Develops a quantum algorithm for linear matrix differential equations with query complexity O~(ν L t / ε) that is nearly optimal and yields polynomial to exponential speedups for open quantum system simulation.
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Optimal hamiltonian simulation by quantum signal processing
15 Pith papers cite this work, alongside 794 external citations. Polarity classification is still indexing.
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representative citing papers
Quantum signal processing angles admit closed-form expressions via orthogonal polynomial theory, allowing O(log(1/ε)) gate block-encodings of smooth functions through Hermite expansions and full characterization of SU(1,1)-QSP polynomials by roots.
Fixed upload circuits approximate tunable ones to error ε with depth O_σ[(log(1/ε))^σ] for any σ>1 (improving prior polynomial bounds) and matching Ω(log(1/ε)) lower bounds for mismatch-class targets via auxiliary extensions and Turán-Nazarov analysis.
QRSI spans degenerate quantum eigenspaces almost surely by conjugating the Hamiltonian with random unitaries on g parallel branches and using subspace estimation, while exactly preserving the spectral gap.
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
Continuous TE-PAI provides an unbiased randomized protocol for Hamiltonian simulation free of Trotter error at finite circuit depth, combined with structure-aware variance reduction that achieves up to 96% sampling-cost savings in n=30 tensor-network simulations.
End-to-end QSP-based quantum circuits solve linear PDEs on IBM hardware with tunable error and handle non-homogeneous Dirichlet boundaries for a plasma Poisson problem.
Quadratic bosonic Hamiltonian simulation is BQP-complete for a broad class that includes classical oscillator networks and continuous-time quantum walks, but becomes PostBQP-hard when extended to more general quadratic interactions.
CBMD decomposes non-Hermitian evolution operators into Hermitian LCU terms via a matrix residue theorem, matching known optimal query bounds and offering a route to polynomial matrix functions.
Quantum algorithm finds eigenvalues of parameterized matrix families by minimizing singular values and applies it to Schrödinger equation collocation with O(sqrt(N)) scaling.
Human-AI collaboration expanded a meta-idea on rational approximation into sign-embedding quantum algorithms for matrix problems, with humans retaining final judgment on routes and refinements.
Quantum algorithms for element-wise polynomial matrix transforms achieve exponential space reduction in polynomial degree with corrections to prior constructions.
Continuous-variable photonic platform with 20,000-mode cluster state simulates advection transport equation, achieving relative errors of 0.8% and 0.92% on first- and second-order moments via homodyne readout.
Extends KMS-detailed balance constructions from open quantum systems to prepare microcanonical ensembles and other stationary states with criteria for efficient implementation.
Quantum simulation methods for Thirring and Gross-Neveu fermionic models with arbitrary flavors, including gate complexity bounds and ground-state preparation up to 20 qubits.
citing papers explorer
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Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems
Develops a quantum algorithm for linear matrix differential equations with query complexity O~(ν L t / ε) that is nearly optimal and yields polynomial to exponential speedups for open quantum system simulation.
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Analytical Angle-Finding and Series Expansions for Quantum Signal Processing via Orthogonal Polynomial Theory
Quantum signal processing angles admit closed-form expressions via orthogonal polynomial theory, allowing O(log(1/ε)) gate block-encodings of smooth functions through Hermite expansions and full characterization of SU(1,1)-QSP polynomials by roots.
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The Cost of Removing Tunability in Quantum Data Re-Uploading
Fixed upload circuits approximate tunable ones to error ε with depth O_σ[(log(1/ε))^σ] for any σ>1 (improving prior polynomial bounds) and matching Ω(log(1/ε)) lower bounds for mismatch-class targets via auxiliary extensions and Turán-Nazarov analysis.
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Quantum Randomized Subspace Iteration
QRSI spans degenerate quantum eigenspaces almost surely by conjugating the Hamiltonian with random unitaries on g parallel branches and using subspace estimation, while exactly preserving the spectral gap.
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Fast mixing of all-to-all quantum systems at high temperatures
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
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Structure-Aware Variance Reduction for Unbiased Randomized Hamiltonian Simulation
Continuous TE-PAI provides an unbiased randomized protocol for Hamiltonian simulation free of Trotter error at finite circuit depth, combined with structure-aware variance reduction that achieves up to 96% sampling-cost savings in n=30 tensor-network simulations.
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Quantum Signal Processing for Linear PDEs: Circuit Design and Experimental Validation
End-to-end QSP-based quantum circuits solve linear PDEs on IBM hardware with tunable error and handle non-homogeneous Dirichlet boundaries for a plasma Poisson problem.
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Complexity of Quadratic Bosonic Hamiltonian Simulation: $\mathsf{BQP}$-Completeness and $\mathsf{PostBQP}$-Hardness
Quadratic bosonic Hamiltonian simulation is BQP-complete for a broad class that includes classical oscillator networks and continuous-time quantum walks, but becomes PostBQP-hard when extended to more general quadratic interactions.
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Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition
CBMD decomposes non-Hermitian evolution operators into Hermitian LCU terms via a matrix residue theorem, matching known optimal query bounds and offering a route to polynomial matrix functions.
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Quantum algorithm for solving generalized eigenvalue problems with application to the Schr\"odinger equation
Quantum algorithm finds eigenvalues of parameterized matrix families by minimizing singular values and applies it to Schrödinger equation collocation with O(sqrt(N)) scaling.
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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms
Human-AI collaboration expanded a meta-idea on rational approximation into sign-embedding quantum algorithms for matrix problems, with humans retaining final judgment on routes and refinements.
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Quantum element-wise transforms
Quantum algorithms for element-wise polynomial matrix transforms achieve exponential space reduction in polynomial degree with corrections to prior constructions.
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Analog photonic simulator for large-scale transport
Continuous-variable photonic platform with 20,000-mode cluster state simulates advection transport equation, achieving relative errors of 0.8% and 0.92% on first- and second-order moments via homodyne readout.
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Dissipative microcanonical ensemble preparation from KMS-detailed balance
Extends KMS-detailed balance constructions from open quantum systems to prepare microcanonical ensembles and other stationary states with criteria for efficient implementation.
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Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
Quantum simulation methods for Thirring and Gross-Neveu fermionic models with arbitrary flavors, including gate complexity bounds and ground-state preparation up to 20 qubits.