Optimal Hamiltonian Simulation by Quantum Signal Processing

Abstract

The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a $d$-sparse Hamiltonian $\hat{H}$ for time-interval $t$ with error $\epsilon$ is $\mathcal{O}(td\Vert \hat{H}{\Vert }_{\text{max}}+\frac{\log (1/\epsilon )}{\log \log (1/\epsilon )})$, which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (1) transducing eigenvalues of $\hat{H}$ into a single ancilla qubit, (2) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (3) projecting this ancilla with near unity success probability.

6 pages, 1 figure. v2: notation simplified & updated for general audience

References in corpus (9)

• Universal computation by quantum walk
• Sinc approximation of algebraically decaying functions
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Universal computation by multi-particle quantum walk
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Fixed-point quantum search with an optimal number of queries
• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• Efficient discrete-time simulations of continuous-time quantum query algorithms
• Quantum imaging by coherent enhancement

Cited by in corpus (467)

• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Hamiltonian Simulation by Qubitization
• Quantum algorithms for quantum chemistry and quantum materials science
• Toward the first quantum simulation with quantum speedup
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• A Theory of Trotter Error
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• Quantum Simulation for High Energy Physics
• Even more efficient quantum computations of chemistry through tensor hypercontraction
• Quantum computational finance: Monte Carlo pricing of financial derivatives
• Simulating Large Quantum Circuits on a Small Quantum Computer
• Low Depth Quantum Simulation of Electronic Structure
• Quantum computing enhanced computational catalysis
• Quantum Computer Systems for Scientific Discovery
• Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• The prospects of quantum computing in computational molecular biology
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Quantum algorithm for linear differential equations with exponentially improved dependence on precision
• Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers
• Nearly optimal lattice simulation by product formulas
• Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing
• Emerging quantum computing algorithms for quantum chemistry
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
• Near-optimal ground state preparation
• Faster quantum simulation by randomization
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Computational advantage of quantum random sampling
• Efficient phase-factor evaluation in quantum signal processing
• Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices
• Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
• Quantum algorithm for simulating real time evolution of lattice Hamiltonians
• Noisy intermediate-scale quantum computers
• Measurement reduction in variational quantum algorithms
• Optimized Compilation of Aggregated Instructions for Realistic Quantum Computers
• Fault-Tolerant Quantum Simulations of Chemistry in First Quantization
• Quantum Algorithm for Spectral Measurement with Lower Gate Count
• Black-box quantum state preparation without arithmetic
• Time-dependent Hamiltonian simulation with $L^1$-norm scaling
• Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
• Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning
• Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems
• From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms
• Downfolding of many-body Hamiltonians using active-space models: extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms
• Digital quantum simulation of molecular vibrations
• Quantum Computing for Neutrino-nucleus Scattering
• Rodeo Algorithm for Quantum Computing
• Quantum Simulation of Chemistry with Sublinear Scaling in Basis Size
• Improved quantum algorithms for linear and nonlinear differential equations
• Memcomputing: Leveraging memory and physics to compute efficiently
• Quantum Computing for Molecular Biology
• Hamiltonian simulation in the low-energy subspace
• Biology and medicine in the landscape of quantum advantages
• Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions
• Classically optimized Hamiltonian simulation
• Quantum SDP-Solvers: Better upper and lower bounds
• Hamiltonian Simulation with Optimal Sample Complexity
• Early fault-tolerant simulations of the Hubbard model
• Locality and digital quantum simulation of power-law interactions
• Product Decomposition of Periodic Functions in Quantum Signal Processing
• Minimizing estimation runtime on noisy quantum computers
