Abstract The imaginary-time evolution method is a well-known approach used for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of deep circuit depth and difficulty in the implementation on noisy intermediate-scale quantum (NISQ) devices. In this study, a nonlocal approximation is developed to tackle this difficulty. We found that by removing the locality condition or local approximation (LA), which was imposed when the imaginary-time evolution operator is converted to a unitary operator, the quantum circuit depth is significantly reduced. We propose two-step approximation methods based on a nonlocality condition: extended LA (eLA) and nonlocal approximation (NLA). To confirm the validity of eLA and NLA, we apply them to the max-cut problem of an unweighted 3-regular graph and a weighted fully connected graph; we comparatively evaluate the performances of LA, eLA, and NLA. The eLA and NLA methods require far fewer circuit depths than LA to maintain the same level of computational accuracy. Further, we developed a “compression” method of the quantum circuit for the imaginary-time steps to further reduce the circuit depth in the QITE method. The eLA, NLA, and compression methods introduced in this study allow us to reduce the circuit depth and the accumulation of error caused by the gate operation significantly and pave the way for implementing the QITE method on NISQ devices.
Abstract The imaginary-time evolution method is a well-known approach used for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of deep circuit depth and difficulty in the implementation on noisy intermediate-scale quantum (NISQ) devices. In this study, a nonlocal approximation is developed to tackle this difficulty. We found that by removing the locality condition or local approximation (LA), which was imposed when the imaginary-time evolution operator is converted to a unitary operator, the quantum circuit depth is significantly reduced. We propose two-step approximation methods based on a nonlocality condition: extended LA (eLA) and nonlocal approximation (NLA). To confirm the validity of eLA and NLA, we apply them to the max-cut problem of an unweighted 3-regular graph and a weighted fully connected graph; we comparatively evaluate the performances of LA, eLA, and NLA. The eLA and NLA methods require far fewer circuit depths than LA to maintain the same level of computational accuracy. Further, we developed a “compression” method of the quantum circuit for the imaginary-time steps to further reduce the circuit depth in the QITE method. The eLA, NLA, and compression methods introduced in this study allow us to reduce the circuit depth and the accumulation of error caused by the gate operation significantly and pave the way for implementing the QITE method on NISQ devices.
Quantum imaginary time evolution (QITE) is one of the promising candidates for finding the eigenvalues and eigenstates of a Hamiltonian on a quantum computer. However, the original proposal suffers from large circuit depth and measurements due to the size of the Pauli operator pool and Trotterization. To alleviate the requirement for deep circuits, we propose a time-dependent drifting scheme inspired by the qDRIFT algorithm [Campbell, E. Phys. Rev. Lett. 2019, 123, 070503]. We show that this drifting scheme removes the depth dependency on the size of the operator pool and converges inversely with respect to the number of steps. We further propose a deterministic algorithm that selects the dominant Pauli term to reduce the fluctuation for the ground state preparation. We also introduce an efficient measurement reduction scheme across Trotter steps that removes its cost dependence on the number of iterations. We analyze the main source of error for our scheme both theoretically and numerically. We numerically test the validity of depth reduction, convergence performance of our algorithms, and the faithfulness of the approximation for our measurement reduction scheme on several benchmark molecules. In particular, the results on the LiH molecule give circuit depths comparable to that of the advanced adaptive variational quantum eigensolver (VQE) methods while requiring much fewer measurements.
Quantum imaginary-time evolution (QITE) provides a systematic route to ground-state preparation, but its cost grows rapidly with the locality D of the unitary approximation, for which the local Pauli basis scales as 4D. We introduce Sparse-QITE, a regularized formulation that promotes compact generators, reducing the number of quantum operations and yielding circuits with fewer gates and lower depth. We derive rigorous bounds on the sparsification error and benchmark the method in one-dimensional transverse-field Ising and antiferromagnetic Heisenberg models. Sparse-QITE exhibits a controllable sparsity--accuracy trade-off while retaining strong compression even in the high-accuracy regime. In scalability experiments with respect to D, the active support grows much more slowly than in standard QITE and, in several regimes, approximately saturates over the domain sizes studied. After circuit construction and transpilation, some of the largest-domain cases require only about 1% of the standard-QITE gate count while maintaining high accuracy. We further introduce adaptive and active-discovery variants: the former selects the regularization strength dynamically during the evolution, while the latter reduces the number of Pauli expectation values that need to be evaluated and, consequently, the measurement requirements. These results establish sparsity-promoting regularization as a route toward more resource-efficient QITE. More broadly, these results suggest that sparsity-promoting regularization may also benefit variational quantum algorithms.
We develop a resource-efficient step-merged quantum imaginary time evolution approach (smQITE) to solve for the ground state of a Hamiltonian on quantum computers. This heuristic method features a fixed shallow quantum circuit depth along the state evolution path. We use this algorithm to determine the binding energy curves of a set of molecules, including H 2, H 4, H 6, LiH, HF, H 2 O, and BeH 2, and find highly accurate results. The required quantum resources of smQITE calculations can be further reduced by adopting the circuit form of the variational quantum eigensolver (VQE) technique, such as the unitary coupled cluster ansatz. We demonstrate that smQITE achieves a similar computational accuracy as VQE at the same fixed-circuit ansatz, without requiring a generally complicated high-dimensional nonconvex optimization. Finally, smQITE calculations are carried out on Rigetti quantum processing units, demonstrating that the approach is readily applicable on current noisy intermediate-scale quantum devices.
Dynamic quantum circuits combine mid-circuit measurement with classical feed-forward, enabling circuit constructions with reduced entangling-gate depth. Here, we investigate their use in Quantum Imaginary Time Evolution (QITE), where circuit depth and parameter growth limit practical implementations of ground-state preparation. For dense classical optimization Hamiltonians, we introduce a reduced-parameter QITE ansatz that restricts entanglement generation via a small set of control qubits, enabling each QITE layer to be implemented with constant two-qubit gate depth using fan-out-based dynamic circuits. In noiseless simulations of exact cover and set partitioning instances, the reduced ansatz yields a higher success probability than standard QITE approaches. We implement unitary, dynamic fan-out, and semi-classical adaptive variants on IBM superconducting hardware. The semi-classical variant performs favorably to the unitary implementation, while the fully dynamic construction exposes the trade-offs between entangling-depth reduction and measurement and feed-forward overhead associated to dynamic circuit implementations. Using a fidelity threshold of 0.5 relative to the noiseless QITE ansatz, we show that dynamic fan-out based QITE would outperform unitary implementations on current devices when the measurement and two-qubit gate errors are reduced by 65% and the feedback latency is halved.
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.
Efficient ground state search is fundamental to advancing combinatorial optimization problems and quantum chemistry. While the Variational Imaginary Time Evolution (VITE) method offers a useful alternative to Variational Quantum Eigensolver (VQE), and Quantum Approximate Optimization Algorithm (QAOA), its implementation on Noisy Intermediate-Scale Quantum (NISQ) devices is severely limited by the gate counts and depth of manually designed ansatz. Here, we present an automated framework for VITE circuit design using Double Deep-Q Networks (DDQN). Our approach treats circuit construction as a multi-objective optimization problem, simultaneously minimizing energy expectation values and optimizing circuit complexity. By introducing adoptive thresholds, we demonstrate significant hardware overhead reductions. In Max-Cut problems, our agent autonomously discovered circuits with approximately 37\% fewer gates and 43\% less depth than standard hardware-efficient ansatz on average. For molecular hydrogen (H2), the DDQN also achieved the Full-CI limit, with maintaining a significantly shallower circuit. These results suggest that deep reinforcement learning can be helpful to find non-intuitive, optimal circuit structures, providing a pathway toward efficient, hardware-aware quantum algorithm design.