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Andrew Yao is a computer scientist whose work spans analysis of algorithms, computational complexity theory, cryptography and quantum computing. His training included doctorates in both physics and computer science.^[ref]

With Danny Dolev, he developed formal models for the security of cryptographic protocols using public-key cryptography. Their Dolev-Yao model makes an active adversary's possible manipulations explicit while treating the underlying encryption and decryption symbolically. The resulting distinction is useful: a protocol can fail through its pattern of messages even if its encryption primitives behave as intended.^[ref]

John Kubiatowicz researches computer systems, with projects spanning operating systems, file systems and quantum computing architecture. His institutional homepage links the Tessellation operating system, OceanStore global storage and the Quantum Architecture Research Center. These projects study how a computing service is organized across the underlying hardware and storage mechanisms.^[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.

Peter Shor is a mathematician whose research includes quantum computing, quantum information theory, algorithms and computational geometry.^[ref] His quantum algorithms for integer factorization and discrete logarithms require a number of steps polynomial in the number of input digits. They made the distinction between classical and quantum computational resources concrete for problems used in cryptography.^[ref]

Quantum computing processes quantum information through controlled physical transformations and quantum measurements. In the quantum circuit model, an initial quantum state evolves through quantum gates, and the Born rule predicts the final outcome probabilities. Quantum interference makes the relative quantum phases of amplitudes computationally useful. David Deutsch's 1985 paper developed a model of universal quantum computation.^[ref]

A one-qubit example shows why amplitudes matter. Starting from $|0⟩$, a Hadamard gate gives $(|0⟩+|1⟩)/\sqrt{2}$; a second Hadamard gate returns $|0⟩$. Insert a Pauli Z gate between the two Hadamard gates and the final state is instead $|1⟩$: the intermediate relative sign changes how amplitudes combine. Measuring the intermediate state alone would give equal probabilities in both cases. A useful quantum algorithm arranges such transformations to make information about the required answer accessible through the final quantum measurement.

Xinyu Wu is a computer scientist whose research has included the theoretical foundations of quantum computing, pseudorandomness in quantum states and quantum channels. A 2021 Carnegie Mellon research profile describes this combination of tools from mathematics, physics and computer science.^[ref]

With Emre Yolcu and Marijn Heule, Wu also studied the complexity of proving colouring properties of Mycielski graphs. Their work connects short formal proofs with experiments on automated proof search.^[ref]