Exponentially reduced circuit depths in Lindbladian simulation

• URL: http://arxiv.org/abs/2412.21062v1
• Date: Mon, 30 Dec 2024 16:31:25 GMT
• Title: Exponentially reduced circuit depths in Lindbladian simulation
• Authors: Wenjun Yu, Xiaogang Li, Qi Zhao, Xiao Yuan,
• Abstract summary: Quantum computers can efficiently simulate Lindbladian dynamics, enabling powerful applications in open system simulation, thermal and ground-state preparation, autonomous quantum error correction, dissipative engineering, and more. Existing methods face a critical trade-off: either relying on resource-intensive multi-qubit operations or employing deep quantum circuits to suppress simulation errors using experimentally friendly methods. We propose an efficient Lindbladian simulation framework that minimizes circuit depths while remaining experimentally accessible.
• Score: 11.176767117446696
• License:
• Abstract: Quantum computers can efficiently simulate Lindbladian dynamics, enabling powerful applications in open system simulation, thermal and ground-state preparation, autonomous quantum error correction, dissipative engineering, and more. Despite the abundance of well-established algorithms for closed-system dynamics, simulating open quantum systems on digital quantum computers remains challenging due to the intrinsic requirement for non-unitary operations. Existing methods face a critical trade-off: either relying on resource-intensive multi-qubit operations with experimentally challenging approaches or employing deep quantum circuits to suppress simulation errors using experimentally friendly methods. In this work, we challenge this perceived trade-off by proposing an efficient Lindbladian simulation framework that minimizes circuit depths while remaining experimentally accessible. Based on the incoherent linear combination of superoperators, our method achieves exponential reductions in circuit depth using at most two ancilla qubits and the straightforward Trotter decomposition of the process. Furthermore, our approach extends to simulate time-dependent Lindbladian dynamics, achieving logarithmic dependence on the inverse accuracy for the first time. Rigorous numerical simulations demonstrate clear advantages of our method over existing techniques. This work provides a practical and scalable solution for simulating open quantum systems on quantum devices.

Related papers

• Efficient quantum simulation of nonlinear interactions using SNAP and Rabi gates [0.7366405857677227]
  We present a deterministic simulation technique that efficiently models nonlinear bosonic dynamics. Our proposed simulation method facilitates high-fidelity modeling of phenomena that emerge from higher-order bosonic interactions.
  arXiv  Detail & Related papers  (2023-12-15T16:44:43Z)
• Efficient quantum algorithm to simulate open systems through a single environmental qubit [0.0]
  We present an efficient algorithm for simulating open quantum systems dynamics described by the Lindblad master equation on quantum computers. Under fixed accuracy conditions, our algorithm enables a reduction in the number of trotter steps compared to other approaches.
  arXiv  Detail & Related papers  (2023-11-16T16:45:30Z)
• Deep Quantum Circuit Simulations of Low-Energy Nuclear States [51.823503818486394]
  We present advances in high-performance numerical simulations of deep quantum circuits. circuits up to 21 qubits and more than 115,000,000 gates can be efficiently simulated.
  arXiv  Detail & Related papers  (2023-10-26T19:10:58Z)
• Overhead-constrained circuit knitting for variational quantum dynamics [0.0]
  We use circuit knitting to partition a large quantum system into smaller subsystems that can each be simulated on a separate device. We show that the same method can be used to reduce the circuit depth by cutting long-ranged gates.
  arXiv  Detail & Related papers  (2023-09-14T17:01:06Z)
• Quantum circuit debugging and sensitivity analysis via local inversions [62.997667081978825]
  We present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most. We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
  arXiv  Detail & Related papers  (2022-04-12T19:39:31Z)
• Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator [0.0]
  We show that a quantum simulator can be used to in-effect solve for the dynamics of a many-body system. We use a neutral-atom Fermi-Hubbard quantum simulator with $L_textexpsimeq290$ lattice sites to benchmark its performance. We derive a simple prediction of the behaviour of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems.
  arXiv  Detail & Related papers  (2021-05-13T16:03:11Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)
• Low-depth Hamiltonian Simulation by Adaptive Product Formula [3.050399782773013]
  Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. Here, we propose an adaptive approach to construct a low-depth time evolution circuit. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.
  arXiv  Detail & Related papers  (2020-11-10T18:00:42Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.