Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2608.00443

Trading Imaginary Time for Randomness in Ground State Preparation

Alvan Arulandu, John M. Martyn, Isaac L. Chuang

quant-phSubmitted Aug 1, 2026• Announced Aug 4, 2026• 0 citations
v1 · Aug 1, 2026v2 · Sep 15, 2026
arXivHTMLPDF

Abstract

Imaginary-time evolution (ITE) is a foundational method for ground state preparation on quantum computers. However, because ITE is non-unitary, existing implementations incur a sample complexity and/or classical cost that scales exponentially with the target imaginary time $β$. Moreover, the state itself converges slower than the energy, making accurate estimation of arbitrary ground state observables even more expensive. In this work, we improve upon standard ITE by introducing twirled imaginary-time evolution (TITE), which pairs ITE with real-time evolution applied for a random duration drawn from a carefully designed distribution. We prove that this randomization quadratically suppresses the trace distance to the ground state, and thus also the error of arbitrary observables, which allows roughly half of the imaginary time to be replaced with real-time evolution ($β\mapsto β/2$) while maintaining the same level of accuracy. Because real-time evolution is unitary and does not incur an overhead in sample complexity or classical computation, this affords a quadratic reduction in the cost of any black-box ITE implementation, including Trotterization and quantum imaginary-time evolution. We demonstrate the efficiency of our algorithm in noisy circuit-level simulations of a non-integrable Ising chain, showing substantial improvements over standard ITE.

Comments
20 pages

Related papers

Imaginary time evolution and ground state preparation using unitary multi-copy protocols

Tal Schwartzman, Torsten V. Zache, Hannes Pichler +1 more

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). Our analysis focuses on 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. Numerical evidence indicates 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. Finally, we outline concrete platform-specific implementations in which multi-copy registers and SWAP-mediated couplings are natural, illustrating how these hybrid analog-digital circuits can complement existing state-preparation methods in the near term.

quant-pharXiv:2603.11208•PRX Quantum•Mar 13, 2026•0 citations

Non-unitary Trotter circuits for imaginary time evolution

Chiara Leadbeater, Nathan Fitzpatrick, David Muñoz Ramo +1 more

We propose an imaginary time equivalent of the well-established Pauli gadget primitive for Trotter-decomposed real time evolution, using mid-circuit measurements on a single ancilla qubit. Imaginary time evolution (ITE) is widely used for obtaining the ground state of a system on classical hardware, computing thermal averages, and as a component of quantum algorithms that perform non-unitary evolution. Near-term implementations on quantum hardware rely on heuristics, compromising their accuracy. As a result, there is growing interest in the development of more natively quantum algorithms. Since it is not possible to implement a non-unitary gate deterministically, we resort to the implementation of probabilistic imaginary time evolution (PITE) algorithms, which rely on a unitary quantum circuit to simulate a block encoding of the ITE operator - that is, they rely on successful ancillary measurements to evolve the system non-unitarily. Compared with previous PITE proposals, the suggested block encoding in this paper results in shorter circuits and is simpler to implement, requiring only a slight modification of the Pauli gadget primitive. This scheme was tested on the transverse Ising model and the fermionic Hubbard model and is demonstrated to converge to the ground state of the system.

arXiv:2304.07917•Apr 16, 2023•0 citations

A Probabilistic Imaginary Time Evolution Algorithm Based on Non-unitary Quantum Circuit

Hao-Nan Xie, Wei, Shi-Jie, Fan Yang +4 more

Imaginary time evolution is a powerful tool applied in quantum physics, while existing classical algorithms for simulating imaginary time evolution suffer high computational complexity as the quantum systems become larger and more complex. In this work, we propose a probabilistic algorithm for implementing imaginary time evolution based on non-unitary quantum circuit. We demonstrate the feasibility of this method by solving the ground state energy of several quantum many-body systems, including H2, LiH molecules and the quantum Ising chain. Moreover, we perform experiments on superconducting and trapped ion cloud platforms respectively to find the ground state energy of H2 and its most stable molecular structure. We also analyze the successful probability of the algorithm, which is a polynomial of the output error and introduce an approach to increase the success probability by rearranging the terms of Hamiltonian.

arXiv:2210.05293•Oct 11, 2022•2 citations

Non-unitary Trotter circuits for imaginary time evolution

Chiara Leadbeater, Nathan Fitzpatrick, David Muñoz Ramo +1 more

Abstract We propose an imaginary time equivalent of the well-established Pauli gadget primitive for Trotter-decomposed real time evolution, using mid-circuit measurements on a single ancilla qubit. Imaginary time evolution (ITE) is widely used for obtaining the ground state (GS) of a system on classical hardware, computing thermal averages, and as a component of quantum algorithms that perform non-unitary evolution. Near-term implementations on quantum hardware rely on heuristics, compromising their accuracy. As a result, there is growing interest in the development of more natively quantum algorithms. Since it is not possible to implement a non-unitary gate deterministically, we resort to the implementation of probabilistic ITE (PITE) algorithms, which rely on a unitary quantum circuit to simulate a block encoding of the ITE operator—that is, they rely on successful ancillary measurements to evolve the system non-unitarily. Compared with previous PITE proposals, the suggested block encoding in this paper results in shorter circuits and is simpler to implement, requiring only a slight modification of the Pauli gadget primitive. This scheme was tested on the transverse Ising model and the fermionic Hubbard model and is demonstrated to converge to the GS of the system.

