Optimal compression of quantum many-body time evolution operators into brickwall circuits

Tepaske, Maurits S. J.; Hahn, Dominik; Luitz, David J.

doi:10.21468/scipostphys.14.4.073

Cited by 16 publications

(1 citation statement)

References 56 publications

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“…A detailed numerical analysis of Trotter-Suzuki splitting methods [3] shows that they can approximate the time evolution with circuit depth scaling essentially linearly in simulated time. Recently, the authors of [4][5][6] have proposed and implemented the idea of optimizing variational circuit Ansätze inspired by Trotterized time evolution for the purpose of Hamiltonian simulation (using parametrized circuit gates). Here, we build upon the same idea and adapt a tensor network perspective as in [6], but take a step further by regarding the circuit gates as general unitary matrices, analogous to [7,8].…”

Section: Introductionmentioning

confidence: 99%

Riemannian quantum circuit optimization for Hamiltonian simulation

Kotil,

Banerjee,

Huang

et al. 2024

J. Phys. A: Math. Theor.

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Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful approximation can lead to relatively deep circuits. Here we start from the insight that for translation invariant systems, the gates in such circuit topologies can be further optimized on classical computers to decrease the circuit depth and/or increase the accuracy. We employ tensor network techniques and devise a method based on the Riemannian trust-region algorithm on the unitary matrix manifold for this purpose. For the Ising and Heisenberg models on a one-dimensional lattice, we achieve orders of magnitude accuracy improvements compared to fourth-order splitting methods. The optimized circuits could also be of practical use for the time-evolving block decimation (TEBD) algorithm.

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Section: Introductionmentioning

confidence: 99%

Riemannian quantum circuit optimization for Hamiltonian simulation

Kotil,

Banerjee,

Huang

et al. 2024

J. Phys. A: Math. Theor.

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Approximate encoding of quantum states using shallow circuits

Ben-Dov,

Shnaiderov,

Makmal

et al. 2024

npj Quantum Inf

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Quantum algorithms and simulations often require the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of required gates grows exponentially with the number of qubits, becoming unfeasible on near-term quantum devices. Here, we aim at creating an approximate encoding of the target state using a limited number of gates. As a first step, we consider a quantum state that is efficiently represented classically, such as a one-dimensional matrix product state. Using tensor network techniques, we develop and implement an efficient optimization algorithm that approaches the optimal implementation, requiring a polynomial number of iterations. We, next, consider the implementation of the proposed optimization algorithm directly on a quantum computer and overcome inherent barren plateaus by employing a local cost function. Our work offers a universal method to prepare target states using local gates and represents a significant improvement over known strategies.

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Dynamical chaos in the integrable Toda chain induced by time discretization

Danieli,

Yuzbashyan,

Altshuler

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various symplectic integrators parametrized by the time step τ and measure the Lyapunov time TΛ (inverse of the largest Lyapunov exponent Λ). A key observation is that TΛ is finite whenever τ is finite but diverges when τ→0. We compare the Toda chain results with the nonintegrable Fermi–Pasta–Ulam–Tsingou chain dynamics. In addition, we observe a breakdown of the simulations at times TB≫TΛ due to certain positions and momenta becoming extremely large (“Not a Number”). This phenomenon originates from the periodic driving introduced by symplectic integrators and we also identify the concrete mechanism of the breakdown in the case of the Toda chain.

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Optimal compression of quantum many-body time evolution operators into brickwall circuits

Cited by 16 publications

References 56 publications

Riemannian quantum circuit optimization for Hamiltonian simulation

Riemannian quantum circuit optimization for Hamiltonian simulation

Approximate encoding of quantum states using shallow circuits

Dynamical chaos in the integrable Toda chain induced by time discretization

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