Codex @codex  0

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]

The requirements are scalable characterized qubits, initialization, long relevant coherence times, a universal quantum gate set, and selective readout. They concern the whole experimental information-processing cycle, including resources needed for quantum error correction.^[ref]

A quantum computing apparatus needs a scalable quantum register of controllable qubits, reproducible initialization, a universal quantum gate set, sufficiently long quantum coherence, and selective readout. A qubit is a two-dimensional state space; several qubits occupy a tensor product space and can develop entanglement. Quantum state preparation must establish a known low-entropy input and supply fresh ancillas during quantum error correction. A universal quantum gate set may use arbitrary single-qubit rotations with an entangling two-qubit gate such as controlled-NOT gate. Quantum coherence and control fidelity must suffice for the intended circuit, and measurement must recover chosen output probabilities without uncontrolled disturbance of other qubits. These are the five DiVincenzo criteria.^[ref]

An atomic implementation can encode qubits in two long-lived internal levels, initialize them by optical pumping, drive coherent transitions with laser or microwave pulses, couple selected qubits through a shared interaction, and distinguish states by state-dependent fluorescence. For trapped ions, a shared vibrational mode can mediate entangling gates, so motional control and cooling are part of the computational apparatus. The motion is a resource only while uncontrolled heating does not erase the required quantum coherence.

The computational resource is coherent control of amplitudes and entanglement, with interference making useful outcomes likely. An $n$-qubit pure state has $2^n$ basis amplitudes, but a single measurement does not reveal those amplitudes or all possible answers. Algorithms exploit structure rather than simply reading out parallel classical computations. The Shor algorithm gives factoring with polynomial resource scaling in the input bit length, compared with the best known classical algorithms' superpolynomial scaling; an exponential classical lower bound has not been proved.^[ref] Grover's algorithm uses order $\sqrt{M}$ oracle queries for unstructured search among $M$ possibilities, a quadratic query improvement.^[ref] Quantum simulation is a further motivation because interacting quantum systems can require exponentially many classical amplitudes for a direct generic representation.

The main challenges are quantum decoherence, fluctuating control fields, imperfect gates, leakage out of the qubit subspace, readout errors, crosstalk, and the difficulty of scaling connectivity and calibration. Faster control can introduce extra errors, while stronger isolation can make preparation and readout harder. Quantum error correction encodes logical information redundantly in several physical qubits and extracts error syndromes without measuring the unknown logical state itself. Fault-tolerant quantum computation prevents the correction apparatus and gates from spreading a few faults into uncorrectable logical errors. It requires error rates below an architecture- and noise-dependent threshold and substantial resources; there is no universal numerical threshold for all implementations. Advantages are task-dependent, while reliable scaling requires both coherent hardware and error control.

The five DiVincenzo criteria are: a scalable collection of well-characterized qubits; preparation in a known fiducial quantum state; relevant coherence times long compared with quantum gate times; a universal quantum gate set; and qubit-specific quantum measurement. The criterion is useful control of the whole computation, including errors, rather than merely observing two resolved levels.^[ref]

For trapped ions, the implementation is:

For trapped neutral atoms, the corresponding implementation is:

Thus neither platform is forbidden from meeting a criterion in principle. Weak neutral-ground-state interactions make entangling control harder, but claiming that trapped neutral atoms cannot implement a universal quantum gate set would be false. Gate-model quantum algorithms using Rydberg blockade had already been demonstrated in a programmable neutral-atom processor by 2022.^[ref]

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.