Quantum theory is a revolutionary advancement in physics and chemistrythat emerged in the early twentieth century. It is an elegantmathematical theory able to explain the counterintuitive behavior ofsubatomic particles, most notably the phenomenon of entanglement. Inthe late twentieth century it was discovered that quantum theory appliesnot only to atoms and molecules, but to bits and logic operations in acomputer. This realization has brought about a revolution in thescience and technology of information processing, making possible kindsof computing and communication hitherto unknown in the Information Age.

Our everyday computers perform calculations and process information using thestandard (or classical) model ofcomputation, which dates back toTuring and vonNeumann. In thismodel, all information is reducible to bits, which can take the valuesof either 0 or 1. Additionally, all processing can be performed via simple logicgates (AND, OR, NOT, XOR, XNOR)acting on one or two bits at a time, or be entirely described by NAND (or NOR).At any point in its computation, aclassical computers state is entirely determined by the states of allits bits, so that a computer with n bits can exist in one of2^n possible states, ranging from 00...0 to11...1 .

The power of the quantum computer, meanwhile, lies in its much richerrepertoire of states. A quantum computer also has bits but instead of0 and 1, its quantum bits, or qubits, can represent a 0, 1, or linearcombination of both, which is a property known as superposition.This on its own is no special thing, since a computer whose bits can beintermediate between 0 and 1 is just an analog computer, scarcely morepowerful than an ordinary digital computer. However, a quantum computertakes advantage of a special kind of superposition that allows forexponentially many logical states at once, all the states from|00...0rangle to |11...1rangle . This is a powerfulfeat, and no classical computer can achieve it.

The vast majority of quantum superpositions, and the ones most useful for quantumcomputation, are entangled. Entangled states are states of the whole computerthat do not correspond to any assignment of digital or analog states ofthe individual qubits. A quantum computer is therefore significantly more powerfulthan any one classical computer whether it be deterministic,probabilistic, or analog.

While todays quantum processors are modest in size, their complexity growscontinuously. We believe this is the right time to build and engage a communityof new quantum learners, spark further interest in those who are curious,and foster a quantum intuition in the greater community.By making quantum concepts more widely understood even on a generallevel we can more deeply explore all the possibilities quantumcomputing offers, and more rapidly bring its exciting power to a worldwhose perspective is limited by classical physics.

With this in mind, we created the IBM Quantum Composer to provide the hands-onopportunity to experiment with operations on a real quantum computingprocessor. This field guide contains a series of topicsto accompany your journey as you create your own experiments, run them insimulation, and execute them on real quantum processorsavailable via IBM Cloud.

If quantum physics sounds challenging to you, you are not alone. But ifyou think the difficulty lies in hard math, think again. Quantum conceptscan, for the most part, be described by undergraduate-level linear algebra,so if you have ever taken a linear algebra course, the math will seem familiar.

The true challenge of quantum physics is internalizing ideas that arecounterintuitive to our day-to-day experiences in the physical world,which of course are constrained by classical physics. To comprehendthe quantum world, you must build a new intuition for a set of simple butvery different (and often surprising) laws.

The counterintuitive principles of quantum physics are:

1.A physical system in a definite state can still behaverandomly.

2.Two systems that are too far apart to influence each other cannevertheless behave in ways that, though individually random,are somehow strongly correlated.

Unfortunately, there is no single simple physicalprinciple from which these conclusions follow and we must guard againstattempting to describe quantum concepts in classical terms!The best we can do is to distill quantum mechanics down to a fewabstract-sounding mathematical laws, from which all the observed behaviorof quantum particles (and qubits in a quantum computer) can be deduced andpredicted.

Keep those two counterintuitive ideas in the back of your mind, let goof your beliefs about how the physical world works, and begin exploringthe quantum world!

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Learn quantum computing: a field guide - IBM Quantum