• Exact and efficient Lanczos method on a quantum computer
• Trading T gates for dirty qubits in state preparation and unitary synthesis
• Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost
• Mitigating algorithmic errors in Hamiltonian simulation
• Quantum algorithm for calculating molecular vibronic spectra
• Quantum Simulation of the Sachdev-Ye-Kitaev Model by Asymmetric Qubitization
• Provably accurate simulation of gauge theories and bosonic systems
• Concentration for random product formulas
• Quantum Algorithm for the Vlasov Equation
• Simulating the dynamics of time-dependent Hamiltonians with a truncated Dyson series
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Time-dependent unbounded Hamiltonian simulation with vector norm scaling
• Time-marching based quantum solvers for time-dependent linear differential equations
• Preparation of excited states for nuclear dynamics on a quantum computer
• Nearly tight Trotterization of interacting electrons
• Simulating Open Quantum Systems Using Hamiltonian Simulations
• Quantum Algorithms for Estimating Physical Quantities using Block-Encodings
• On applications of quantum computing to plasma simulations
• Efficient Fully-Coherent Quantum Signal Processing Algorithms for Real-Time Dynamics Simulation
• Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT
• Subspace Variational Quantum Simulator
• Quantum inverse iteration algorithm for programmable quantum simulators
• Exponential quantum speedup in simulating coupled classical oscillators
• On the energy landscape of symmetric quantum signal processing
• Efficient Quantum Walk Circuits for Metropolis-Hastings Algorithm
• Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization
• Near- and long-term quantum algorithmic approaches for vibrational spectroscopy
• Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters
• Circuit Transformations for Quantum Architectures
• Primitive Quantum Gates for Dihedral Gauge Theories
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
• Experimental observation of information flow in the anti-$\mathcal{P}\mathcal{T}$-symmetric system
• Compilation by stochastic Hamiltonian sparsification
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model
• Hamiltonian simulation with random inputs
• Computing Ground State Properties with Early Fault-Tolerant Quantum Computers
• Hybridized Methods for Quantum Simulation in the Interaction Picture
• Quantum simulation of gauge theory via orbifold lattice
• Initial state preparation for quantum chemistry on quantum computers
• Toward Quantum Simulations of ${\mathbb{Z}}_2$ Gauge Theory Without State Preparation
• Towards quantum advantage via topological data analysis
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution
• Quantum algorithm for estimating Renyi entropies of quantum states
• Spectral density estimation with the Gaussian Integral Transform
• Fast-forwarding quantum evolution
• Variational Hamiltonian simulation for translational invariant systems via classical pre-processing
• Variational quantum eigensolvers for sparse Hamiltonians
• Hamiltonian Simulation by Uniform Spectral Amplification
• First-Order Trotter Error from a Second-Order Perspective
• Destructive Error Interference in Product-Formula Lattice Simulation
• Realization of quantum signal processing on a noisy quantum computer
• Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
• Optimized Lie-Trotter-Suzuki decompositions for two and three non-commuting terms
• Analyzing Prospects for Quantum Advantage in Topological Data Analysis
• Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms
• Quantum simulations of excited states with active-space downfolded Hamiltonians
• Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation
• The Impact of Hardware Specifications on Reaching Quantum Advantage in the Fault Tolerant Regime
• Two-Unitary Decomposition Algorithm and Open Quantum System Simulation
• Trapped-Ion Quantum Simulation of Collective Neutrino Oscillations
• Efficient quantum amplitude encoding of polynomial functions
• Digital quantum simulation of molecular dynamics and control
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
• Finding Angles for Quantum Signal Processing with Machine Precision
• Optimal (controlled) quantum state preparation and improved unitary synthesis by quantum circuits with any number of ancillary qubits
• Quantum Computing for Fusion Energy Science Applications
• FABLE: Fast Approximate Quantum Circuits for Block-Encodings
• New Quantum Algorithms for Computing Quantum Entropies and Distances
• Approximate Quantum Circuit Synthesis using Block-Encodings
• Quantum Computing: Lecture Notes
• Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers
• Perturbative quantum simulation
• Shorter quantum circuits via single-qubit gate approximation
• Quantum advantage for computations with limited space
• On the complexity of implementing Trotter steps
• Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle
• A Sparse Model of Quantum Holography
• Resource-Optimized Fermionic Local-Hamiltonian Simulation on Quantum Computer for Quantum Chemistry
• Quantum Phase Processing and its Applications in Estimating Phase and Entropies
• Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory
• Efficient simulation of sparse Markovian quantum dynamics
• Quantum algorithms from fluctuation theorems: Thermal-state preparation
• Superdiffusive quantum stochastic walk definable of arbitrary directed graph
• Efficient Quantum Algorithms for Simulating Lindblad Evolution
• On the Universality of Memcomputing Machines
• Data centers with quantum random access memory and quantum networks
• Amplitude Estimation from Quantum Signal Processing
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation
• An efficient quantum algorithm for preparation of uniform quantum superposition states
• Quantum computation of stopping power for inertial fusion target design
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• qSWIFT: High-order randomized compiler for Hamiltonian simulation
• Toward simulating Superstring/M-theory on a quantum computer
• Controlling error orientation to improve quantum algorithm success rates
• Error-resilient Monte Carlo quantum simulation of imaginary time
• Stable factorization for phase factors of quantum signal processing
• Systems Architecture for Quantum Random Access Memory
• Selected topics of quantum computing for nuclear physics
• Resource estimate for quantum many-body ground-state preparation on a quantum computer
• Application of Pontryagin's Minimum Principle to Grover's Quantum Search Problem
• A quantum hamiltonian simulation benchmark
• Simulating lossy Gaussian boson sampling with matrix product operators
• Fragmented imaginary-time evolution for early-stage quantum signal processors
• Hamiltonian simulation with nearly optimal dependence on spectral norm
• Adaptive variational simulation for open quantum systems
• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• Continuous-variable assisted thermal quantum simulation
• Quantum Regularized Least Squares
• Second-quantized fermionic operators with polylogarithmic qubit and gate complexity
• Low-depth Hamiltonian Simulation by Adaptive Product Formula
• Quantum computing of reacting flows via Hamiltonian simulation
• Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics
• Perturbation theory with quantum signal processing
• Entanglement accelerates quantum simulation
• Simulating nonnative cubic interactions on noisy quantum machines
• Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Q# and NWChem: Tools for Scalable Quantum Chemistry on Quantum Computers
• Characterizing non-Markovian Off-Resonant Errors in Quantum Gates
• Quantum simulation of battery materials using ionic pseudopotentials
• Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems
• Efficient Hamiltonian Simulation for Solving Option Price Dynamics
• Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation
• Doubling Efficiency of Hamiltonian Simulation via Generalized Quantum Signal Processing
• Circuit complexity of quantum access models for encoding classical data
• HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware
• Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries
• Synthesizing efficient circuits for Hamiltonian simulation
• Importance sampling for stochastic quantum simulations
• Quantum Signal Processing for simulating cold plasma waves
• Short-depth circuits for efficient expectation value estimation
• Quantum Error Mitigation Relying on Permutation Filtering
• Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian
• Quantum Simulation of Second-Quantized Hamiltonians in Compact Encoding
• On efficient quantum block encoding of pseudo-differential operators
• Quantum linear system solver based on time-optimal adiabatic quantum computing and quantum approximate optimization algorithm
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Derivative Pricing using Quantum Signal Processing
• Block-encoding dense and full-rank kernels using hierarchical matrices: applications in quantum numerical linear algebra
• Optimizing the information extracted by a single qubit measurement
• Spacetime-Efficient Low-Depth Quantum State Preparation with Applications
• Quantum algorithm for total least squares data fitting
• Compact quantum algorithms for time-dependent differential equations
• A stochastic quantum Krylov protocol with double factorized Hamiltonians
• Problem specific classical optimization of Hamiltonian simulation
