Learn quantum computing: a field guide

Explore topics on concepts and important circuits that make up the foundation of quantum computing, and try them out on IBM Quantum Composer.


Quantum theory is a revolutionary advancement in physics and chemistry that emerged in the early twentieth century. It is an elegant mathematical theory able to explain the counterintuitive behavior of subatomic particles, most notably the phenomenon of entanglement. In the late twentieth century it was discovered that quantum theory applies not only to atoms and molecules, but to bits and logic operations in a computer. This realization has brought about a revolution in the science and technology of information processing, making possible kinds of computing and communication hitherto unknown in the Information Age.

Our everyday computers perform calculations and process information using the standard (or classical) model of computation, which dates back to Turing and von Neumann. In this model, all information is reducible to bits, which can take the values of either 0 or 1. Additionally, all processing can be performed via simple logic gates (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, a classical computer’s state is entirely determined by the states of all its bits, so that a computer with n bits can exist in one of 2^n possible states, ranging from 00...0 to 11...1 .

The power of the quantum computer, meanwhile, lies in its much richer repertoire of states. A quantum computer also has bits — but instead of 0 and 1, its quantum bits, or qubits, can represent a 0, 1, or linear combination of both, which is a property known as superposition. This on its own is no special thing, since a computer whose bits can be intermediate between 0 and 1 is just an analog computer, scarcely more powerful than an ordinary digital computer. However, a quantum computer takes advantage of a special kind of superposition that allows for exponentially many logical states at once, all the states from |00...0\rangle to |11...1\rangle . This is a powerful feat, and no classical computer can achieve it.

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

While today’s quantum processors are modest in size, their complexity grows continuously. We believe this is the right time to build and engage a community of 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 general level — we can more deeply explore all the possibilities quantum computing offers, and more rapidly bring its exciting power to a world whose perspective is limited by classical physics.

With this in mind, we created the IBM Quantum Composer to provide the hands-on opportunity to experiment with operations on a real quantum computing processor. This field guide contains a series of topics to accompany your journey as you create your own experiments, run them in simulation, and execute them on real quantum processors available via IBM Cloud®.

If quantum physics sounds challenging to you, you are not alone. But if you think the difficulty lies in “hard math”, think again. Quantum concepts can, 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 are counterintuitive to our day-to-day experiences in the physical world, which of course are constrained by classical physics. To comprehend the quantum world, you must build a new intuition for a set of simple but very different (and often surprising) laws.

The counterintuitive principles of quantum physics are:

1. A physical system in a definite state can still behave randomly.

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

Unfortunately, there is no single simple physical principle from which these conclusions follow – and we must guard against attempting to describe quantum concepts in classical terms! The best we can do is to distill quantum mechanics down to a few abstract-sounding mathematical laws, from which all the observed behavior of quantum particles (and qubits in a quantum computer) can be deduced and predicted.

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


Authors of the topics in this field guide include:

  • Charlie Bennett

  • Lev Bishop

  • Sergey Bravyi

  • Andrew Cross

  • Jay Gambetta

  • Paul Nation

  • John Smolin

  • Kristan Temme

  • Abby Cross (editor)