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A theoretical physicist who formulated physical requirements for a quantum computer: controllable qubits, initialization, coherence lasting long enough for operations, universal quantum logic gates and readout. His analysis lets proposed hardware platforms be compared through the same operational tasks.^[ref]

With Daniel Loss, he proposed encoding qubits in single-electron spins in coupled quantum dots, using electrically controlled coupling for two-qubit operations.^[ref]

John M. Martinis coauthored a 1985 observation of quantized energy levels in a current-biased Josephson junction. The relevant coordinate was the phase difference across an electrical circuit element, rather than the position of one isolated particle. The measured levels agreed with a quantum mechanics calculation using junction parameters measured in the classical regime. This showed that a fabricated superconducting circuit could possess a discrete excitation spectrum suitable for controlled quantum experiments.^[ref]

A physicist researching superconducting devices and quantum computers based on Josephson junctions.^[ref]

Oded Regev introduced learning with errors as a foundation for lattice-based cryptography. His paper connects appropriately parameterized noisy modular linear equations to worst-case lattice problems through a quantum reduction, and constructs a classical public-key encryption scheme from that learning assumption.^[ref]

The distinction between a quantum reduction and a classical cryptosystem matters: the encryption and decryption procedures need not run on a quantum computer, even though the reduction establishing the hardness connection uses quantum computation. The work also makes the error distribution part of the problem definition. Removing the errors gives ordinary modular linear equations and changes the computational task fundamentally. Regev's research homepage identifies this lattice-based work among his contributions.^[ref]

A quantum algorithm specifies quantum state preparation, a sequence of quantum gates and quantum measurements, and any classical computation controlling them. For a pure quantum state $|\psi ⟩={\sum }_x{\alpha }_x|x⟩$, computational-basis measurement returns $x$ with probability $|{\alpha }_x{|}^2$, as prescribed by the Born rule. David Deutsch formulated a universal quantum computer using unitary operators and measurement.^[ref]

For example, one Hadamard gate prepares $H|0⟩=(|0⟩+|1⟩)/\sqrt{2}$. Computational-basis measurement gives either bit with probability $1/2$. Applying another Hadamard gate before measuring instead gives $H^2|0⟩=|0⟩$: the amplitudes for outcome one cancel by quantum interference. This illustrates why manipulating probability amplitudes matters; merely preparing a superposition does not reveal every component.

An analysis of algorithms must state the counted resources: quantum gate count, number of qubits, quantum state preparation cost and repetitions needed for the required probability of a correct result. Quantum query complexity counts quantum oracle calls separately; one such call need not be one elementary quantum gate.

A quantum computer is a physical device that performs controlled quantum computation and extracts an output through quantum measurement. A programmable quantum computer combines physical qubits, control hardware and classical processing that specifies operations and interprets repeated measurements.

David P. DiVincenzo organized the central physical requirements into five capabilities: scalable and characterized qubits; initialization in a known quantum state; sufficiently long relevant decoherence times compared with operation times; a universal set of quantum gates; and quantum measurement of selected qubits. These requirements connect an abstract quantum circuit with an experiment: knowing the intended gate sequence is useful only if the apparatus can initialize, control and read the encoded system accurately.^[ref]

The encoding can use different physical systems. Two selected internal levels of a trapped ion, for example, can represent the basis states of a qubit. The remaining levels and environmental couplings then become part of the physical control problem.

An experimental physicist who coauthored a programmable neutral-atom quantum computer demonstration. Focused light beams addressed individual qubits in a two-dimensional array, while interactions between Rydberg atoms enabled entangling operations. The experiment combined quantum logic gates into quantum algorithms, testing whether a collection of controlled chemical atoms could execute complete circuits.^[ref]