• Efficient Quantum Simulation of Open Quantum System Dynamics on Noisy Quantum Computers
• Fault-tolerant quantum computation of molecular observables
• Experimental quantum channel discrimination using metastable states of a trapped ion
• Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems
• Infinite quantum signal processing
• Optimal Hamiltonian simulation for time-periodic systems
• Quantum mean centering for block-encoding-based quantum algorithm
• Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems
• Average-case Speedup for Product Formulas
• Continuous Hamiltonian dynamics on digital quantum computers without discretization error
• Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer
• Quantum Gaussian filter for exploring ground-state properties
• A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits
• Quantum Gradient Algorithm for General Polynomials
• 2QAN: A quantum compiler for 2-local qubit Hamiltonian simulation algorithms
• Quantum algorithm for the advection-diffusion equation and the Koopman-von Neumann approach to nonlinear dynamical systems
• Analysis of quantum Krylov algorithms with errors
• Faster quantum chemistry simulations on a quantum computer with improved tensor factorization and active volume compilation
• Quantum Topological Data Analysis with Linear Depth and Exponential Speedup
• SimuQ: A Framework for Programming Quantum Hamiltonian Simulation with Analog Compilation
• Algebraic Reasoning of Quantum Programs via Non-idempotent Kleene Algebra
• Exponentially faster implementations of Select(H) for fermionic Hamiltonians
• Quantum diffusion map for nonlinear dimensionality reduction
• Effects of Cosine Tapering Window on Quantum Phase Estimation
• Minimum Trotterization Formulas for a Time-Dependent Hamiltonian
• Wave Matrix Lindbladization II: General Lindbladians, Linear Combinations, and Polynomials
• Efficient explicit gate construction of block-encoding for Hamiltonians needed for simulating partial differential equations
• Efficient and precise quantum simulation of ultra-relativistic quark-nucleus scattering
• Quantum Computing Perspective for Electromagnetic Wave Propagation in Cold Magnetized Plasmas
• Doubling the order of approximation via the randomized product formula
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• Algorithmic Shadow Spectroscopy
• A quantum algorithm for the linear Vlasov equation with collisions
• Quantum advantage for noisy channel discrimination
• Well-conditioned multiproduct Hamiltonian simulation
• Fast Black-Box Quantum State Preparation Based on Linear Combination of Unitaries
• Incoherent quantum algorithm dynamics of an open system with near-term devices
• Site-by-site quantum state preparation algorithm for preparing vacua of fermionic lattice field theories
• Classical and Quantum Algorithms for Tensor Principal Component Analysis
• Simple and high-precision Hamiltonian simulation by compensating Trotter error with linear combination of unitary operations
• Explicit Quantum Circuit for Simulating the Advection-Diffusion-Reaction Dynamics
• Quantifying $T$-gate-count improvements for ground-state-energy estimation with near-optimal state preparation
• Hamiltonian simulation for low-energy states with optimal time dependence
• Quantum Computing for Energy Correlators
• Experimental Quantum Learning of a Spectral Decomposition
• Signal processing techniques for efficient compilation of controlled rotations in trapped ions
• Implementing smooth functions of a Hermitian matrix on a quantum computer
• Quantum state preparation for multivariate functions
• Riemannian quantum circuit optimization for Hamiltonian simulation
• Quantum algorithms for escaping from saddle points
• Compilation of a simple chemistry application to quantum error correction primitives
• Small quantum computers and large classical data sets
• Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis
• Quantum Quantitative Trading: High-Frequency Statistical Arbitrage Algorithm
• Quantum algorithms for generator coordinate methods
• Parallel Quantum Algorithm for Hamiltonian Simulation
• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
• Calculating the many-body density of states on a digital quantum computer
• Efficient and practical Hamiltonian simulation from time-dependent product formulas
• Single-step high-fidelity three-qubit gates by anisotropic chiral interactions
• Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
• Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms
• Faster spectral density calculation using energy moments
• Fast digital methods for adiabatic state preparation
• Multi-nucleon structure and dynamics via quantum computing
• On Quantum Simulation Of Cosmic Inflation
• Higher-order quantum transformations of Hamiltonian dynamics
