Solves quantum purity amplification for arbitrary n, m, eigenstates, and dimension d, with asymptotic input scaling O(m/(ε D_min²)) independent of d and non-asymptotic bounds from generalized Young diagrams.
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Quantum A lgorithm for Linear Systems of Equations
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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.
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.
A reduction from weak agnostic learning of class C to efficient tomography of states with bounded l1-extent w.r.t. C, with a concrete algorithm for stabilizer states running in poly(n, (ξ/ε)^log(ξ/ε)) time.
Quantum algorithm block-encodes Riccati solutions for m-particle m-hole RPA using Riesz projectors and QSVT, claiming linear system-size scaling under sparsity and polynomial cost in excitation rank m.
A classical polynomial-time algorithm for optimized sampling of lottery tickets in neural networks removes the exponential dependence on data dimension from prior classical approaches.
Hybrid Path-Sums offer a new symbolic framework with rewriting rules and assertions to represent, simplify, and verify properties of hybrid quantum-classical programs.
Quantum algorithms achieve polylog(N) complexity for high-dimensional linear SDEs by amplitude-encoding the solution and noise via Dyson series or Euler-Maruyama approximations plus quantum linear systems solvers.
A new method for unitary synthesis on quantum hardware cuts CNOT gates by up to 36% and compiles up to 553 times faster than standard tools on square and heavy-hex lattices.
Integrating amplitude estimation into QNN readout achieves O(1/N) estimation error with one shot instead of the usual O(1/sqrt(N)) Monte Carlo scaling.
Cobble is a domain-specific language for quantum block encodings that compiles high-level matrix expressions to optimized circuits using analyses and quantum singular value transformation, achieving 2.6x-25.4x speedups over unoptimized baselines on benchmarks.
Quantum circuits for coherent multilayer neural network inference achieve quadratic to polylogarithmic speedups over classical methods depending on quantum data access models for inputs and weights.
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.
GQPINNs add symmetry awareness to quantum PINNs via equivariant circuits, yielding lower mean absolute error and fewer parameters than standard QPINNs on linear and nonlinear PDE benchmarks.
Presents LCNU-plus-embedding data loading for any polynomial Carleman-linearized autonomous system and applies it to the 3D LBE, yielding Ns ~ O(α²Q²) terms and explicit T-gate resource estimates for two solvers.
A non-interactive time-delayed publicly verifiable scheme for quantum computation compiled from private 2-round protocols via time-lock puzzles and commitments, proven secure in the quantum random oracle model with CRS.
A teleportation-based parallelization architecture for neutral-atom quantum error correction delivers up to 3x speedup over extractor methods at fixed space cost and enables simulated quantum advantage at 11,495 atoms and 15-hour runtime.
Quantum integer multiplier with O(log^2 n) circuit depth and T-depth via parallel partial products and binary adder tree in the Clifford+T model.
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
A quantum algorithm for rovibrational Hamiltonian simulation on fault-tolerant quantum computers using hybrid DVR and Walsh-Hadamard QROM, claiming exponential resource savings over prior quantum and classical methods.
Proposes a quantum-walker qRAM on a single binary tree using local operations that reduces resources while preserving optimal query complexity.
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.
Extends KMS-detailed balance constructions from open quantum systems to prepare microcanonical ensembles and other stationary states with criteria for efficient implementation.
citing papers explorer
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Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs
Solves quantum purity amplification for arbitrary n, m, eigenstates, and dimension d, with asymptotic input scaling O(m/(ε D_min²)) independent of d and non-asymptotic bounds from generalized Young diagrams.
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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.
-
Tomography of quantum states with bounded extent
A reduction from weak agnostic learning of class C to efficient tomography of states with bounded l1-extent w.r.t. C, with a concrete algorithm for stabilizer states running in poly(n, (ξ/ε)^log(ξ/ε)) time.
-
Quantum Solvers for Nonlinear Matrix Equations in Quantum Chemistry
Quantum algorithm block-encodes Riccati solutions for m-particle m-hole RPA using Riesz projectors and QSVT, claiming linear system-size scaling under sparsity and polynomial cost in excitation rank m.
