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Quantum Algorithm Zoo
A catalog of quantum algorithms by problem area, with claimed speedups and references, including simulation.
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Lecture Notes on Quantum Computation
Preskill’s course notes on quantum information and computation, from foundations through error correction and fault tolerance.
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A Proof of the Aaronson–Ambainis Conjecture
Announces a proof, reportedly found by an AI system and checked in Lean, of a conjecture on quantum speedups for random inputs; claimed by its authors and not yet independently verified.
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Reference Architecture of a Quantum-Centric Supercomputer
IBM’s reference design for integrating quantum processors with classical high-performance computing.
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Machine Learning on Heterogeneous, Edge, and Quantum Hardware for Particle Physics
ML-HEQUPP: a community survey of machine learning on specialized and quantum hardware for particle physics.
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Observation of String-Breaking Dynamics in a Quantum Simulator
String breaking observed in real time on a trapped-ion quantum simulator.
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Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories
Confinement and string dynamics in a (2+1)D lattice gauge theory on a superconducting processor.
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Chemistry Beyond the Scale of Exact Diagonalization on a Quantum-Centric Supercomputer
Sample-based quantum diagonalization: a quantum processor and a supercomputer working together on molecules beyond exact diagonalization.
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Quantum Simulations of Hadron Dynamics in the Schwinger Model Using 112 Qubits
Real-time hadron wavepacket dynamics on 112 qubits of IBM hardware.
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Quantum-Centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
A perspective on combining quantum processors with classical supercomputers, and the problems they might tackle together.
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Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits
Scalable circuits for preparing the Schwinger model vacuum, run on 100+ superconducting qubits.
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Quantum Computing for High-Energy Physics: State of the Art and Challenges
The QC4HEP working group summary: theory, simulation, data analysis and the road ahead.
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Evidence for the Utility of Quantum Computing before Fault Tolerance
IBM’s 127-qubit Ising dynamics experiment with error mitigation, at a scale that challenged brute-force classical simulation.
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Quantum Simulation for High-Energy Physics
The Snowmass 2021 roadmap for quantum simulation in high-energy physics.
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Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
Schwinger model simulation on trapped ions, using the gauge symmetry to suppress errors.
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SU(2) Hadrons on a Quantum Computer
Hadron masses in a non-Abelian SU(2) lattice gauge theory computed on quantum hardware.
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A Theory of Trotter Error
Tight bounds on product-formula error that exploit commutativity, often far below earlier estimates.
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Simulating Lattice Gauge Theories within Quantum Technologies
A broad review of analog and digital approaches to lattice gauge theory simulation, with tensor networks.
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The Quantum Computers in Our Future
A short column on what quantum computers might do, written for a general audience.
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Simulating Quantum Field Theory with a Quantum Computer
A plenary overview of the prospects and challenges for simulating quantum field theory on quantum computers.
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Quantum-Classical Computation of Schwinger Model Dynamics Using Quantum Computers
Schwinger model dynamics on cloud quantum computers, using symmetries and classical computation to shrink the problem.
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Quantum Computing in the NISQ Era and Beyond
Names and frames the era of noisy intermediate-scale quantum devices and what they might do.
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Toward the First Quantum Simulation with Quantum Speedup
Concrete gate counts for simulating a spin system beyond classical reach, comparing product formulas and newer methods.
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Hamiltonian Simulation by Qubitization
Qubitization: optimal simulation for Hamiltonians given as a linear combination of unitaries.
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Optimal Hamiltonian Simulation by Quantum Signal Processing
Quantum signal processing gives Hamiltonian simulation with optimal query complexity.
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Real-Time Dynamics of Lattice Gauge Theories with a Few-Qubit Quantum Computer
The first digital quantum simulation of a gauge theory: pair creation in the Schwinger model on trapped ions.
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Quantum Simulations of Lattice Gauge Theories Using Ultracold Atoms in Optical Lattices
A review of proposals for simulating Abelian and non-Abelian lattice gauge theories with cold atoms.
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Quantum Algorithms for Fermionic Quantum Field Theories
Extends the scattering algorithm to fermions, using the Gross–Neveu model.
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Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
A review of analog quantum simulation of gauge theories with cold atoms, including quantum link models.
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Quantum Computation of Scattering in Scalar Quantum Field Theories
The full-length version of the Science paper, with complete error and cost analysis.
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Quantum Algorithms for Quantum Field Theories
Aaronson’s commentary on the Jordan–Lee–Preskill algorithm and why it matters for the reach of quantum computing.
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Quantum Algorithms for Quantum Field Theories
A polynomial-time quantum algorithm for computing scattering in a scalar quantum field theory, including preparing wavepackets of particles.
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Simulating Lattice Gauge Theories on a Quantum Computer
An early concrete scheme for encoding U(1), SU(2) and SU(3) lattice gauge theories into qubits.
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Quantum Computation and Quantum Information
The standard textbook on quantum computing and quantum information: circuits, algorithms, error correction and information theory.
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Complexity Limitations on Quantum Computation
Structural results on where BQP sits among classical complexity classes, including limits on what oracles can show.