• Solving reaction dynamics with quantum computing algorithms
• Simulation of linear non-Hermitian boundary-value problems with quantum singular value transformation
• A quantum algorithm for simulating non-sparse Hamiltonians
• Duality in Quantum Quenches and Classical Approximation Algorithms: Pretty Good or Very Bad
• Mapping renormalized coupled cluster methods to quantum computers through a compact unitary representation of non-unitary operators
• Improved amplitude amplification strategies for the quantum simulation of classical transport problems
• TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry
• Selection and improvement of product formulae for best performance of quantum simulation
• Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems
• Quantum Hypothesis Testing with Group Structure
• Solving the Hele-Shaw flow using the Harrow-Hassidim-Lloyd algorithm on superconducting devices: A study of efficiency and challenges
• Two-level Quantum Walkers on Directed Graphs II: An Application to qRAM
• Design nearly optimal quantum algorithm for linear differential equations via Lindbladians
• Graph Optimization Perspective for Low-Depth Trotter-Suzuki Decomposition
• Generalising quantum imaginary time evolution to solve linear partial differential equations
• Accelerating quantum imaginary-time evolution with random measurements
• Toward Mixed Analog-Digital Quantum Signal Processing: Quantum AD/DA Conversion and the Fourier Transform
• In the shadow of the Hadamard test: Using the garbage state for good and further modifications
• Halving the Cost of Quantum Algorithms with Randomization
• Entanglement-assisted phase estimation algorithm for calculating dynamical response functions
• Efficient Quantum Algorithm for Filtering Product States
• Sparse random Hamiltonians are quantumly easy
• Estimating Gibbs partition function with quantumClifford sampling
• A Comprehensive Cross-Model Framework for Benchmarking the Performance of Quantum Hamiltonian Simulations
• Practicality of quantum adiabatic algorithm for chemistry applications
• Quantum Algorithm For Estimating Eigenvalue
• Exploiting anticommutation in Hamiltonian simulation
• Time-dependent Hamiltonian Simulation via Magnus Expansion: Algorithm and Superconvergence
• Nonlinear transformation of complex amplitudes via quantum singular value transformation
• Block encoding bosons by signal processing
• Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations
• Quantum advantage from energy measurements of many-body quantum systems
• Polynomial Equivalence of Complexity Geometries
• Complexity of Digital Quantum Simulation in the Low-Energy Subspace: Applications and a Lower Bound
• Explicit block encodings of boundary value problems for many-body elliptic operators
• Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos
• Compressed variational quantum eigensolver for the Fermi-Hubbard model
• TE-PAI: Exact Time Evolution by Sampling Random Circuits
• Quantum Algorithm for the Advection-Diffusion Equation by Direct Block Encoding of the Time-Marching Operator
• Complementary polynomials in quantum signal processing
• Simulating nonlinear optical processes on a superconducting quantum device
• An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications
• Interaction graph engineering in trapped-ion quantum simulators with global drives
• Efficient ground-state energy estimation and certification on early fault-tolerant quantum computers
• A Quantum Algorithm Framework for Discrete Probability Distributions with Applications to Rényi Entropy Estimation
• Hybrid algorithms to solve linear systems of equations with limited qubit resources
• Roadmap for quantum simulation of the fractional quantum Hall effect
• Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes
• Molecular Properties from Quantum Krylov Subspace Diagonalization
• On multivariate polynomials achievable with quantum signal processing
• Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian
• Near-term quantum algorithm for computing molecular and materials properties based on recursive variational series methods
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Tensor Network enhanced Dynamic Multiproduct Formulas
• Quantum topological data analysis via the estimation of the density of states
• Statistics of topological defects across a phase transition in a digital superconducting quantum processor
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• QSlack: A slack-variable approach for variational quantum semi-definite programming
• Implementation of Continuous-Time Quantum Walk on Sparse Graph
• Dilution of error in digital Hamiltonian simulation
• Nearly-frustration-free ground state preparation
• Quantum Algorithm for Estimating Betti Numbers Using Cohomology Approach
