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.
hub
Hamiltonian Simulation in the Interaction Picture
15 Pith papers cite this work. Polarity classification is still indexing.
15
Pith papers citing it
abstract
We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture, where some portions are made time-dependent. This can provide a favorable complexity trade-off as the algorithm scales exponentially better with derivatives of the time-dependent component than the original Hamiltonian. We show that this leads to an exponential improvement in gate complexity for simulating some classes of diagonally dominant Hamiltonian. Additionally we show that this can reduce the gate-complexity scaling for simulating $N$-site Hubbard models for time $t$ with arbitrary long-range interactions as well as reduce the cost of quantum chemistry simulations within a similar-sized plane-wave basis to $\widetilde{\mathcal{O}}(N^2t)$ from $\widetilde{\mathcal{O}}(N^{11/3}t)$. We also show a quadratic improvement in query complexity for simulating sparse time-dependent Hamiltonians, which may be of independent interest.
hub tools
citation-role summary
background 2
method 2
citation-polarity summary
representative citing papers
Quantum fast multipole method yields electronic structure simulation gate complexity t(η^{4/3}N^{1/3} + η^{1/3}N^{2/3})(η N t / ε)^{o(1)}, providing roughly O(η) speedup over prior work for N < η^7.
Bivariate quantum signal processing simulates non-Hermitian Hamiltonians H_eff = H_R + i H_I with query-optimal complexity O((α_R + β_I)T + log(1/ε)/log log(1/ε)) in the separate-oracle model.
Single-ancilla approximate block encoding of A = sum alpha_j H_j is achieved via generalized quantum signal processing applied to Hamiltonian simulation, yielding near-optimal depth with one or O(log log(1/epsilon)) ancilla.
Using multi-product formulas in LCHS produces commutator-sensitive error bounds and better quadrature scaling than norm-based analyses for dissipative dynamics.
Introduces Amplitude-Phase Separation (APS) decomposition for quantum simulation of non-unitary dynamics, with complementary error scaling advantages in time-independent cases and unification of prior methods like LCHS and NDME.
Resource estimates for quantum simulation of pionless and pionful nuclear lattice EFTs, including time evolution and energy estimation, with new error bounds from symmetries and locality yielding orders-of-magnitude improvements for the pionless case.
Second-order Trotterization of many-body Coulomb Hamiltonians achieves a 1/4 convergence rate for general initial conditions in the Hamiltonian domain with polynomial particle-number scaling, and improves to first or second order under state-dependent conditions such as high-angular-momentum excited
Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.
Quantum simulation framework for ground-state energies of 4- and 8-electron double quantum dots on surface-code fault-tolerant hardware, with resource estimates of 226k-314k physical qubits and 24 hours to 3.4 days runtime at 10^{-3} noise.
MPO encodings of the Magnus expansion and Dyson series for accurate time evolution of time-dependent 1D quantum Hamiltonians on finite or infinite lattices with long-range interactions.
Comparative resource analysis finds PMR offers complementary advantages and favorable scaling versus leading methods for time-independent and time-dependent Hamiltonian simulation.
Review of quantum computing methods and potential for non-ground-state quantum chemistry including reaction dynamics, mechanisms, and finite temperatures.
The paper reviews advances in quantum simulation of out-of-equilibrium dynamics in gauge theories, covering particle production, string breaking, thermalization, and related phenomena.
citing papers explorer
-
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.
-
Quantum simulation of electronic structure via quantum fast multipole method
Quantum fast multipole method yields electronic structure simulation gate complexity t(η^{4/3}N^{1/3} + η^{1/3}N^{2/3})(η N t / ε)^{o(1)}, providing roughly O(η) speedup over prior work for N < η^7.
-
Simulation of Non-Hermitian Hamiltonians with Bivariate Quantum Signal Processing
Bivariate quantum signal processing simulates non-Hermitian Hamiltonians H_eff = H_R + i H_I with query-optimal complexity O((α_R + β_I)T + log(1/ε)/log log(1/ε)) in the separate-oracle model.
-
Low-ancilla block encodings via Hamiltonian simulation
Single-ancilla approximate block encoding of A = sum alpha_j H_j is achieved via generalized quantum signal processing applied to Hamiltonian simulation, yielding near-optimal depth with one or O(log log(1/epsilon)) ancilla.
-
Linear Combination of Hamiltonian Simulation with Commutator Scaling
Using multi-product formulas in LCHS produces commutator-sensitive error bounds and better quadrature scaling than norm-based analyses for dissipative dynamics.
-
Quantum Simulation of Non-Unitary Dynamics via Amplitude-Phase Separation
Introduces Amplitude-Phase Separation (APS) decomposition for quantum simulation of non-unitary dynamics, with complementary error scaling advantages in time-independent cases and unification of prior methods like LCHS and NDME.
-
Quantum Algorithms for Simulating Nuclear Effective Field Theories
Resource estimates for quantum simulation of pionless and pionful nuclear lattice EFTs, including time evolution and energy estimation, with new error bounds from symmetries and locality yielding orders-of-magnitude improvements for the pionless case.
-
Trotterization with Many-body Coulomb Interactions: Convergence for General Initial Conditions and State-Dependent Improvements
Second-order Trotterization of many-body Coulomb Hamiltonians achieves a 1/4 convergence rate for general initial conditions in the Hamiltonian domain with polynomial particle-number scaling, and improves to first or second order under state-dependent conditions such as high-angular-momentum excited
-
Quantum Gibbs sampling through the detectability lemma
Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.
-
Nanostructure modelling with early fault tolerant quantum computers
Quantum simulation framework for ground-state energies of 4- and 8-electron double quantum dots on surface-code fault-tolerant hardware, with resource estimates of 226k-314k physical qubits and 24 hours to 3.4 days runtime at 10^{-3} noise.
-
Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series
MPO encodings of the Magnus expansion and Dyson series for accurate time evolution of time-dependent 1D quantum Hamiltonians on finite or infinite lattices with long-range interactions.
-
Permutation Matrix Representation for Quantum Simulation: Comparative Resource Analysis
Comparative resource analysis finds PMR offers complementary advantages and favorable scaling versus leading methods for time-independent and time-dependent Hamiltonian simulation.
-
Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
Review of quantum computing methods and potential for non-ground-state quantum chemistry including reaction dynamics, mechanisms, and finite temperatures.
-
Quantum simulation of out-of-equilibrium dynamics in gauge theories
The paper reviews advances in quantum simulation of out-of-equilibrium dynamics in gauge theories, covering particle production, string breaking, thermalization, and related phenomena.
- Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition