The binary representation of data and instructions formulates conventional computing in which a register element r stores a bit b that may take on a value of either b0 or b1. Quantum computing also requires a physical register r but now the register may take the value of a quantum bit, or qubit, q. Conceptually, the qubit is defined as a normalized superposition over the exclusive outcomes b0 and b1. This hypothesis leads to a diagrammatic representation for the possible values of a qubit given as the surface of the unit sphere. Whereas the opposing north and south poles of the sphere represent the classical bit values of b0 = 0 and b1 = 1, every point on the surface corresponds to a possible qubit (q) value.

The superposition principle extends to more than a single quantum register element. Quantum mechanics permits multiple register elements to store superpositions collectively over multiple binary values. This phenomenon is known as entanglement. Quantum entanglement represents a form of information that conventional bits cannot reproduce. While the register elements remain independently addressable, the information they store is coupled and hence not expressed or represented piecewise. For example, two entangled registers may either both be in the b0 state and in the b1 state, but exclude any possibility of anti-correlated values.

The principles of superposition and entanglement lead to an important conceptual difference in the interpretation of register value. Although the qubit maps to a point on the unit sphere, observing the qubit through measurement results in a projection to either b0 or b1 values. This transition from a qubit to a bit is the infamous ‘collapse’ of the quantum state induced by measurement. The implication is that the value q itself is not observable. Instead, interpret the qubit superposition state, q in terms of the probability to observe either b0 to b1. The probabilities p0 and p1 provide the likelihood that the observed outcome will be b0 and b1, respectively.

Classical computers use electrical signals that are either on or off to convey information as bits, the smallest unit of data on a computer, represented as two binary values, zero (when ‘off’) or one (when ‘on’). Zeros and ones are strung together to form binary codes for text and other data on classical computers. Quantum computers use quantum systems, such as electrons or photons, to represent quantum bits or qubits that can be in a state of 0 or 1, or an arbitrary superposition of them, for example, an equal combination of both. Entanglement occurs when there is a non-separable joint state of multiple qubits in superposition. For example, two distant parties could share a state where both qubits are in a superposition of 0 and 1, but such that they are perfectly correlated — a superposition of both sides having 0 or both sides having 1. Balanced superpositions of this form are known as Bell pairs. Superposition and entanglement are the defining features that distinguish quantum information from classical information. In addition to enabling quantum state teleportation over quantum networks, they underpin the exponential algorithmic power of quantum computers.

Testing these intriguing principles of quantum information depends on the ability to manipulate individual atoms, molecules, electrons, and photons. Building quantum computers is challenging because nature cannot easily discern an ideal qubit. Technology-based on advanced material physics coupled with a great deal of engineering will plausibly isolate this kind of system and yet control them to perform computations with sufficient precision. Numerous different candidate systems are being explored including low-power superconducting circuits, electromagnetically trapped ions, single-atom dopants in silicon lattices, neutral atoms in optical lattices, and vacancy defects in diamond and silicon carbide as well as many, many others.