David Wakeham
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View article: The Structure and Interpretation of Quantum Programs I: Foundations
The Structure and Interpretation of Quantum Programs I: Foundations Open
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables su…
View article: Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation Open
We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems. In particular, we examine the computation of the cumulative distribution function (CDF) of the spectral measure …
View article: A Short History of Rocks: or, How to Invent Quantum Computing
A Short History of Rocks: or, How to Invent Quantum Computing Open
This essay gives a short, informal account of the development of digital logic from the Pleistocene to the Manhattan Project, the introduction of reversible circuits, and Richard Feynman's allied proposal for quantum computing. We argue th…
View article: Inference, interference and invariance: How the Quantum Fourier Transform can help to learn from data
Inference, interference and invariance: How the Quantum Fourier Transform can help to learn from data Open
How can we take inspiration from a typical quantum algorithm to design heuristics for machine learning? A common blueprint, used from Deutsch-Josza to Shor's algorithm, is to place labeled information in superposition via an oracle, interf…
View article: Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation Open
We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems. In particular, we examine the computation of the cumulative distribution function (CDF) of the spectral measure …
View article: Microstate distinguishability, quantum complexity, and the eigenstate thermalization hypothesis
Microstate distinguishability, quantum complexity, and the eigenstate thermalization hypothesis Open
In this work, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the eigenstate thermalization hypothesis (ETH). After identifying simple operators with an algebra of low-energy observables an…
View article: Quantum tasks require islands on the brane
Quantum tasks require islands on the brane Open
In recent work, it was argued that quantum computations with inputs and outputs distributed in spacetime, or quantum tasks, impose constraints on entanglement in holographic theories. The resulting constraint was named the connected wedge …
View article: Why is a soap bubble like a railway?
Why is a soap bubble like a railway? Open
At a certain infamous tea party, the Mad Hatter posed the following riddle: why is a raven like a writing-desk? We do not answer this question. Instead, we solve a related nonsense query: why is a soap bubble like a railway? The answer is …
View article: Eigenstate Thermalization and Disorder Averaging in Gravity
Eigenstate Thermalization and Disorder Averaging in Gravity Open
Naively, resolving the black hole information paradox requires microscopic details about quantum gravity. Recent work suggests that, instead, a unitary Page curve can be recovered by adding disorder-averaged replica instantons to the path …