Imaginary Time Propagation on a Quantum Chip

Abstract

Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems, and the heart of a number of numerical methods that have been used with great success in quantum chemistry, condensed matter and nuclear physics. We propose an algorithm to implement imaginary time propagation on a quantum computer. Our algorithm is devised in the context of an efficient encoding into an optimized gate, drawing on the underlying characteristics of the quantum device, of a unitary operation in an extended Hilbert space. However, we proved that for simple problems it can be successfully applied to standard digital quantum machines. This work paves the way for porting quantum many-body methods based on imaginary-time propagation to near-term quantum devices, enabling the future quantum simulation of the ground states of a broad class of microscopic systems.

arXiv comment12 pages, 8 figures, 3 tables

References in corpus (29)

• A variational eigenvalue solver on a quantum processor
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• The theory of variational hybrid quantum-classical algorithms
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Scalable Quantum Simulation of Molecular Energies
• Toward the first quantum simulation with quantum speedup
• Variational ansatz-based quantum simulation of imaginary time evolution
• Simulating Lattice Gauge Theories within Quantum Technologies
• Robust determination of molecular spectra on a quantum processor
• Cloud Quantum Computing of an Atomic Nucleus
• Quantum Circuits for General Multiqubit Gates
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
• Local chiral effective field theory interactions and quantum Monte Carlo applications
• Efficient Bayesian Phase Estimation
• The problem of equilibration and the computation of correlation functions on a quantum computer
• Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip
• Near-optimal ground state preparation
• Quantum Monte Carlo calculations of neutron matter with chiral three-body forces
• Quantum Simulation of Helium Hydride in a Solid-State Spin Register
• Simulations of Subatomic Many-Body Physics on a Quantum Frequency Processor
• Preparation of excited states for nuclear dynamics on a quantum computer
• Nonunitary quantum circuit
• Optimal Control for the Quantum Simulation of Nuclear Dynamics
• High-fidelity software-defined quantum logic on a superconducting qudit
• Engineered thermalization and cooling of quantum many-body systems
• Noise-Resilient Quantum Dynamics Using Symmetry-Preserving Ansatzes
• Ground States via Spectral Combing on a Quantum Computer
• A linear time quantum algorithm for 3SAT using irreversible quantum operations

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• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
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• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (II) Single-Baryon $\beta$-Decay in Real Time
• Quantum computing of the ${}^6$Li nucleus via ordered unitary coupled clusters
• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States
• Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer
• Classical and Quantum Computing of Shear Viscosity for $2+1D$ SU(2) Gauge Theory
• An Alternative Approach to Quantum Imaginary Time Evolution
• Projection algorithm for state preparation on quantum computers
• Error-resilient Monte Carlo quantum simulation of imaginary time
• A quantum-classical co-processing protocol towards simulating nuclear reactions on contemporary quantum hardware
• Quantum Computing for Energy Correlators
• Emergent Hydrodynamic Mode on SU(2) Plaquette Chains and Quantum Simulation
• Solving reaction dynamics with quantum computing algorithms
• Randomised benchmarking for universal qudit gates
• Efficient solution of the non-unitary time-dependent Schrodinger equation on a quantum computer with complex absorbing potential
• Quantum techniques for eigenvalue problems
• Exact block encoding of imaginary time evolution with universal quantum neural networks
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories
• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
• Neutron-nucleus dynamics simulations for quantum computers
• Route towards classical frustration and band flattening via optical lattice distortion
• Toward scalable quantum computations of atomic nuclei
• Controlled Gate Networks: Theory and Application to Eigenvalue Estimation
• Beyond asymptotic reasoning: the practicalities of a quantum ground state projector based on the wall-Chebyshev expansion
• Classical optimization with imaginary time block encoding on quantum computers: The MaxCut problem
• A penalty-free quantum algorithm to find energy eigenstates
• Constrained Search in Imaginary Time