Quantum Science and Technology•Jun 4, 2024•13 citations

Accelerating quantum imaginary-time evolution with random measurements

Ioannis Kolotouros, David Joseph, Anand Kumar Narayanan

Quantum imaginary-time evolution (QITE) is a promising tool to prepare thermal or ground states of Hamiltonians, as convergence is guaranteed when the evolved state overlaps with the ground state. However, its implementation using a a hybrid quantum-classical approach, where the dynamics of the parameters of the quantum circuit are derived by McLachlan's variational principle, is impractical as the number of parameters m increases, since each step in the evolution takes Θ ( m 2 ) state preparations to calculate the quantum Fisher information matrix (QFIM). In this work, we accelerate QITE by rapid estimation of the QFIM, while conserving the convergence guarantees to the extent possible. To this end, we prove that if a parameterized state is rotated by a 2-design and measured in the computational basis, then the QFIM can be inferred from partial derivative cross correlations of the probability outcomes. One sample estimate costs only Θ ( m ) state preparations, leading to rapid QFIM estimation when a few samples suffice. The second family of estimators takes greater liberties and replace QFIMs with averaged classical Fisher information matrices (CFIMs). In an extreme special case optimized for rapid (over accurate) descent, just one CFIM sample is drawn. We justify the second estimator family by proving rapid descent. Guided by these results, we propose the algorithm, which we showcase and test in several molecular systems, with the goal of preparing ground states.

arXiv:2407.03123•Physical Review A•Jan 14, 2025•8 citations

A quantum double-bracket algorithm for imaginary-time evolution with exponentially shorter depth

Ioannis Kolotouros, Raul Garcia-Patron

Imaginary-time evolution (ITE) is a widely used technique for preparing the ground state of a target Hamiltonian. Building on the recently proposed framework of Double-Bracket quantum ITE (DB-QITE), we introduce a probabilistic variant (PDBQITE) that achieves an exponential reduction in circuit depth. Our algorithm requires only a single ancilla qubit and a quantum circuit that consists of one controlled real-time evolution and one mid-circuit measurement per iteration. The trade-off is an exponential decay of the total success probability with the number of iterations, for which we derive an analytical lower bound that is independent of system size. Our numerical simulations show that the per-step success probability remains close to unity, making it realistic to execute many iterations, thus providing a substantial improvement over prior constructions. We show that PDBQITE outperforms the near-term probabilistic algorithm PITE for ground-state preparation of molecular Hamiltonians, and that a hybrid QAOA-PDBQITE scheme achieves higher approximation ratios than QAOA at the same circuit depth on random regular graphs for the MaxCut problem.