• Uniform observable error bounds of Trotter formulae for the semiclassical Schrödinger equation
• Randomized semi-quantum matrix processing
• Modular quantum signal processing in many variables
• Optimal Low-Depth Quantum Signal-Processing Phase Estimation
• Infinite quantum signal processing for arbitrary Szegő functions
• Ladder Operator Block-Encoding
• Learning from physics experiments, with quantum computers: Applications in muon spectroscopy
• Quantum walk processes in quantum devices
• A Generalized Circuit for the Hamiltonian Dynamics Through the Truncated Series
• Efficient multi-qubit subspace rotations via topological quantum walks
• Quantum algorithms for spectral sums
• Tridiagonal matrix decomposition for Hamiltonian simulation on a quantum computer
• LSQCA: Resource-Efficient Load/Store Architecture for Limited-Scale Fault-Tolerant Quantum Computing
• Quantum algorithms for calculating determinant and inverse of matrix and solving linear algebraic systems
• Quantum phase estimation based filtering: performance analysis and application to low-energy spectral calculation
• Encoding of linear kinetic plasma problems in quantum circuits via data compression
• Quantum simulation by qubitization without Toffoli gates
• Some Error Analysis for the Quantum Phase Estimation Algorithms
• Impact of dynamics, entanglement, and Markovian noise on the fidelity of few-qubit digital quantum simulation
• Improved quantum algorithm for calculating eigenvalues of differential operators and its application to estimating the decay rate of the perturbation distribution tail in stochastic inflation
• Empirical determination of the simulation capacity of a near-term quantum computer
• Lower Bounds for Unitary Property Testing with Proofs and Advice
• Calculating response functions of coupled oscillators using quantum phase estimation
• Choco-Q: Commute Hamiltonian-based QAOA for Constrained Binary Optimization
• Quantum eigenvalue processing
• Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation
• Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers
• Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model
• Variational post-selection for ground states and thermal states simulation
• Semicoherent Symmetric Quantum Processes: Theory and Applications
• Correspondence between open bosonic systems and stochastic differential equations
• The Short Path Algorithm Applied to a Toy Model
• Quantum circuits for partial differential equations in Fourier space
• Heisenberg-limited adaptive gradient estimation for multiple observables
• Double-bracket algorithm for quantum signal processing without post-selection
• Parallelization techniques for quantum simulation of fermionic systems
• Unification of Finite Symmetries in Simulation of Many-body Systems on Quantum Computers
• Nonlinear Spectroscopy via Generalized Quantum Phase Estimation
• QKAN: quantum Kolmogorov-Arnold networks with applications in machine learning and multivariate state preparation
• On solving classes of positive-definite quantum linear systems with quadratically improved runtime in the condition number
• Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer
• Quantum advantage in temporally flat measurement-based quantum computation
• Quantum Lower Bounds by Sample-to-Query Lifting
• Optimal Particle-Conserved Linear Encoding for Practical Fermionic Simulation
• Adaptive Circuit Learning of Born Machine: Towards Realization of Amplitude Embedding and Quantum Data Loading
• Topological Signal Processing on Quantum Computers for Higher-Order Network Analysis
• Expanding Hardware-Efficiently Manipulable Hilbert Space via Hamiltonian Embedding
• Parameterized quantum comb and simpler circuits for reversing unknown qubit-unitary operations
• Prospects for NMR Spectral Prediction on Fault-Tolerant Quantum Computers
• Superconducting qubits in the millions: the potential and limitations of modularity
• Non-unitary Coupled Cluster Enabled by Mid-circuit Measurements on Quantum Computers
• Quantum and classical algorithms for nonlinear unitary dynamics
• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution
• Parallel Quantum Signal Processing Via Polynomial Factorization
• Faster Algorithmic Quantum and Classical Simulations by Corrected Product Formulas
• Expressivity of deterministic quantum computation with one qubit
• Context aware quantum simulation of a matrix stored in quantum memory
• Phase estimation with partially randomized time evolution
• Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers
• IF-QAOA: A Penalty-Free Approach to Accelerating Constrained Quantum Optimization
• Exponential distillation of dominant eigenproperties
• Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
• Scalable Quantum Computational Science: A Perspective from Block-Encodings and Polynomial Transformations
• Elucidating Many-Body Effects in Molecular Core Spectra through Real-Time Approaches: Efficient Classical Approximations and a Quantum Perspective
• Simulating quantum dynamics: Evolution of algorithms in the HPC context
• Spectral sparsification of matrix inputs as a preprocessing step for quantum algorithms
• Efficient implementation of unitary transformations
• Blockwise Optimization for Projective Variational Quantum Dynamics (BLOP-VQD): Algorithm and Implementation for Lattice Systems
• On the commutator scaling in Hamiltonian simulation with multi-product formulas
• Divergence-free algorithms for solving nonlinear differential equations on quantum computers
• Two exact quantum signal processing results
• Engineering Non-Gaussian Bosonic Gates through Quantum Signal Processing
• Quantum algorithms based on quantum trajectories
• Nuwa: A Quantum Circuit Transpiler Based on a Finite-Horizon Heuristic for Placement and Routing
• Implementing Finite Impulse Response Filters on Quantum Computers
• Phase Estimation with Compressed Controlled Time Evolution
• Quantum Machine Learning For Classical Data
• Quantum algorithm for PageRank computation through multistep quantum resonant transitions
• Feedback-Based Quantum Strategies for Constrained Combinatorial Optimization Problems
• Discrete Superconvergence Analysis for Quantum Magnus Algorithms of Unbounded Hamiltonian Simulation
• Quantum approximated cloning-assisted density matrix exponentiation
• Adaptive random compiler for Hamiltonian simulation
• Efficient quantum algorithm for solving structured problems via multi-step quantum computation
• Trotter error time scaling separation via commutant decomposition
• Generalized Parity Measurements and Efficient Large Multi-component Cat State Preparation with Quantum Signal Processing
• Halving the cost of quantum multiplexed rotations
• Symmetric channel verification for purifying noisy quantum channels
• Quantum algorithm for solving generalized eigenvalue problems with application to the Schrödinger equation
• Quantum linear system algorithm with optimal queries to initial state preparation
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Error analysis of quantum operators written as a linear combination of permutations
• Universal approximation of continuous functions with minimal quantum circuits
• Classical optimization with imaginary time block encoding on quantum computers: The MaxCut problem
• Robustness of near-thermal dynamics on digital quantum computers
• Quantum Signal Processing and Quantum Singular Value Transformation on $U(N)$
• Quantum Simulation via Stochastic Combination of Unitaries
• Bayesian inference of general noise-model parameters from the syndrome statistics of surface codes
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations
• Quantum Algorithm For Solving Nonlinear Algebraic Equations
• Anomalous transport in U(1)-symmetric quantum circuits
• Saving resources through repeat-until-success positive-operator-valued-measure measurements in quantum computation
• Error Interference in Quantum Simulation
• Optimal Hamiltonian recognition of unknown quantum dynamics
• Quantum community detection via deterministic elimination
• An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations
• Quantum memory assisted observable estimation
• Quantum Encoding of Structured Data with Matrix Product States
• Quantum algorithm for anisotropic diffusion and convection equations with vector norm scaling
• Sublinear quantum algorithms for estimating von Neumann entropy
• Quantum Heaviside Eigen Solver
• Quantum Simulation-Based Optimization for Cooling System Design
• Quantum multi-row iteration algorithm for linear systems with non-square coefficient matrices
• Quantum oracles for the finite element method
• Reflection-Based Adiabatic State Preparation
• An adversary bound for quantum signal processing
• Singular value transformation for unknown quantum channels
• Quantum Circuits Are Just a Phase
• Quantum amplitude damping for solving homogeneous linear differential equations: A noninterferometric algorithm
• Quantum Simulation of Nuclear Dynamics in First Quantization
• Quantum Framework for Simulating Linear PDEs with Robin Boundary Conditions
• Quantum Algorithm for a Convergent Series of Approximations towards the Exact Solution of the Lowest Eigenstates of a Hamiltonian
• Regularization from Superpositions of Time Evolutions
• Quantum phase estimation with optimal confidence interval using three control qubits
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
• Non-normality and dissipation in Markovian quantum dynamics: Implications for quantum simulation
• Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations