An arXiv preprint describes a method for reconstructing imaginary-time evolution from measured real-time correlation functions. In three exactly solvable one-dimensional examples, exact and analytically continued diffusion distributions showed excellent agreement, while a scattering comparison agreed well at small times and showed deviations at longer times. IBM demonstrations produced reasonable one-qubit results, but the two-qubit results failed after only a few Trotter steps.
The construction represents the nonunitary imaginary-time-evolution operator as a linear combination of real-time evolution operators when the Hamiltonian, the mathematical description of the quantum system, meets the Hermitian condition specified in the derivation and its ground-state energy has a lower bound c.
To make the calculation numerical, the study truncates the real-time integral and approximates it with Gaussian quadrature, a weighted numerical estimate of an integral. The IBM protocol uses Trotterized real-time evolution of the total Hamiltonian, dividing the evolution into smaller steps.
The benchmarks stay small and exactly solvable
An illustrative 2 × 2 Hermitian Hamiltonian matrix was used to demonstrate the analytic-continuation relation. That comparison reported systematic error at a real-time cutoff of 50 time units; at a cutoff of 250, the error was largely removed.
The applications covered Brownian motion with constant drift, the Ornstein–Uhlenbeck process and one-dimensional quantum-mechanical scattering. The paper's worked tests remain within these three exactly solvable one-dimensional examples.
Exact and analytically continued probability distributions showed excellent agreement in the diffusion demonstrations. The paper did not report a formal error interval for this result.
For the difference between interacting and non-interacting correlation functions in the scattering calculation, exact and continued results agreed well at small times, while deviations appeared at longer times. The analysis reported cutoff and boundary-condition effects alongside those deviations.
Hardware tests expose the boundary
The hardware evaluation included one- and two-qubit IBM tests benchmarked against exact solutions. In the Brownian-motion demonstration, reconstructed matrix elements showed reasonable agreement with a real-time cutoff of 200 time units.
The paper reports an approximate single-qubit gate fidelity of 99.976% and Trotterization up to 2,000 time steps. It describes the one-qubit results as encouraging, but this result does not establish robust multi-qubit performance.
The two-qubit test failed after only a few Trotter steps. The analysis identified two-qubit gate-operation errors and thermal-relaxation errors, and the authors said further error mitigation is needed for systematically controlled calculations on larger quantum systems.
A separate one-qubit scattering test showed reasonable qualitative agreement with the exact result using a real-time cutoff of 100 time units. The paper indicates that larger cutoffs could improve agreement.
What the results do not establish
Taken together, the evidence is a proof of concept for small, benchmarked cases. It does not establish accurate or systematically controlled imaginary-time evolution for large quantum systems, or reliable two-qubit performance under the reported conditions.
The tested results leave open how the construction performs for larger and non-exactly-solvable Hamiltonians, and whether error mitigation can support systematically controlled multi-qubit calculations.
The document is an arXiv version-1 preprint dated 20 August 2026. On the evidence presented, its contribution is a tested reconstruction strategy for small, benchmarked cases, with unresolved questions about error control and scale.
Paper data and sources
Original title: Imaginary time evolution of a quantum system through analytic continuation from real-time quantum simulation
Authors: Peng Guo, Anto Shibu, Joshua Lin, Yong Zhao
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text