Quantum Information & Computation
Volume 26
RESEARCH ARTICLE Open access

Quasiprobabilistic Imaginary-Time Evolution on Quantum Computers

Annie Ray, Esha Swaroop, Ningping Cao, Michael Vasmer, Anirban Chowdhury

Author affiliations
  • Annie Ray1
  • Esha Swaroop1
  • Ningping Cao2
  • Michael Vasmer3
  • Anirban Chowdhury4
  1. Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada; Department of Physics and Astronomy, University of Waterloo, Waterloo, Canada; Perimeter Institute for Theoretical Physics, 31 Caroline St N, Waterloo, ON, Canada
  2. Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada; Perimeter Institute for Theoretical Physics, 31 Caroline St N, Waterloo, ON, Canada
  3. Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada; Perimeter Institute for Theoretical Physics, 31 Caroline St N, Waterloo, ON, Canada; Inria Paris, 48 rue Barrault, Paris, France
  4. IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, NY, USA

pp. 89-113 · 10.2478/qic-2026-0005

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Abstract

Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for imaginary-time evolution have resource requirements that are prohibitive for current quantum devices and face performance issues due to noise. Here, we propose a new algorithm for computing imaginary-time evolved expectation values on quantum computers, inspired by probabilistic error cancellation, an error-mitigation technique. Our algorithm works by decomposing a Trotterization of imaginary-time evolution into a probabilistic linear combination of operations, each of which is then implemented on a quantum computer. The measurement data is then classically post-processed to obtain the expectation value of the imaginary-time evolved state. Our algorithm requires no ancillary qubits and can be made noise-resilient without additional error-mitigation. It is well-suited for estimating thermal expectation values by making use of the notion of a thermal pure quantum state. We demonstrate our algorithm by performing numerical simulations of thermal pure quantum state preparation for the 1D Heisenberg Hamiltonian on 8 qubits, and by using an IBM quantum computer to estimate the energy of the same Hamiltonian on 2 qubits. We observe promising results compared to the exact values, illustrating the potential of our algorithm for probing the physics of quantum many-body systems on current hardware.
Open accessCC BY-NC-ND 4.0

Keywords

  • quantum algorithms
  • imaginary-time evolution
  • quantum error mitigation
  • thermal expectation values

Suggested citation

Annie Ray, Esha Swaroop, Ningping Cao, Michael Vasmer, Anirban Chowdhury (2026). Quasiprobabilistic Imaginary-Time Evolution on Quantum Computers. Quantum Information & Computation, 26(1), 89-113. https://doi.org/10.2478/qic-2026-0005

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