Probabilistic imaginary-time evolution in state-vector-based and shot-based simulations and on quantum devices
arXiv:2504.04958 · doi:10.1103/2s2p-kvcx
Abstract
Imaginary-time evolution, an important technique in tensor network and quantum Monte Carlo algorithms on classical computers, has recently been adapted to quantum computing. In this study, we focus on probabilistic imaginary-time evolution (PITE) algorithm and derive its formulation in the context of state-vector-based simulations, where quantum state vectors are directly used to compute observables without statistical errors. We compare the results with those of shot-based simulations, which estimate observables through repeated projective measurements. Applying the PITE algorithm to the Heisenberg chain, we investigate optimal initial conditions for convergence. We further demonstrate the method on the transverse-field Ising model using a state-of-the-art trapped-ion quantum device. Finally, we explore the potential of error mitigation in this framework, highlighting practical considerations for near-term digital quantum simulations.
12 pages, 9 figures, final version. Sample codes available at Zenodo: https://doi.org/10.5281/zenodo.17295160
References in corpus (32)
- Quantum Computing in the NISQ era and beyond
- A variational eigenvalue solver on a quantum processor
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Efficient classical simulation of slightly entangled quantum computations
- Barren plateaus in quantum neural network training landscapes
- The theory of variational hybrid quantum-classical algorithms
- Noisy intermediate-scale quantum (NISQ) algorithms
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Variational ansatz-based quantum simulation of imaginary time evolution
- Theory of variational quantum simulation
- tket : A Retargetable Compiler for NISQ Devices
- Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
- A Race Track Trapped-Ion Quantum Processor
- Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
- Simulating quantum many-body dynamics on a current digital quantum computer
- Variational quantum algorithms for discovering Hamiltonian spectra
- Real- and imaginary-time evolution with compressed quantum circuits
- Massively parallel quantum computer simulator, eleven years later
- Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
- Algorithms for quantum simulation at finite energies
- Many-body physics in the NISQ era: quantum programming a discrete time crystal
- Off-diagonal Wave Function Monte Carlo Studies of Hubbard Model I
- Digital Quantum Simulation of Non-Equilibrium Quantum Many-Body Systems
- Making Trotters Sprint: A Variational Imaginary Time Ansatz for Quantum Many-body Systems
- Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer
- Discretized quantum adiabatic process for free fermions and comparison with the imaginary-time evolution
- Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer
- Quantum computing Floquet energy spectra
- Calculating the many-body density of states on a digital quantum computer
- Noise-Robust Detection of Quantum Phase Transitions
- Prolonging a discrete time crystal by quantum-classical feedback
- Simulating Floquet scrambling circuits on trapped-ion quantum computers