quant-pharXiv:2609.37095•Sep 30, 2026•0 citations
Imaginary-time evolution (ITE) is a foundational method for ground state preparation on quantum computers. However, because ITE is non-unitary, existing implementations incur a sample complexity and/or classical cost that scales exponentially with the target imaginary time βββ. Moreover, the state itself converges slower than the energy, making accurate estimation of arbitrary ground state observables even more expensive. In this work, we improve upon standard ITE by introducing twirled imaginary-time evolution (TITE), which pairs ITE with real-time evolution applied for a random duration drawn from a carefully designed distribution. We prove that this randomization quadratically suppresses the trace distance to the ground state, and thus also the error of arbitrary observables, which allows roughly half of the imaginary time to be replaced with real-time evolution (β↦β/2β\mapsto β/2β↦β/2) while maintaining the same level of accuracy. Because real-time evolution is unitary and does not incur an overhead in sample complexity or classical computation, this affords a quadratic reduction in the cost of any black-box ITE implementation, including Trotterization and quantum imaginary-time evolution. We demonstrate the efficiency of our algorithm in noisy circuit-level simulations of a non-integrable Ising chain, showing substantial improvements over standard ITE.
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). Our analysis focuses on 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. Numerical evidence indicates 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. Finally, we outline concrete platform-specific implementations in which multi-copy registers and SWAP-mediated couplings are natural, illustrating how these hybrid analog-digital circuits can complement existing state-preparation methods in the near term.
We propose an imaginary time equivalent of the well-established Pauli gadget primitive for Trotter-decomposed real time evolution, using mid-circuit measurements on a single ancilla qubit. Imaginary time evolution (ITE) is widely used for obtaining the ground state of a system on classical hardware, computing thermal averages, and as a component of quantum algorithms that perform non-unitary evolution. Near-term implementations on quantum hardware rely on heuristics, compromising their accuracy. As a result, there is growing interest in the development of more natively quantum algorithms. Since it is not possible to implement a non-unitary gate deterministically, we resort to the implementation of probabilistic imaginary time evolution (PITE) algorithms, which rely on a unitary quantum circuit to simulate a block encoding of the ITE operator - that is, they rely on successful ancillary measurements to evolve the system non-unitarily. Compared with previous PITE proposals, the suggested block encoding in this paper results in shorter circuits and is simpler to implement, requiring only a slight modification of the Pauli gadget primitive. This scheme was tested on the transverse Ising model and the fermionic Hubbard model and is demonstrated to converge to the ground state of the system.
Imaginary time evolution is a powerful tool applied in quantum physics, while existing classical algorithms for simulating imaginary time evolution suffer high computational complexity as the quantum systems become larger and more complex. In this work, we propose a probabilistic algorithm for implementing imaginary time evolution based on non-unitary quantum circuit. We demonstrate the feasibility of this method by solving the ground state energy of several quantum many-body systems, including H2, LiH molecules and the quantum Ising chain. Moreover, we perform experiments on superconducting and trapped ion cloud platforms respectively to find the ground state energy of H2 and its most stable molecular structure. We also analyze the successful probability of the algorithm, which is a polynomial of the output error and introduce an approach to increase the success probability by rearranging the terms of Hamiltonian.
Abstract We propose an imaginary time equivalent of the well-established Pauli gadget primitive for Trotter-decomposed real time evolution, using mid-circuit measurements on a single ancilla qubit. Imaginary time evolution (ITE) is widely used for obtaining the ground state (GS) of a system on classical hardware, computing thermal averages, and as a component of quantum algorithms that perform non-unitary evolution. Near-term implementations on quantum hardware rely on heuristics, compromising their accuracy. As a result, there is growing interest in the development of more natively quantum algorithms. Since it is not possible to implement a non-unitary gate deterministically, we resort to the implementation of probabilistic ITE (PITE) algorithms, which rely on a unitary quantum circuit to simulate a block encoding of the ITE operator—that is, they rely on successful ancillary measurements to evolve the system non-unitarily. Compared with previous PITE proposals, the suggested block encoding in this paper results in shorter circuits and is simpler to implement, requiring only a slight modification of the Pauli gadget primitive. This scheme was tested on the transverse Ising model and the fermionic Hubbard model and is demonstrated to converge to the GS of the system.
Quantum imaginary-time evolution (QITE) is a promising tool to prepare thermal or ground states of Hamiltonians, as convergence is guaranteed when the evolved state overlaps with the ground state. However, its implementation using a a hybrid quantum-classical approach, where the dynamics of the parameters of the quantum circuit are derived by McLachlan's variational principle, is impractical as the number of parameters m increases, since each step in the evolution takes Θ ( m 2 ) state preparations to calculate the quantum Fisher information matrix (QFIM). In this work, we accelerate QITE by rapid estimation of the QFIM, while conserving the convergence guarantees to the extent possible. To this end, we prove that if a parameterized state is rotated by a 2-design and measured in the computational basis, then the QFIM can be inferred from partial derivative cross correlations of the probability outcomes. One sample estimate costs only Θ ( m ) state preparations, leading to rapid QFIM estimation when a few samples suffice. The second family of estimators takes greater liberties and replace QFIMs with averaged classical Fisher information matrices (CFIMs). In an extreme special case optimized for rapid (over accurate) descent, just one CFIM sample is drawn. We justify the second estimator family by proving rapid descent. Guided by these results, we propose the algorithm, which we showcase and test in several molecular systems, with the goal of preparing ground states.
Imaginary-time evolution (ITE) is a widely used technique for preparing the ground state of a target Hamiltonian. Building on the recently proposed framework of Double-Bracket quantum ITE (DB-QITE), we introduce a probabilistic variant (PDBQITE) that achieves an exponential reduction in circuit depth. Our algorithm requires only a single ancilla qubit and a quantum circuit that consists of one controlled real-time evolution and one mid-circuit measurement per iteration. The trade-off is an exponential decay of the total success probability with the number of iterations, for which we derive an analytical lower bound that is independent of system size. Our numerical simulations show that the per-step success probability remains close to unity, making it realistic to execute many iterations, thus providing a substantial improvement over prior constructions. We show that PDBQITE outperforms the near-term probabilistic algorithm PITE for ground-state preparation of molecular Hamiltonians, and that a hybrid QAOA-PDBQITE scheme achieves higher approximation ratios than QAOA at the same circuit depth on random regular graphs for the MaxCut problem.