were close to each other, they exerted the highest level of mutual influence.

When the photons pass through the dense gas cloud, they send a number of atoms into electronically excited states known as Rydberg states, Firstenberg explains. In these states, one of the electrons in the atom starts moving in an orbit that is 1,000 times wider than the diameter of an unexcited atom. This electron creates an electric field that influences a huge number of adjacent atoms, turning them into a kind of imaginary glass ball.

The image of a glass ball reflects the fact that the second photon present in the area cannot ignore the environment the first photon has created and, in response, it alters its speed as if it has passed through glass. So, when two photons pass relatively close to each other, they move at a different speed than they would have if each had been traveling alone. And when the speed of the photon changes, so does the position of the peaks and valleys of the wave it carries. In the optimal case for the use of photons in quantum computing, the positions of the peaks and valleys become completely inverted relative to one another, owing to the influence the photons have on each other a phenomenon known as a 180-degree phase shift.

From bottom left, clockwise: Dr. Lee Drori, Tomer Danino Zohar, Dr. Alexander Poddubny, Prof. Ofer Firstenberg, Dr. Gal Winer, Dr. Eilon Poem and Dr. Bankim Chandra Das. Credit: Weizmann Institute of Science

The direction that the research took was as unique and extraordinary as the paths of the photons in the gas cloud. The study, which also included Dr. Eilon Poem and Dr. Alexander Poddubny, began eight years ago and has seen two generations of doctoral students pass through Firstenbergs laboratory.

Over time, the Weizmann scientists managed to create a dense, ultracold gas cloud, packed with atoms. As a result, they achieved something unprecedented: photons that underwent a phase shift of 180-degrees and sometimes more. When the gas cloud was at its densest and the photons were close to each other, they exerted the highest level of mutual influence. But when the photons moved away from each other or the atomic density around them dropped, the phase shift weakened and disappeared.

The prevalent assumption was that this weakening would be a gradual process, but researchers were in for a surprise: A pair of vortices developed when two photons were a certain distance apart. In each of these vortices, the photons completed a 360-degree phase shift and, at their center there were almost no photons at all just as in the dark center we know from other vortices.

The scientists found that the presence of a single photon affected 50,000 atoms, which in turn influenced the motion of a second photon.

To understand photon vortices, think of what happens when you drag a vertically held plate through the water. The rapid movement of the water pushed by the plate meets the slower movement around it. This creates two vortices that, when viewed from above, appear to be moving together along the waters surface, but in fact, they are part of a three-dimensional configuration known as a vortex ring: The submerged part of the plate creates half a ring, which connects the two vortices visible on the surface, forcing them to move together.

Another familiar instance of vortex rings is smoke rings. In the last stages of the study, the researchers observed this phenomenon when they introduced a third photon, which added an extra dimension to the findings: The scientists discovered that the two vortices observed when measuring two photons are part of a three-dimensional vortex ring generated by the mutual influence of the three photons. These findings demonstrate just how similar the newly discovered vortices are to those known from other environments.

The vortices may have stolen the show in this study, but the researchers are continuing to work toward their goal of quantum data processing. The next stage of the study will be to fire the photons into each other and measure the phase shift of each photon separately. Depending on the strength of the phase shifts, the photons could be used as qubits the basic units of information in quantum computing. Unlike the units of regular computer memory, which can either be 0 or 1, quantum bits can represent a range of values between 0 and 1 simultaneously.

Reference: Quantum vortices of strongly interacting photons by Lee Drori, Bankim Chandra Das, Tomer Danino Zohar, Gal Winer, Eilon Poem, Alexander Poddubny and Ofer Firstenberg, 13 July 2023,Science. DOI: 10.1126/science.adh5315

Prof. Ofer Firstenbergs research is supported by the Leona M. and Harry B. Helmsley Charitable Trust, the Shimon and Golde Picker Weizmann Annual Grant and the Laboratory in Memory of Leon and Blacky Broder, Switzerland.

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Vortex Power: The Swirl of Light Revolutionizing Quantum Computing - SciTechDaily

You have recently been selected to the Tech Nations Future Fifty programme. What are your expectations and how does it feel to be identified as a future unicorn?

Were delighted to have been selected as the sole representative of a rich and diverse UK quantum tech industry. The quantum computing marketing is expected to grow to $28-72B over the next decade so I expect many unicorns to emerge, and we certainly hope to be one of them. Tech Nation has an excellent track record of picking and supporting high-growth leaders. Were excited to make the most of the opportunities the programme offers.

Quantum computing is an amazing idea the ability to harness the power of the atom to perform computation will transform many industries. Back in 2016, I was a research fellow at the University of Cambridge, and at that time, the majority view was that building a useful quantum computer wouldn't be possible in our lifetime - it was simply too big and too hard a problem. I disagreed but needed to validate this. By meeting with teams building quantum computers, I saw an amazing rate of progress a 'Moore's Law' of quantum computing with a doubling in power every two years, just like classical computers have done. That was the catalyst moment for me, and it became clear that if that trend continued, the next big problem would be quantum error correction. I founded Riverlane to make useful quantum computers a reality sooner!

Were building a technology called the quantum error correction stack, which corrects errors in quantum computers. Todays quantum computers can only perform a thousand or so operations before they fail under the weight of these errors. Quantum error correction technology will ultimately enable trillions of error-free operations, unlocking their full and transformative potential.

Implementing quantum error correction to achieve this milestone requires specialised knowledge of quantum science, engineering, software development and chip manufacturing. That makes quantum error correction systems difficult for each quantum computer maker to develop independently. Our strategy is not dissimilar to NVIDIA in providing a core enabling technology for an entirely new computing category.

When Riverlane was founded in 2016, there was a lot of focus on developing software applications to solve novel problems on small-scale quantum computers, a phase known as the noisy intermediate-scale quantum (NISQ) era. However, after the limits of NISQ became apparent due to considerable error rates hindering calculations, the industry shifted focus to building large and reliable quantum computers that could overcome the error problem

This is something weve been working on from the start through the invention of our quantum error correction stack but were now doubling down on its development to meet this growing demand from the industry. An important part to this has been scaling our team to nearly 100 people across our two offices in Cambridge (UK) and Boston (US) - two world-leading centres for quantum computing research and development.

Its a common misconception that you need a PhD in quantum physics or computer science to work in our field. The reality is we need people with a wide range of skills and from the broadest possible mix of backgrounds and demographics. Collectively, were a group that loves tackling hard and complex problems if not the hardest! This requires a culture that blends extremes of creativity, curiosity, problem-solving and analytical skills, plus an alchemy of driving urgency and zen like patience. Im also proud of the extraordinary openness and diversity of our team, including a healthy gender mix in a field where this is the exception not the norm.

Ive been fascinated with quantum physics since I was a student. Back then, the idea of building a computer that applied the unique properties of subatomic particles into computers to transform our understanding of nature and the universe was pure science fiction. Building a company that is now achieving this feels almost miraculous. Building a company with the right mix of skills and shared focus to do far faster than previously imaginable is brutally tricky and joyously rewarding in equal parts

Last September, we launched the worlds first quantum error correction chip. As the quantum computing industry develops, these chips will get better and better, faster and faster. Theyll ultimately enable the quantum industry to scale beyond its current limitations to achieve its full potential to solve currently impossible problems in areas like healthcare, climate science and chemistry. At a recent quantum conference, someone stood up and said quantum computing will be bigger than fire. I wouldnt go quite that far! But theyll unlock a fundamental new era of human knowledge and thats super exciting.

Have a bold and ambitious vision thats underpinned by a proven insight and data. In my case, it was that the presumption that a quantum computer was simply too hard to ever build could be disproven and overcome. Once you have this, be ready to learn fast and pivot fast in your tactics but never lose sight of your goal.

I spend at least a third of my time travelling. Meeting global leaders in our field face to face to hear their ideas, track their progress and build partnerships is priceless. When Im home, Im lucky enough to live about a mile from our office in Cambridge. No matter the weather, I walk to and from work every day. Cambridge is a beautiful place - the thinking time and fresh air give me energy and a calm headspace.

Steve Brierley is the CEO of Riverlane.

Tech Nations Future Fifty Programmeis designed to support late-stage companies with access and growth opportunities, the programme has supported some of the UKs most prominent unicorns, including Monzo, Darktrace, Revolut, Starling, Skyscanner and Deliveroo.

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Riverlane, the company making quantum computing useful far sooner than anticipated - Maddyness

Capitalize on the synergy between AI and quantum with these millionaire-maker quantum computing stocks

Quantum computing, with its unparalleled data processing speed, has the potential to usher in a new era in tech. Moreover, the synergy between AI and quantum computing will elevate millionaire-maker quantum computing stocks to new heights. The industry is likely to achieve these kinds of returns as a result of becoming a new critical technology at the center of data processing and connection.

Moreover, quantum tech is leaving traditional silicon-based systems in the dust. Beyond this, some of the most influential companies in the tech world are driving the industry, promising exciting opportunities for investors. However, backing the right horses in the race for quantum supremacy is important to maximize your upside potential.

That said, here are three millionaire-maker quantum computing stocks worth investing in for the long haul. Thats because the industry still operates on the fringes of science and technology, making it a long-term play for those looking for generous returns.

IonQ (NYSE:IONQ) is the top pure-play quantum computing stock, perhaps the most promising among its peers. It has made some impressive strides of late, achieving ion stability for an hour, a feat that far comfortably outpaces its competition. Its promise is reflected in its recent strong financial performance. It recently reported its first-quarter (Q1) results, where sales soared 77.2% on a year-over-year (YOY) basis to $7.6 million. Additionally, its loss of 19 cents per share beat expectations by six cents. For the full year, it expects sales between $37 million and $41 million, over 70% growth at the mid-point on a YOY basis. Moreover, the company recently partnered with Oak Ridge National Laboratory (ORNL) to leverage quantum technology to modernize the power grid. This stellar partnership, along with others, demonstrates IonQs ability to innovate and expand its applications, offering healthy long-term upside ahead for its investors.

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Investing in quantum computing can be complicated and speculative at the same time. To simplify the process, the Defiance Quantum ETF (NYSEARCA:QTUM) works best, with it investing in AI stocks to provide a balanced cushion.

The QTUM ETF offers investors exposure to some of the leading global businesses in transformative technologies such as machine learning, quantum computing, and cloud platforms. It holds investments in 70 different stocks, with its top 10 holdings representing just 20% of its $252 million net assets. Hence, its holdings are highly diversified, with an expense ratio of just 0.40%. Some of the companies in its investment portfolio are MicroStrategy(NASDAQ:MSTR),Nvidia(NASDAQ:NVDA), andMKS Instruments(NASDAQ:MKSI) to name a few.

Moreover, QTUM stock has been a smashing success for its investors in the past five years, generating a total return of over 175%, 361% higher than the median of all ETFs. In the past year alone, its up 30% and is positioned for healthy long-term gains.

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Microsoft (NASDAQ:MSFT), a tech giant, has tentacles in virtually every major tech vertical, and quantum computing is no different. The AI revolution took Microsofts business up a notch or two last year, and it is eyeing quantum computing as the next frontier. Its partnership with quantum computing pure-play Quantinuum could be a breakthrough for the entire sector. According to a recent statement from one of Microsofts executives, the company has made massive progress in reducing qubit error rates, which is critical for commercializing quantum technology. Its qubit-virtualization system applied to Quantinuums ion-trap hardware, led to more than 14,000 error-free experiments. The breakthrough will set the stage for Quantinuums Helios H-Series quantum computer by next year. Moreover, the collaboration between the two tech companies aims to go from 100 reliable logical qubits to a whopping 1,000 qubits. If these lofty plans come to fruition, I wont be surprised if MSFT stock goes on another monumental run like last year.

On thedate of publication, Muslim Farooque did not have (eitherdirectly or indirectly) any positions in the securities mentioned in this article.The opinions expressed in this article are those of the writer, subject to the InvestorPlace.comPublishing Guidelines

Muslim Farooque is a keen investor and an optimist at heart. A life-long gamer and tech enthusiast, he has a particular affinity for analyzing technology stocks. Muslim holds a bachelors of science degree in applied accounting from Oxford Brookes University.

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3 Quantum Computing Stocks to Turn $100000 Into $1 Million: June Edition - InvestorPlace

In this section, we first introduce the composition and principles of the important components of RQENN including the trainable encoding method based on parameterized binary index and recurrent cell. Then we introduce the RQENN-based classification model. Finally, we present the task flow of applying RQENN classification model to vulnerability detection.

Classical neural network models for processing NLP tasks first need to tokenize the text and build a word dictionary, according to which the text is converted into a digital index sequence of words. Each digital index corresponds to a one-hot vector, which are transformed into dense vectors by word embedding methods involved in the network training to obtain a more accurate vector representation. However, similar methods migrated to QNN do not work. Specifically, in the classical model, the one-hot vectors are sparse and orthogonal, which means that when word embedding is performed, each word gets only some of the weights from the embedding weight matrix (W) as the representation vector. This process can be viewed as using the one-hot vector as the key to query the corresponding value in the weight map (W), as shown in Fig.1a. Thus, in the case of random initialization of weights, the initial representation vectors of all words are uncorrelated, and they establish lexical connections as the training process proceeds. However, in the quantum model, due to the properties of quantum superposition and entanglement, the quantum state obtained from encoded words (e.g., (|{psi }_{1}rangle) in Fig.1b) is difficult to be sparse and orthogonal as the classical one-hot vectors. This implies that the initially encoded quantum state of each word has some kind of connection, and the use of this quantum state as the "key" inevitably leads to the "value" obtained from the query being related to all the elements in the unitary matrix, which contains various non-semantic connections. The use of this quantum state as the "key" inevitably leads to a query that yields a "value" that is related to all the elements of the Missy's orthogonal weight matrix, and the results obtained contain various non-semantic connections. This prevents QNN from learning the semantics of words through the quantum embedding method.