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Quantum Field Theory
A compact review of quantum field theory’s central ideas and achievements, written for the American Physical Society’s centenary.
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Universal Quantum Simulators
Proof that a quantum computer can efficiently simulate local quantum systems, making Feynman’s proposal precise with Trotter-style product formulas.
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A Fast Quantum Mechanical Algorithm for Database Search
Grover’s algorithm: a quadratic speedup for unstructured search, and a building block for amplitude amplification.
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An Introduction to Quantum Field Theory
The standard graduate textbook on quantum field theory: perturbation theory, renormalization, gauge theories and the Standard Model.
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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
Shor’s algorithm: the first exponential quantum speedup for a problem of practical importance.
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Simulating Physics with Computers
The 1981 lecture that proposed using quantum systems to simulate quantum physics, the starting point for quantum simulation and quantum computing.
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Quantum Field Theory Lectures
Typeset notes from Coleman’s celebrated Harvard course on quantum field theory.
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Hamiltonian Formulation of Wilson’s Lattice Gauge Theories
The Hamiltonian lattice formulation of gauge theories, including staggered fermions, that most quantum simulations of gauge theories start from.
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An Investigation of the Laws of Thought
Boole’s algebra of logic and probability; ch. 1 opens with his statement of aims.
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The Mathematical Analysis of Logic
Boole’s first treatment of logic as an algebra of classes with 1 and 0.
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De onbetrouwbaarheid der logische principes
The unreliability of the logical principles: excluded middle questioned for infinite collections.
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Letter to Euler
The letter in which Goldbach’s conjecture first appears.
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Die formalen Regeln der intuitionistischen Logik
The formal rules of intuitionistic logic.
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Ein Beitrag zur Mannigfaltigkeitslehre
Where Cantor first states the continuum hypothesis.
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The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis
Gödel’s constructible universe: the continuum hypothesis cannot be refuted from the standard axioms.
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The Independence of the Continuum Hypothesis
Forcing: the continuum hypothesis cannot be proved from the standard axioms.
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What Is Cantor’s Continuum Problem?
Gödel argues the continuum hypothesis has a definite answer, probably false.
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Is the Continuum Hypothesis a Definite Mathematical Problem?
Feferman argues that it may not be.
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Zur Geschichte der Aussagenlogik
On the history of propositional logic: Stoic logic recognised as propositional logic.
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Pojęcie prawdy w językach nauk dedukcyjnych
The concept of truth in formalized languages, and the undefinability of truth.
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Introduction to a General Theory of Elementary Propositions
Truth tables as a decision method, and completeness of propositional logic.
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Tractatus Logico-Philosophicus
Propositions as truth-functions; tautology and contradiction as limiting cases.
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Formal Logic: or, The Calculus of Inference, Necessary and Probable
Where De Morgan’s laws for negating “and” and “or” are stated.
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The Logic of Quantum Mechanics
Quantum propositions as subspaces of Hilbert space, a non-distributive lattice.
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Complexity of the Realization of a Linear Function in the Class of Π-Circuits
A quadratic lower bound on formula size for parity.
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The Synthesis of Two-Terminal Switching Circuits
The counting argument: almost every Boolean function needs exponentially large circuits.
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A Set of Five Independent Postulates for Boolean Algebras, with Application to Logical Constants
One connective suffices: the Sheffer stroke.
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A Reduction in the Number of the Primitive Propositions of Logic
The stroke read as NAND, the reading that became standard.
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A Boolian Algebra with One Constant
An unpublished manuscript showing a single connective can express all the others.
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Letter to Allan Marquand
Proposes building logic machines from electrical switches in series and parallel.
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A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations
The parallel-prefix method behind the Kogge–Stone carry-lookahead adder.
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A Symbolic Analysis of Relay and Switching Circuits
Shannon’s master’s thesis: switching circuits designed with Boolean algebra.
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Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components
Reliable computation from unreliable parts, an ancestor of the threshold theorem.
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A Logical Calculus of the Ideas Immanent in Nervous Activity
Threshold neurons as logic: networks of them compute truth functions.
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First Draft of a Report on the EDVAC
The stored-program design, its circuits described in McCulloch–Pitts notation.
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Irreversibility and Heat Generation in the Computing Process
Landauer’s principle: erasing a bit releases at least kT ln 2 of heat.
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Logical Reversibility of Computation
Any computation can be done reversibly: compute, copy, uncompute.
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Reversible Computing
The Toffoli gate, universal for reversible computation.
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Experimental Verification of Landauer’s Principle Linking Information and Thermodynamics
Erasing one bit held by a trapped bead, approaching the kT ln 2 bound.
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Letter to Frege
Russell reports his paradox to Frege.
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Grundgesetze der Arithmetik, vol. 2
The volume going to press when Russell’s paradox arrived.
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Is Logic Empirical?
Putnam’s case that quantum mechanics refutes the distributive law.
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A Philosopher Looks at Quantum Mechanics (Again)
Putnam revisits, and abandons, his earlier view.
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The Problem of Hidden Variables in Quantum Mechanics
No assignment of definite values to all quantum yes-or-no questions respects their structure.
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