Efficient Fully-Coherent Quantum Signal Processing Algorithms for Real-Time Dynamics Simulation

Abstract

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are often time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by a property called fully-coherent: the algorithm succeeds with arbitrarily high success probability $1-\delta$, while only requiring a single copy of the initial state. We subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time $t$, $\ln (1/\delta )$, and $\ln (1/\epsilon )$ for error tolerance $\epsilon$: $\Theta (\Vert \mathcal{H}\Vert |t|+\ln (1/\epsilon )+\ln (1/\delta ))$. Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H${}_2$ molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.

References in corpus (35)

• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Real time evolution using the density matrix renormalization group
• Quantum Amplitude Amplification and Estimation
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Universal computation by quantum walk
• Hamiltonian Simulation by Qubitization
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Elucidating Reaction Mechanisms on Quantum Computers
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• Toward the first quantum simulation with quantum speedup
• A Theory of Trotter Error
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• A Grand Unification of Quantum Algorithms
• Nonequilibrium dynamical mean-field theory
• Even more efficient quantum computations of chemistry through tensor hypercontraction
• A review of progress in the physics of open quantum systems: theory and experiment
• Taming the dynamical sign problem in real-time evolution of quantum many-body problems
• Time-dependent density-matrix renormalization group: A systematic method for the study of quantum many-body systems out-of-equilibrium
• Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
• The methodology of resonant equiangular composite quantum gates
• Quantum algorithm for simulating real time evolution of lattice Hamiltonians
• Quantum simulation of non-equilibrium dynamics and thermalization in the Schwinger model
• Multi-configuration time-dependent density-functional theory based on range separation
• Faster Digital Quantum Simulation by Symmetry Protection
• Real-Time Dynamics in Quantum Impurity Models with Diagrammatic Monte Carlo
• Bounding the costs of quantum simulation of many-body physics in real space
• Nearly tight Trotterization of interacting electrons
• Quantum algorithm for time-dependent Hamiltonian simulation by permutation expansion
• Real-time density-matrix coupled-cluster approach for closed and open systems at finite temperature
• Time Dependent Adaptive Configuration Interaction Applied to Attosecond Charge Migration
• Simulating high-temperature superconductivity model Hamiltonians with atoms in optical lattices
• Exploiting anticommutation in Hamiltonian simulation

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• Superconducting qubits in the millions: the potential and limitations of modularity
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• Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
• Prospects for NMR Spectral Prediction on Fault-Tolerant Quantum Computers
• Quantum algorithm for solving generalized eigenvalue problems with application to the Schrödinger equation
• Beyond asymptotic reasoning: the practicalities of a quantum ground state projector based on the wall-Chebyshev expansion
• Explicit decoders using fixed-point amplitude amplification based on QSVT
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
• Optimal Hamiltonian recognition of unknown quantum dynamics
• Quantum Imaginary-Time Evolution with Polynomial Resources in Evolution Time