(a) The process of token 'NULL' being encoded into a quantum circuit. The (|{psi }_{1}rangle) obtained after rotation input layer is treated as a quantum one-hot vector. It further applies QEmbedding to obtain (|{psi }_{2}rangle) which can be treated as a quantum dense vector used as token representation. (b) Classical word embedding computation process. The one-hot vector is treated as a key to query value in the map of weights.

To address this problem, we propose a trainable encoding method based on parameterized binary index to encode code tokens as quantum state data and efficiently learn the semantics of the tokens. The specific steps are as follows:

Step I: Tokenize source code into tokens to create a dictionary and then tokens are mapped to numeric indexes.

Step II: Convert the numeric indexes from decimal to binary representation. For a dictionary containing (N) words, an index is represented by an (n=lceil lo{g}_{2}Nrceil) bits binary numbers.

Step III: Replace "0" and "1" in the binary number indexes with the trainable parameters "({theta }_{0})" and "({theta }_{1})", forming parameterized binary indexes.

Step IV: Encode parameterized binary index using (n=lceil lo{g}_{2}Nrceil) qubits. Each bit of the input is encoded to the corresponding qubit through an Ry rotation gate.

Step V: Add a trainable layer containing parameters to the quantum circuit as a quantum embedding (QEmbedding) implementation.

The Ry rotation input layer and the QEmbedding layer in the above steps together form the trainable encoding layer.

As a simple example, for the following source code training set:

$$left[ {text{``}{text{VAR1 }} = {text{ NULL''}}, , text{``}{text{VAR2 }} = {text{ NULL''}}, , text{``}{text{VAR1 }} = {text{ VAR2''}}} right],$$

we can build such a dictionary to map all code tokens to numeric indexes:

$${ text{`}= text{'} : , 0,text{`}{text{VAR1'}} :{ 1},text{`}{text{NULL'}} :{ 2},text{`}{text{VAR2'}} :{ 3}} .$$

These numeric indexes are further converted to parameterized binary indexes:

$${ text{`}= text{'} : , {theta }_{0}{theta }_{0},text{`}{text{VAR1'}} :{ {theta }_{0}{theta }_{1}},text{`}{text{NULL'}} :{{theta }_{1}{theta }_{0}},text{`}{text{VAR2'}} :{ {theta }_{1}{theta }_{1}}} .$$

Next, we determine the angles of the Ry gates and construct the quantum circuit based on the parameterized binary index of the word to be encoded. Taking encoding token 'NULL' as an example, as shown in Fig.1b, its corresponding indexes ({theta }_{1}{theta }_{0}) are encoded bit-by-bit to a circuit with 2 qubits as the Ry gates angles. Then a QEmbedding layer is further added to jointly form the quantum trainable encoding circuits.

As Eqs.(13) shown below. (|{psi }_{0}rangle) is the initial state. The quantum circuit encodes the index ({theta }_{1}{theta }_{0}) into the quantum state (|{psi }_{1}rangle) by rotation input layer. It is a ({2}^{n})-dimensional vector. It has (N) different cases, corresponding to (N) possible combinations of the input rotation layer parameters. The parameters "({theta }_{0})" and "({theta }_{1})" are involved in the training process of QNN to eliminate possible inherent connections, so that (|{psi }_{1}rangle) has the same function as the classic one-hot vector. The one-hot vector is a form transformed by symbols that is easy to use by the classic network model, and the obtained (|{psi }_{1}rangle) is a form transformed by symbols that is easy to use by QNN. This is the unique aspect of trainable encoding based on parameterized binary index and the key to improving model performance. Next, (|{psi }_{1}rangle) learns lexical connections between encoded words through a trainable QEmbedding layer ({U}_{qe}({{varvec{theta}}}_{qe})), which is similar to the classic word embedding principle. The obtained quantum state (|{psi }_{2}rangle) is described in Eq.(3), where ({U}_{qe}({{varvec{theta}}}_{qe})={[begin{array}{cccc}{{varvec{u}}}_{0}^{dagger}& {{varvec{u}}}_{1}^{dagger}& {{varvec{u}}}_{2}^{dagger}& {{varvec{u}}}_{3}^{dagger}end{array}]}^{dagger}). At this point, the ({2}^{n})-dimensional dense vectors corresponding to (|{psi }_{2}rangle) are the representations of the words, except that the words are converted from indexes to quantum-friendly quantum state representations instead of classical vector representations.

$$|{psi }_{0}rangle ={[begin{array}{cccc}{varepsilon }_{0}& {varepsilon }_{1}& {varepsilon }_{2}& {varepsilon }_{3}end{array}]}^{dagger}$$

(1)

$$left|{psi }_{1}right.rangle =left{begin{array}{c}Ryleft({theta }_{0}right)otimes Ryleft({theta }_{0}right)left|{psi }_{0}right.rangle ,,, index={theta }_{0}{theta }_{0}\ Ryleft({theta }_{0}right)otimes Ryleft({theta }_{1}right)left|{psi }_{0}right.rangle ,,, index={theta }_{0}{theta }_{1}\ Ryleft({theta }_{1}right)otimes Ryleft({theta }_{0}right)left|{psi }_{0}right.rangle ,,, index={theta }_{1}{theta }_{0}\ Ryleft({theta }_{1}right)otimes Ryleft({theta }_{1}right)left|{psi }_{0}right.rangle , ,, index={theta }_{1}{theta }_{1}end{array}right.$$

(2)

$$|{psi }_{2}rangle ={U}_{qe}({{varvec{theta}}}_{qe})|{psi }_{1}rangle ={[begin{array}{cccc}{{varvec{u}}}_{0}^{dagger}|{psi }_{1}rangle & {{varvec{u}}}_{1}^{dagger}|{psi }_{1}rangle & {{varvec{u}}}_{2}^{dagger}|{psi }_{1}rangle & {{varvec{u}}}_{3}^{dagger}|{psi }_{1}rangle end{array}]}^{dagger}$$

(3)

Compared with the trainable encoding method based on parameterized binary index, if the binary index obtained in Step II is used for encoding, the fixed angle of the rotation gate (0 or 1) will result in constant non-lexical connections between (|{psi }_{1}rangle) of different words. These connections are brought into training process of the quantum word embedding layer, possibly affecting the normal learning of lexical connections of the code tokens. In fact, it can also make the (N) quantum states (|{psi }_{1}rangle) orthogonal to each other like classical one-hot vectors by choosing a suitable fixed angle of the rotation gate, this method is called the "orthogonal method". It determines the specific angles "({theta }_{0})" and "({theta }_{1})" to be used for replacing the binary "0" and "1" before training. By respectively applying (N) different rotation layers with angles "({theta }_{0})" and "({theta }_{1})" on (N) independent quantum circuits, we can obtain (N) quantum states. We use the gradient descent algorithm to minimize the sum of the absolute values of the two-by-two inner products of these (N) quantum states under random initialization of the quantum initial states. This approach references the property of mutual orthogonality between one-hot vectors, which ultimately yields ({theta }_{0}=-frac{pi }{2}) and ({theta }_{1}=frac{pi }{2}), and encoding using this value will make (|{psi }_{1}rangle) as orthogonal as possible for different tokens. But there are also differences between QEmbedding and classical embedding. Each element of the weight matrix in classical embedding is a trainable parameter, while QEmbedding only controls the changes of the matrix through a small number of parameter-containing unitary gates. It cannot be proved that the always orthogonal (|{psi }_{1}rangle) is more helpful for learning (|{psi }_{2}rangle). Therefore, in this paper, we add "({theta }_{0})" and "({theta }_{1})" as trainable parameters to the learning process of RQENN, which is the reason for using parameterized binary indexes in Step III. We will show in the Results section the performance of the model when using trainable encoding based on binary index, orthogonality method, and parameterized binary index as data inputs, further demonstrating the effectiveness of the proposed methods.

The trainable encoding method defined in the above section is a crucial component in the construction of our recurrent quantum embedding neural network cell. Much like classical RNNs, we define such a cell that will be successively applied to the input presented to the network for capturing contextual connections in the code. More specifically, the cell is comprised of a trainable encoding stage and a working stage, which are used to learn the semantics of input tokens and memorize contextual dependencies, respectively. This cell is applied iteratively in RQENN, and its internal state is passed on to the next iteration of the network. RQENN cells at all time steps share the same trainable parameters.

Figure2 illustrates the RQENN cell, which learns the quantum word embedding of the current time step input ({{varvec{x}}}_{t}=({x}_{{t}_{0}},...,{x}_{{t}_{n}})) in the encoding stage and combines it with the cell input hidden state (|{psi }_{t-1}rangle) in the work stage to learn the mapping relation from this combined state to the cell output hidden state (|{psi }_{t}rangle). The equation for this process is as follow:

$$|{psi }_{t}rangle ={U}_{qnn}{U}_{qe}{U}_{in}({{varvec{x}}}_{t})|{psi }_{t-1}rangle$$

(4)

where ({U}_{in}), ({U}_{qe}) and ({U}_{qnn}) denote the unitary matrix of the rotation input layer, QEmbedding layer and quantum weight (QWeight) layer, respectively.

Recurrent quantum embedding neural network cell. It consists of a trainable encoding stage and a QNN work stage, where the principle of the encoding stage is as described in the above section. It transforms the internal state in into the state out at each time step and iterates this process.

The encoding stage uses the trainable encoding method described above. In the rotation input layer, an Ry gate is applied on the ith qubit to rotate the angle to the ith value of the parameterized binary index. In the QEmbedding layer, a (m) layer ansatz composed of alternate rotation layer and entanglement layer is used to learn the quantum word embedding representation. Each layer of the ansatz consists of 2 rotation layers and 2 entanglement layers consisting of staggered entanglements between adjacent qubits. In the working stage, a (n) layer one-dimensional alternating layered Hardware Efficient Ansatz48,49 was used to build the QWeight layer. This ansatz is implemented by sequentially applying a two-qubit unitary to adjacent qubits. Each two-qubit unitary entangles the last qubit obtained from a previous unitary with the next one. The unique recurrent circuit cell architecture with scalable layer in multi-stage is the key to improving model performance. This two-qubit unitary consists of two Ry gates and a Cnot gate that have been proven effective50, and its unitary transformation is described by Eq. (5). We show below the specific implementations of the different network layers by equations. Equation (6) shows the unitary transformation of the rotation input layer, where (tin {1,...,T}) represents the time step. A token is input into the network at each time step, and (T) is set as the total code length. Equations (7, 8) and Eq. (9) are the unitary transformations of the QEmbedding layer and QWeight layer respectively.

$${U}_{l,i}^{left[2right]}left({{varvec{theta}}}_{l,i}right)=Cno{t}_{i,i+1}{otimes }_{j=0}^{1}R{y}_{i+j}left({theta }_{l,i,j}right), lin left{text{0,1}right} and iin left{0,dots ,n-2right}$$

(5)

$${U}_{in}left({{varvec{x}}}_{t}right)={otimes }_{i=0}^{n}left(R{y}_{i}left({x}_{{t}_{i}}right)right), {x}_{{t}_{i}}in left{{theta }_{0},{theta }_{1}right} and tin {1,...,T}$$

(6)

$${U}_{q{e}_{l}}({{varvec{theta}}}_{q{e}_{l}})=prod_{i=1}^{lfloor (n-1)/2rfloor }Cno{t}_{2i-text{1,2}i}{otimes }_{i=0}^{n-1}R{y}_{i}({theta }_{l,n+i})prod_{i=1}^{lfloor n/2rfloor }Cno{t}_{2i-text{2,2}i-1}{otimes }_{i=0}^{n-1}R{y}_{i}({theta }_{l,i})$$

(7)

$${U}_{qe}left({{varvec{theta}}}_{qe}right)={U}_{q{e}_{1}}left({{varvec{theta}}}_{q{e}_{1}}right){U}_{q{e}_{0}}left({{varvec{theta}}}_{q{e}_{0}}right)$$

(8)

$${U}_{qnn}left({{varvec{theta}}}_{qnn}right)={U}_{1,n-2}^{left[2right]}left({{varvec{theta}}}_{1,n-2}right)dots {U}_{text{1,0}}^{left[2right]}left({{varvec{theta}}}_{text{1,0}}right){U}_{0,n-2}^{left[2right]}left({{varvec{theta}}}_{0,n-2}right)dots {U}_{text{0,0}}^{left[2right]}left({{varvec{theta}}}_{text{0,0}}right)$$

(9)

We use RQENN cell to build classifiers applied to vulnerability detection. Similar to RNN, RQENN initializes the hidden state at (t=0) by adding a layer of Hadamard gates initially, and then the RQENN cell is iteratively applied to a sequence of the input source code ({{varvec{x}}}_{1},{{varvec{x}}}_{2},...,{{varvec{x}}}_{T}) as shown in Fig.3 to capture the contextual connections in the source code. The entire model also includes measuring the expectation value of a single qubit for the last two qubits. This expectation value is described as Eq.(10):

$${E}_{i}left({varvec{X}},{varvec{Theta}}right)=langle {0}^{otimes n}|{H}^{daggerotimes n}{U}_{QC}^{dagger}left({varvec{X}},{varvec{Theta}}right){widehat{M}}_{i}{U}_{QC}({varvec{X}},{varvec{Theta}}){H}^{otimes n}|{0}^{otimes n}rangle ,hspace{0.5em}hspace{0.5em}iin {n-1,n-2}$$

(10)

where ({U}_{QC}({varvec{X}},{varvec{Theta}})={U}_{cell}({{varvec{x}}}_{1},{varvec{Theta}})...{U}_{cell}({{varvec{x}}}_{T},{varvec{Theta}})) is the a quantum circuit composed of all cells, and ({U}_{cell}({{varvec{x}}}_{t},{varvec{Theta}})={U}_{qnn}({{varvec{theta}}}_{qnn}){U}_{qe}({{varvec{theta}}}_{qe}){U}_{in}({{varvec{x}}}_{t},{{varvec{theta}}}_{in})). ({varvec{Theta}}) is the parameter set of the cell, and ({varvec{X}}=[{{{varvec{x}}}_{1},dots ,{varvec{x}}}_{T}]) is the input index sequence. ({widehat{M}}_{i}) is the operator used to calculate the expectation of the ith qubit, i.e.

RQENN classifier. The model is built by iteratively applying the same RQENN cell to the input code token sequence. Measurements are performed on the last two qubits separately to obtain the expectation values as classification logits.

$${widehat{M}}_{i}=left{begin{array}{c}Iotimes Iotimes ...otimes {sigma }_{z}otimes I,hspace{0.5em}i=n-2\ Iotimes Iotimes ...otimes Iotimes {sigma }_{z},hspace{0.5em}i=n-1end{array}right.$$

(11)

The two calculated expectation values are used to determine the data category by comparing the numerical magnitudes, and we use them as logits to calculate the cross-entropy loss function for classification.

The goal of our vulnerability detection is to detect whether a program's source code may contain vulnerabilities using the RQENN classifier. In this paper, we perform the vulnerability detection task using the pipeline shown in Fig. 4, which consists of the following three steps:

Vulnerability detection task flow. We extract normalized labeled code gadgets from the source code as training data and then generate parameterized binary indexes from them, which are fed into the RQENN classifier. After training, the model can detect the presence of vulnerabilities in the source code.

Step I: Generating normalized code gadgets and labels from source code. First, we extract the data dependency graph (DDG) of the code using the open source code analysis tool Joern. Next, we extract labeled code gadgets based on manually defined vulnerability features. Specifically, we locate the node containing the vulnerable library function/API call in the extracted DDG, such as the "strcat" function shown in left side of Fig.4, and slice the code into small pieces according to the connection to the node. The types of API calls are categorized into forward (e.g., the "recv" function) and backward API calls (e.g., the "strcat" function here) according to whether or not they take external input from a socket, and forward slices and backward slices are generated accordingly. The forward slices obtain the set of statements of the nodes in the DDG that are recursively pointed forward from the API node, and the backward slices obtain the set of statements of the nodes in the DDG that are recursively pointed to the API node. These slices are code gadgets, which are labeled '0' or '1' depending on whether they contain vulnerabilities or not. In the next step we normalized the code gadget. The processing methods include removing comments and strings, normalizing user-defined variable names ('VAR1' etc.) and function names ('FUN1' etc.). Finally, the normalized labeled code gadget is obtained.

Step II: The normalized labeled code gadgets are treated as text data from which parameterized binary index sequences are generated. First, we preprocess the data set, clean the original text, remove punctuation marks and non-ascii characters, etc. Then we split and pad the preprocessed text and build a dictionary, which is converted into a parameterized binary index dictionary according to the method mentioned before. Finally, the token sequences after tokenization are converted into parameterized binary index sequences according to the dictionary.

Step III: Training and evaluating RQENN Models. We input the sequence of parameterized binary indexes into the RQENN model in order, execute the quantum circuit on the simulator or a real machine, and complete the training and validation of the RQENN model according to the quantum circuit learning framework18. The model can detect the presence of vulnerabilities in the source code.

Read the rest here:

Recurrent quantum embedding neural network and its application in vulnerability detection | Scientific Reports - Nature.com

Mayor Brandon Johnson is throwing his weight behind the quantum computing movement thats gaining traction in Chicago.

The Johnson administration is working with county and state officials to create an inventive package for PsiQuantum to redevelop the former U.S. Steel South Works on the citys South Side into a state-of-the-art quantum computing facility, Crains reported.

The effort is to persuade California-based PsiQuantum, a pioneer in quantum computing, to choose the former U.S. Steel site over the former Texaco refinery in southwest suburban Lockport. Also vying to host the facility, Lockport officials cite its access to significant water and electric power resources essential for supercomputers cooling requirements. Plus, the Lockport site is being offered for free and has been environmentally remediated.

Chicago may need to invest up to $150 million to match Lockports proposal, the outlet reported, citing an anonymous source. Parts of the South Works site are environmentally cleared.

The development, expected to involve billions of dollars in investment, would help revitalize a South Side community thats struggled since the closure of local steel mills. PsiQuantum is expected to make its decision within the next month.

The proposed incentive package further demonstrates Gov. J.B. Pritzkers desire to position Illinois as a hub for quantum development. He views this cutting-edge technology as a long-term driver of high-paying jobs, attracting researchers and skilled workers.

Pritzker envisions the PsiQuantum facility as the cornerstone of a $20 billion quantum research campus. The campus is intended to attract global companies eager to harness the technologys advanced data processing capabilities for artificial intelligence and other advancements.

The Illinois General Assembly has approved up to $500 million in funding for site preparation and incentives. While details of Chicagos incentive package havent been disclosed, officials said it is highly competitive.

The citys offer could include changes to the zoning code to accommodate the unique requirements of a computer-related development such as a data center, along with potential tax-increment financing districts. In addition, Cook County is considering a Class 8 property tax break, which significantly reduces assessments for industrial developments.

Quinn Donoghue

PsiQuantum, Related eye big industrial sites for redevelopment

IBMs quantum computing moves could put industrial space in demand

Blackstones next play: Data centers for AI boom

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Chicago Trying to Lure PsiQuantum to Former Steel Plant - The Real Deal

Technology firms, both public and private, have been working hard to develop quantum computing technologies for decades. The reasons for that are straightforward. Quantum machines, which harness the quantum mechanics undergirding subatomic particles, have a number of advantages over classical computers. Portfolio optimization and climate predictive algorithms that improve with more complexity are better handled by quantum computers.

U.S. equities markets have surged with the rise of generative artificial intelligence (AI) and its potential to create enormous efficiencies and profits for firms across various industries. While AI has brought quantum computing back into the spotlight, a lack of practical ways to scale these complex products has severely dented the performance of pure-play quantum computing stocks, such as IonQ (NYSE:IONQ) and Rigetti Computing (NASDAQ:RGTI).

Fortunately, not every public company invested in quantum computing has seen doom and gloom. Below are the three best quantum computing stocks investors should buy in June.

Source: shutterstock.com/LCV

International Business Machines (NYSE:IBM) is a legacy American technology business. It has its hands in everything from cloud infrastructure, artificial intelligence, and technology consulting services to quantum computers.

The firm committed to developing quantum computing technologies in the early 2000s and tends to publish new findings in the burgeoning field frequently. In December 2023, IBM released a new quantum chip system, Quantum System Two, that leverages the firms Heron processor, which has 133 qubits. Qubits are analogous to bytes on a classical computer. But instead of being confined to states of 0s and 1s, qubits, by way of superposition, can assume both states at the same time.

Moreover, what makes Quantum System Two particularly innovative is its use of both quantum and classical computing technologies. In a press release, IBM states, It combines scalable cryogenic infrastructure and classical runtime servers with modular qubit control electronics. IBM believes the combination of quantum computation and communication with classical computing resources can create a scalable quantum machine.

IBMs innovations in quantum computing technologies as well as AI has not gone unnoticed either. Shares have risen 31.3% over the past 12 months. The computing giants relatively cheap valuation coupled with its exposure to novel, high-growth fields could boost the value of its shares in the long-term.

Source: sdx15 / Shutterstock.com

Investors have given Nvidia (NASDAQ:NVDA) attention and praise over the past 12 months due to its critical role in AI computing technologies. The chipmakers advanced GPUs, including the H100 and H200 processors, are some of the most coveted chips on the market. The new Blackwell chips, coming to the market in the second half of 2024, bring to the table even better performance.

Though Nvidias prowess in the world of AI captures much of the headlines, the firm has already made inroads into the next stage of computing. In 2023, Nvidia announced a new quantum system in conjunction with startup Quantum Machines. It leverages what Nvidia calls the Grace Hoper Super Chip (GH200) as well as the chipmaker advanced CUDA Quantum (CUDA-Q) developer software.

In 2024, Nvidia released its Quantum Cloud platform, which allows users to build and test quantum computing algorithms in the cloud. The chipmakers GPUs and its open-source CUDA platform will likely be essential to scaling up the quantum computing space.

Nvidias share price has surged 214.2% over the past 12 months.

Source: Bartlomiej K. Wroblewski / Shutterstock.com

Quantum computers are complex machines that require all kinds of components. Furthermore, it is vital for quantum systems to operate at extremely low temperatures in order to operate efficiently.

FormFactor (NASDAQ:FORM) specializes in developing cryogenic systems or systems that are meant to deal with low temperatures. Everything from wafer testing probes to low-vibration probe stations as well as sophisticated refrigerators call cryostats, FormFactor provides. Also, the firms analytical probe tools are useful for developing advanced chips, such as NAND flash memory.

With quantum computing systems and advanced memory chips in greater demand these days, FormFactor could see revenues and earnings rise in the near and medium terms. FormFactors share price has surged 77.5% over the past 12 months, underscoring that investors are taking notice of the companys long-term value.

At the beginning of May, FormFactor released first quarter results for fiscal year 2024 and topped revenue estimates while EPS came in line with market expectations. The firm expects strong demand for advanced memory chips, such as DRAM, will help propel revenue growth in the following quarters.

On the date of publication, Tyrik Torresdid not have (either directly or indirectly) any positions in the securities mentioned in this article.The opinions expressed in this article are those of the writer, subject to the InvestorPlace.comPublishing Guidelines.

Tyrik Torres has been studying and participating in financial markets since he was in college, and he has particular passion for helping people understand complex systems. His areas of expertise are semiconductor and enterprise software equities. He has work experience in both investing (public and private markets) and investment banking.

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The 3 Best Quantum Computing Stocks to Buy in June 2024 - InvestorPlace

Last updated: June 13, 2024 09:00 EDT | 11 min read

Quantum computers might sound like another buzzword in the tech world, yet their threat to cryptocurrency is very real and approaching fast. Scientists may differ on the timeline, but they all agree: Q-day is not a matter of if, but when.

Weve spoken to quantum experts around the world to hear the latest estimates on when it will happen, what can be done to protect cryptocurrency, and whether these powerful machines could somehow benefit the crypto world.

Unlike traditional computers, which use bits as the smallest unit of data, each bit being a 1 or a 0, quantum computers use quantum bits, or qubits. These qubits can exist in 0 and 1 states or in multiple states at oncea property called superposition.

This allows quantum computers to perform calculations simultaneously and process large amounts of data much faster than standard computers.

As quantum computers can hold and process many possible outcomes at once, it reduces the time needed to solve problems that depend on trying many different solutions, such as factoring large numbers, which is the foundation of most cryptocurrency encryption.

Factoring large numbers, or integer factorization, is a mathematical process of breaking down a large number into smaller, simpler numbers called factors, which, when multiplied together, result in the original number. The process is called prime factorization if these integers are further restricted to prime numbers.

In cryptocurrency, security heavily relies on the mathematical relationship between private and public keys. A public key is a long string of characters associated with the wallet address. It can be shared openly. A private key, used to sign transactions, must remain confidential. This mathematical relationship is one-way, meaning that a public key can be derived from the private key but not the other way around.

Itan Barmes, who is the Global quantum cyber readiness capability lead at Deloitte, explained in a conversation with Cryptonews:

The quantum computer breaks this one-way relationship between the two. So, if you have someones public key, you can calculate their private key, impersonate them, transfer their funds elsewhere.

The task is currently nearly impossible for conventional computers. However, in 1999, mathematician Peter Shor showed that a quantum computer could solve the factoring problem much faster. Shors algorithm can also solve the Discrete Logarithm Problem, which is the basis for the security of most blockchains. This means if such a powerful quantum computer existed, it could break the cryptocurrency security model.

Not all cryptocurrencies would face the same level of risk from quantum attacks. In 2020, Itan Barmes and a team of Deloitte researchers examined the entire Bitcoin blockchain to determine how many coins were vulnerable. They discovered that about 25% of Bitcoins could be at risk.

Pay To Public Key (P2PK)

Pay to Pubkey Hash (P2PKH)

These addresses directly use the public key, making them visible and vulnerable to quantum attacks.

These addresses use a cryptographic hash of the public key. They dont expose the public key directly until coins are moved.

Vulnerable coins include those held in P2PK (Pay To Public Key) addresses, which directly expose the public key, making them easy targets for a quantum attack. Coins in reused P2PKH (Pay to Pubkey Hash) addresses are also at risk because these addresses display their public key when the owner moves the funds. This attack is called the storage attack, as it applies to coins residing in static addresses. Itan Barmes further explained:

A quantum attack only applies to specific coins, not everything. If we conducted the same research today, the percentage of vulnerable coins would be lower because the number of vulnerable addresses remains more or less the same, but due to mining, there are more coins in circulation.

Itan Barmes added that in addition to the storage attack, there is also an attack on active transactions, as the public key is exposed for the first time.

Such an attack must be performed within the mining time (for Bitcoin, around 10 minutes), which adds a requirement for the quantum computer to not only be powerful enough but also fast. This so-called transit attack is likely to be possible later than the storage attack due to this additional requirement.

Ideally, Bitcoin users must generate a new address for each transaction. Yet, recent research by Bitmex suggests that about 50% of transaction outputs still go to previously used addresses, which means the practice of address reuse is more common in Bitcoin transactions than we may think.

Are we nearing the point where quantum computers can pose a real threat? In 2017, a group of researchers, including Divesh Aggarwal and Gavin Brennen, published an article warning that the elliptic curve signature scheme used by Bitcoin could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates.

Cryptonews reached out to the authors to ask whether their estimation has shifted. Gavin Brennen from Macquarie University in Australia replied that although a lot has changed in quantum computing space since then, the basic message is still the same:

Quantum computers pose a threat to blockchains, primarily by attacks on digital signatures, and cryptocurrencies should get started sooner rather than later to upgrade their systems to use post-quantum cryptography before their asset valuations are threatened.

To be able to break cryptocurrency security, quantum computers will likely need thousands, if not millions, of qubits. Currently, the most advanced machines have around 1000.

Another critical challenge is error reduction. Quantum bits are highly sensitive to their environment; even the slightest disturbance, like a change in temperature or vibration, can cause errors in computations, a problem known as quantum decoherence.

Dozens of companies, both public and private, are now actively advancing the development of large quantum computers. IBM has ambitious plans to build a 100,000-qubit chipset and 100 million gates by the end of this decade.

PsiQuantum aims to achieve 1 million photonic qubits within the same timeframe. Quantum gate fidelities and quantum error correction have also significantly advanced. Gavin Brennen continued:

What all this means is that estimates on the size of quantum computers needed to crack the 256-bit elliptic curve digital signatures used in Bitcoin have dropped from 10-20 million qubits to around a million. One article published by the French quantum startup Alice & Bob estimates that it could be cracked with 126,000 physical qubits, though that does assume a highly specialized error model for the quantum computer. In my opinion, a plausible timeline for cracking 256-bit digital signatures is by the mid-2030s.

Gavin Brennen added that substantial technological improvements would be required to reduce all types of gate errors, connect modules, and combine fast classical and quantum control, which is a challenging but surmountable problem.

Yet, if quantum technology becomes powerful enough to break cryptocurrency security, we may not even know about it, believes Marcos Allende, a quantum physicist and CTO of the LACChain Global Alliance. In an email conversation with Cryptonews, Allende wrote:

What is certain is that those who reach that power first will use it silently, making it impossible to guess that selected hackings are happening because of having quantum computers.

Many scientists remain skeptical about the quantum threat to cryptocurrency. Winfried Hensinger, a physicist at the University of Sussex in Brighton, UK, speaking to Nature magazine, described quantum computers as Theyre all terrible. They cant do anything useful.

Several challenges keep quantum computing from reaching its full potential. The delicate nature of qubits makes it difficult to maintain them in a quantum state for extended periods. Another challenge is cooling requirements. Many quantum processors must operate at temperatures close to absolute zero, which means they need complicated and costly refrigeration technology. Finally, the quantum systems would need to be integrated with the existing classical ones.

Just having 200 million qubits not connected to each other is not going to do anything. There are a lot of fundamental physics problems that need to be resolved before we get there. We are still very much at the beginning. But even in the past year, theres been tremendous improvement. The technology can accelerate in a way that all the timelines will be much shorter than we expect, Itan Barmes told Cryptonews.

Tommie van der Bosch, Partner at Deloitte and Blockchain & Digital Asset Leader of Deloitte North and South Europe, believes that the question is not if quantum computing will break cryptocurrency security but when: The fact that its a possibility is enough to start taking action. You should have a plan.

Indeed, this year several key crypto companies and the World Economic Forum (WEF) have shared concerns about the implications of quantum computing on cryptocurrency security.

The WEF, in its post published in May, warned that central bank digital currency (CBDC) could become a prime target for quantum attacks. Ripples recent report has also said that quantum computers could break the digital signatures that currently protect blockchain assets.

Earlier this year, Buterin, Ethereum founder, suggested the Ethereum blockchain would need to undergo a recovery fork to avoid the scenario when bad actors already have access to them and are able to use them to steal users funds.

To protect against these potential quantum attacks, blockchain systems will need to integrate post-quantum cryptographic algorithms. However, incorporating them into existing blockchain protocols is not easy.

New cryptographic methods must first be developed, tested, and standardized. This process can take years and requires the consensus of the cryptographic community to ensure the new methods are secure and efficient.

In 2016, the National Institute of Standards and Technology (NIST) started a project to set new standards for post-quantum cryptography. The project aims to finalize these standards later this year. In 2022, three digital signature methodsCRYSTALS-Dilithium, FALCON, and SPHINCS+were chosen for standardization.

Once standardized, these new cryptographic algorithms need to be implemented within the blockchains existing framework. After that, all network participants need to adopt the updated protocol.

Itan Barmes explained, Lets say someone could tell us exactly the date, three years from now, when we will have these kinds of quantum computers. How quickly do you think we can change the Bitcoin protocol to make it resilient to these attacks? The decentralized governance of Bitcoin can turn out to be a double-edged sword, by preventing timely action.

Quantum-resistant algorithms often require more processing power and larger key sizes, which could lead to performance issues on the blockchain. These include slower transaction times and increased computational requirements for mining and verification processes.

Tommie van der Bosch told Cryptonews that, ultimately, the rise of quantum computing could affect the entire economic model of cryptocurrencies.

Coins that upgrade to quantum-resistant protocols in time might gain a competitive advantage. Investors and users could prefer these quantum-safe cryptocurrencies, as they may see them as more secure long-term holdings. This shift could lead to an increase in demand for such cryptocurrencies, potentially enhancing their value and market share compared to those that are slower to adapt. Tommie van der Bosch told Cryptonews:

Lets draw a parallel with the banking system. Weve all seen the effects of a bank collapsing or even the rumor of one. Your money suddenly seems at risk. How quickly do people shift their assets? It can trigger a domino effect.

The development of quantum computing could also bring regulatory changes. Regulators could start enforcing stricter standards around trading and custody of cryptocurrencies that havent updated their cryptographic protocols. Such measures would aim to protect investors from sinking funds into potentially vulnerable assets.

Itan Barmes remarked, Not many people are aware that the cryptographic algorithm used in Bitcoin and essentially all cryptocurrencies is not part of the NIST recommendation (NIST SP800-186). The issue is already present if organizations require compliance to NIST standards. The issue becomes even more complex if algorithms need to be replaced; Whos responsibility is it to replace them?

Could quantum computing actually benefit the cryptocurrency industry? Gavin Brennen suggests it might. In an email exchange with Cryptonews, Brennen discussed the development of quantum-enabled blockchains.

Quantum computers could accelerate mining, although Brennen notes that the improvement over traditional mining rigs would be limited and require quantum computers with hundreds of millions of qubitsfar beyond current capabilities.

New computational problems have been suggested, like the boson sampling problem, that are slow for all types of classical computers but would be fast on a quantum device. Interestingly, the boson sampler is a small, specialized processor using photons of light, that is not as powerful as a full quantum computer, but much cheaper to build, and that solves a problem immune to ASIC speedups with an energy footprint that is orders of magnitude lower for reaching PoW consensus.

Currently, proof-of-work (PoW) requires vast amounts of electrical power for mining, raising concerns about sustainability and environmental impact. Boson sampling could become a greener alternative, significantly reducing the energy footprint of blockchain operations while maintaining security and efficiency.

Excerpt from:

Quantum Computers May Break Bitcoin by 2030, But We Won't Know About It - Cryptonews

Scientists have stumbled upon a remarkable discovery that challenges our understanding of the quantum world. New research revealed the existence of a previously unknown type of vortex that emerges when photons, the elusive particles of light, engage in a mesmerizing dance of interaction.

The implications of this finding extend far beyond the realm of pure science, holding the potential to revolutionize the field of quantum computing.

The research team, led by a brilliant quartet of scientists Dr. Lee Drori, Dr. Bankim Chandra Das, Tomer Danino Zohar, and Dr. Gal Winer embarked on this journey of discovery in the hallowed halls of Prof. Ofer Firstenbergs laboratory at the Weizmann Institute of Sciences Physics of Complex Systems Department.

Their initial goal was to explore efficient ways of harnessing the power of photons for data processing in quantum computers.

Little did they know that their quest would lead them down an unexpected path, into a world where the rules of classical physics are bent and the secrets of the quantum realm are laid bare.

Photons, the fundamental particles of light, are known for their wave-like behavior. However, getting them to interact with each other is no easy feat. It requires the presence of matter that acts as an intermediary.

To create the perfect environment for photon interactions, the researchers designed a unique setup: a 10-centimeter glass cell containing a dense cloud of rubidium atoms, tightly packed in the center.

As photons passed through this cloud, the researchers closely examined their state to see if they had influenced one another.

When the photons pass through the dense gas cloud, they send a number of atoms into electronically excited states known as Rydberg states, Prof. Firstenberg explains.

He goes on to describe how, in these Rydberg states, a single electron within the atom begins to orbit at an astonishing distance, up to 1,000 times the diameter of an unexcited atom.

This electron, with its vastly expanded orbit, generates an electric field so powerful that it envelops and influences countless neighboring atoms, effectively transforming them into what Prof. Firstenberg poetically refers to as an imaginary glass ball.'

As the researchers delved deeper into the interactions between photons, they stumbled upon something extraordinary.

When two photons passed relatively close to each other, they moved at a different speed than they would have if each had been traveling alone. This change in speed altered the positions of the peaks and valleys of the waves they carried.

In the ideal scenario for quantum computing applications, the positions of the peaks and valleys would become completely inverted relative to one another, a phenomenon known as a 180-degree phase shift. However, what the researchers observed was even more fascinating.

When the gas cloud was at its densest and the photons were in close proximity, they exerted the highest level of mutual influence.

But as the photons moved away from each other or the atomic density around them decreased, the phase shift weakened and disappeared.

Instead of a gradual process, the researchers were surprised to find that a pair of vortices developed when two photons were a certain distance apart.

To visualize photon vortices, imagine dragging a vertically held plate through water. The rapid movement of the water pushed by the plate meets the slower movement around it, creating two vortices that appear to be moving together along the waters surface.

In reality, these vortices are part of a three-dimensional configuration called a vortex ring.

The researchers discovered that the two vortices observed when measuring two photons are part of a three-dimensional vortex ring generated by the mutual influence of three photons.

These findings showcase the striking similarities between the newly discovered vortices and those found in other environments, such as smoke rings.

While the discovery of photon vortices has taken center stage, the researchers remain dedicated to their original goal of advancing quantum data processing.

The next phase of their study will involve firing photons into each other and measuring the phase shift of each photon separately.

The strength of these phase shifts could determine the potential for photons to be used as qubits, the basic units of information in quantum computing.

Unlike regular computer memory units, which can only be 0 or 1, quantum bits have the ability to represent a range of values between 0 and 1 simultaneously.

The prevalent assumption was that this weakening would be a gradual process, but researchers were in for a surprise, Dr. Eilon Poem and Dr. Alexander Poddubny, key contributors to the study, reveal.

They go on to describe the astonishing discovery that when two photons reached a specific distance from each other, a pair of vortices spontaneously emerged.

These vortices, characterized by a complete 360-degree phase shift of the photons, featured a peculiar void at their center, eerily reminiscent of the dark, calm eye found at the heart of other well-known vortices in nature.

The journey that led to this discovery spanned eight years and saw two generations of doctoral students pass through Prof. Firstenbergs laboratory.

Over time, the Weizmann scientists successfully created a dense, ultracold gas cloud packed with atoms, enabling them to achieve the unprecedented: photons that underwent a phase shift of 180 degrees or more.

As the research team continues to unravel the mysteries of photon interactions and their potential applications in quantum computing, one thing is certain: their findings have opened up a new realm of possibilities in the world of physics and beyond.

The full study was published in the journal Science.

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Quantum computer photons create a vortex when they collide - Earth.com