Stochastic Approximation of Variational Quantum Imaginary Time Evolution

The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an exponentially large wave function, quantum computers are emerging as a promising platform for this task. However, variational approaches, suitable for near-term quantum computers, struggle with a prohibitive number of measurements and impractical runtimes for relevant system sizes. Here, we suggest a stochastic approach to variational quantum imaginary-time evolution, which allows a significant reduction in runtimes. Our approach allows trading off invested resources and accuracy, which makes it also suitable for ground state preparation, where simulating the exact dynamics is not required. We demonstrate the efficiency of our algorithm in simulations and show a hardware experiment performing the imaginary-time evolution of the transverse field Ising model on 27 qubits.

[1]  G. Carleo,et al.  Variational Quantum Time Evolution without the Quantum Geometric Tensor , 2023, 2303.12839.

[2]  P. P. Orth,et al.  Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations , 2023, 2301.02592.

[3]  Stefan Woerner,et al.  Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection , 2022, Quantum.

[4]  J. Gambetta,et al.  Scalable Mitigation of Measurement Errors on Quantum Computers , 2021, PRX Quantum.

[5]  Theodore J. Yoder,et al.  Scalable error mitigation for noisy quantum circuits produces competitive expectation values , 2021, Nature Physics.

[6]  G. Carleo,et al.  Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information , 2021, Quantum.

[7]  Marcello Benedetti,et al.  Hardware-efficient variational quantum algorithms for time evolution , 2020, Physical Review Research.

[8]  A. Green,et al.  Real- and Imaginary-Time Evolution with Compressed Quantum Circuits , 2020, PRX Quantum.

[9]  Stefan Woerner,et al.  Variational quantum Boltzmann machines , 2020, Quantum Machine Intelligence.

[10]  W. Zeng,et al.  Digital zero noise extrapolation for quantum error mitigation , 2020, 2020 IEEE International Conference on Quantum Computing and Engineering (QCE).

[11]  J. Haegeman,et al.  Geometry of variational methods: dynamics of closed quantum systems , 2020, 2004.01015.

[12]  J. Stokes,et al.  Quantum Natural Gradient , 2019, Quantum.

[13]  F. Brandão,et al.  Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution , 2019, Nature Physics.

[14]  Ying Li,et al.  Theory of variational quantum simulation , 2018, Quantum.

[15]  Peter Zoller,et al.  Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states , 2018, Physical Review A.

[16]  C. Gogolin,et al.  Evaluating analytic gradients on quantum hardware , 2018, Physical Review A.

[17]  Ivano Tavernelli,et al.  Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions , 2018, Physical Review A.

[18]  Kristan Temme,et al.  Supervised learning with quantum-enhanced feature spaces , 2018, Nature.

[19]  Ying Li,et al.  Variational ansatz-based quantum simulation of imaginary time evolution , 2018, npj Quantum Information.

[20]  Patrick J. Coles,et al.  Learning the quantum algorithm for state overlap , 2018, New Journal of Physics.

[21]  S. Benjamin,et al.  Practical Quantum Error Mitigation for Near-Future Applications , 2017, Physical Review X.

[22]  J. McClean,et al.  Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz , 2017, Quantum Science and Technology.

[23]  P. Coveney,et al.  Scalable Quantum Simulation of Molecular Energies , 2015, 1512.06860.

[24]  E. Farhi,et al.  A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.

[25]  R. Cleve,et al.  Quantum fingerprinting. , 2001, Physical review letters.

[26]  D. Gottesman.  The Heisenberg Representation of Quantum Computers , 1998, quant-ph/9807006.

[27]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[28]  J. Spall.  Accelerated second-order stochastic optimization using only function measurements , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[29]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[30]  M. Powell.  A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation , 1994 .