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Hybrid Path-Sums for Hybrid Quantum Programs
Hybrid Path-Sums offer a new symbolic framework with rewriting rules and assertions to represent, simplify, and verify properties of hybrid quantum-classical programs.
-
Quantum algorithm for solving high-dimensional linear stochastic differential equations via amplitude encoding of the noise term
Quantum algorithms achieve polylog(N) complexity for high-dimensional linear SDEs by amplitude-encoding the solution and noise via Dyson series or Euler-Maruyama approximations plus quantum linear systems solvers.
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Architecture-aware Unitary Synthesis
A new method for unitary synthesis on quantum hardware cuts CNOT gates by up to 36% and compiles up to 553 times faster than standard tools on square and heavy-hex lattices.
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Single-shot quantum neural networks with amplitude estimation
Integrating amplitude estimation into QNN readout achieves O(1/N) estimation error with one shot instead of the usual O(1/sqrt(N)) Monte Carlo scaling.
-
Cobble: Compiling Block Encodings for Quantum Computational Linear Algebra
Cobble is a domain-specific language for quantum block encodings that compiles high-level matrix expressions to optimized circuits using analyses and quantum singular value transformation, achieving 2.6x-25.4x speedups over unoptimized baselines on benchmarks.
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Accelerating Inference for Multilayer Neural Networks with Quantum Computers
Quantum circuits for coherent multilayer neural network inference achieve quadratic to polylogarithmic speedups over classical methods depending on quantum data access models for inputs and weights.
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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.
-
Geometric Quantum Physics Informed Neural Network
GQPINNs add symmetry awareness to quantum PINNs via equivariant circuits, yielding lower mean absolute error and fewer parameters than standard QPINNs on linear and nonlinear PDE benchmarks.
-
Quantum Data Loading for Carleman Linearized Systems: Application to the Lattice-Boltzmann Equation
Presents LCNU-plus-embedding data loading for any polynomial Carleman-linearized autonomous system and applies it to the 3D LBE, yielding Ns ~ O(α²Q²) terms and explicit T-gate resource estimates for two solvers.
-
Time-Delayed Publicly Verifiable Quantum Computation for Classical Verifiers
A non-interactive time-delayed publicly verifiable scheme for quantum computation compiled from private 2-round protocols via time-lock puzzles and commitments, proven secure in the quantum random oracle model with CRS.
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Architecting Early Fault Tolerant Neutral Atoms Systems with Quantum Advantage
A teleportation-based parallelization architecture for neutral-atom quantum error correction delivers up to 3x speedup over extractor methods at fixed space cost and enables simulated quantum advantage at 11,495 atoms and 15-hour runtime.
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A Polylogarithmic-Depth Quantum Multiplier
Quantum integer multiplier with O(log^2 n) circuit depth and T-depth via parallel partial products and binary adder tree in the Clifford+T model.
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Numerical approximation of the Koopman-von Neumann equation: Operator learning and quantum computing
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
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Simulating high-accuracy nuclear motion Hamiltonians using discrete variable representation and Walsh-Hadamard QROM on fault-tolerant quantum computers
A quantum algorithm for rovibrational Hamiltonian simulation on fault-tolerant quantum computers using hybrid DVR and Walsh-Hadamard QROM, claiming exponential resource savings over prior quantum and classical methods.
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A resource-efficient quantum-walker Quantum RAM
Proposes a quantum-walker qRAM on a single binary tree using local operations that reduces resources while preserving optimal query complexity.
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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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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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End-to-End Speedup for Quantum Simulation-Based Optimization in Power Grid Management
QAOA-based QuSO achieves end-to-end speedup over classical baselines for power grid unit commitment with up to 14 qubits using 16 layers in high-load scenarios via efficient classical pre-computation.
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On the coherent extension of some Fano-type learning bounds
Extends Fano bounds to sufficiency of low conditional entropy and defines a quantum entanglement task for infinite-dimensional systems with bounds via maximal singlet fraction of finite-dimensional approximations.
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Towards an Optimally Distributed Quantum Fourier Transform Circuit
Presents an optimal gate-packing partitioning scheme for the QFT that aims to minimize e-bit count in distributed quantum systems and validates it on hardware.