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arXiv:2603.11208 · PRX Quantum

Unitary imaginary time evolution and ground state preparation using multi-copy protocols

Tal Schwartzman, Torsten V. Zache, Hannes Pichler, H. R. Sadeghpour

quant-phhep-thphysics.atom-phSubmitted Mar 11, 2026• Announced Mar 13, 2026• 0 citations
v1 · Mar 11, 2026v2 · Aug 12, 2026v3 · Aug 14, 2026
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Abstract

Efficient low-energy state preparation is a key objective in quantum computation and quantum simulation. Quantum imaginary-time evolution replaces real-time dynamics with imaginary-time dynamics, exponentially suppressing higher-energy eigenstates. We introduce deterministic unitary protocols that approximate imaginary-time evolution for ground-state preparation. The protocols require multiple copies of the system, real-time evolution under the system Hamiltonian, and controlled-SWAP operations (or more general SWAP-generated unitaries). We analyze two concrete circuit families: a tree architecture with provable polynomial-in-depth convergence but rapidly growing width, and a compact "hedge" architecture that achieves comparable accuracy with only polynomial width in a heuristic construction supported by numerics. We provide numerical evidence that mid-circuit post-selection can accelerate convergence with practical success probabilities. Separately, we demonstrate that circuit volume can be traded for the shot complexity of post-circuit observable estimation in the ground-state preparation setting. We outline concrete implementation of platform-specific routes, where multi-copy registers and SWAP-mediated couplings are natural, thereby illustrating how these hybrid analog-digital circuits can complement existing state-preparation methods in the near term.

DOI
10.1103/1tf6-bc55
Comments
12 pages, 5 figures

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Efficient low-energy state preparation is a key objective in quantum computation and quantum simulation. Quantum imaginary-time evolution replaces real-time dynamics with imaginary-time dynamics, exponentially suppressing higher-energy eigenstates. We introduce deterministic unitary protocols that approximate imaginary-time evolution for ground-state preparation. The protocols require multiple copies of the system, real-time evolution under the system Hamiltonian, and controlled-SWAP operations (or more general SWAP-generated unitaries). We analyze two concrete circuit families: a tree architecture with provable polynomial-in-depth convergence but rapidly growing width, and a compact "hedge" architecture that achieves comparable accuracy with only polynomial width in a heuristic construction supported by numerics. We provide numerical evidence that mid-circuit post-selection can accelerate convergence with practical success probabilities. Separately, we demonstrate that circuit volume can be traded for the shot complexity of post-circuit observable estimation in the ground-state preparation setting. We outline concrete implementation of platform-specific routes, where multi-copy registers and SWAP-mediated couplings are natural, thereby illustrating how these hybrid analog-digital circuits can complement existing state-preparation methods in the near term.
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We describe a protocol for preparing the ground state of a Hamiltonian HHH on a quantum computer. This is done by designing a quantum algorithm that implements the imaginary time evolution operator: e−τHe^{-τH}e−τH. The method relies on the so-called ``qubitization'' procedure of Low and Chuang which, assuming the existence of a unitary encoding of the Hamiltonian H=⟨G∣UH∣G⟩H = \langle G| U_H |G\rangleH=⟨G∣UH​∣G⟩, produces a new operator WHW_HWH​ whose moments are the Chebyshev polynomials of HHH when projected on ∣G⟩|G\rangle∣G⟩. Using this result and the expansion of e−τHe^{-τH}e−τH in terms of Chebyshev polynomials we construct a circuit that implements an approximation of the imaginary time evolution operator which, at large time, projects any state on the ground state, provided a non-trivial initial overlap between the two. We illustrate our method on two models: the transverse field Ising model and a single qubit toy model.
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Imaginary time evolution is a powerful technique for computing the ground state of quantum Hamiltonians, where the convergence to ground state in asymptotic imaginary time is guaranteed. However, implementing this method on quantum computers is challenging due to its nonunitary nature. Here, we propose a fully quantum approach for simulation of imaginary time evolutions which eliminates the need for intermediate classical computation or state tomography. Our method leverages the recently introduced state-based quantum simulation technique, in which using quantum states besides quantum gates allows to simulate a broader class of evolutions beyond the natural quantum dynamics. Specifically, we demonstrate how by using a set of quantum states and by applying only controlled-SWAP gates and measurements, one can simulate the nonunitary imaginary time evolution. We illustrate our results in an example.