Trotter error mitigation by error profiling with shallow quantum circuit

• URL: http://arxiv.org/abs/2503.09710v1
• Date: Wed, 12 Mar 2025 18:02:44 GMT
• Title: Trotter error mitigation by error profiling with shallow quantum circuit
• Authors: Sangjin Lee, Youngseok Kim, Seung-Woo Lee,
• Abstract summary: We propose a resource-efficient scheme to reduce the algorithmic Trotter error with relatively shallow circuit depth.<n>Our approach offers an efficient way of quantum simulation on near-term quantum processors with shallow circuits.
• Score: 5.281011822909396
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Understanding the dynamics of quantum systems is crucial in many areas of physics, but simulating many-body systems presents significant challenges due to the large Hilbert space to navigate and the exponential growth of computational overhead. Quantum computers offer a promising platform to overcome these challenges, particularly for simulating the time evolution with Hamiltonians. Trotterization is a widely used approach among available algorithms in this regard, and well suited for near-term quantum devices. However, it introduces algorithmic Trotter errors due to the non-commutativity of Hamiltonian components. Several techniques such as multi-product formulas have been developed to mitigate Trotter errors, but often require deep quantum circuits, which can introduce additional physical errors. In this work, we propose a resource-efficient scheme to reduce the algorithmic Trotter error with relatively shallow circuit depth. We develop a profiling method by introducing an auxiliary parameter to estimate the error effects in expectation values, enabling significant error suppression with a fixed number of Trotter steps. Our approach offers an efficient way of quantum simulation on near-term quantum processors with shallow circuits.

Related papers

• Exponentially Decaying Quantum Simulation Error with Noisy Devices [9.189340715455696]
  This work systematically characterizes the robustness of Trotter simulation errors in noisy quantum devices. We derive the optimal number of Trotter steps and the noise requirement to guarantee total simulation precision.
  arXiv  Detail & Related papers  (2025-04-14T14:10:24Z)
• Data-Efficient Error Mitigation for Physical and Algorithmic Errors in a Hamiltonian Simulation [0.17999333451993949]
  We propose a data-efficient 1D extrapolation method to mitigate physical and algorithmic errors of Trotterized quantum circuits.<n>We numerically demonstrate our proposed methods and confirm that our proposed extrapolation method suppresses both statistical and systematic errors more than the previous extrapolation method.
  arXiv  Detail & Related papers  (2025-03-07T00:05:52Z)
• Efficient estimation of trainability for variational quantum circuits [43.028111013960206]
  We find an efficient method to compute the cost function and its variance for a wide class of variational quantum circuits. This method can be used to certify trainability for variational quantum circuits and explore design strategies that can overcome the barren plateau problem.
  arXiv  Detail & Related papers  (2023-02-09T14:05:18Z)
• Trotter Errors and the Emergence of Chaos in Quantum Simulation [0.0]
  We run quantum simulations on a small, highly accurate quantum processor. We show how one can optimize simulation accuracy by balancing algorithmic (Trotter) errors against native errors specific to the quantum hardware at hand.
  arXiv  Detail & Related papers  (2022-12-07T18:39:33Z)
• Making Trotterization adaptive and energy-self-correcting for NISQ devices and beyond [0.0]
  Simulation of continuous time evolution requires time discretization on both classical and quantum computers. We introduce a quantum algorithm to solve this problem, providing a controlled solution of the quantum many-body dynamics of local observables. Our algorithm can be potentially useful on a more general level whenever time discretization is involved concerning, for instance, also numerical approaches based on time-evolving block decimation methods.
  arXiv  Detail & Related papers  (2022-09-26T12:54:32Z)
• 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)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Long-Time Error-Mitigating Simulation of Open Quantum Systems on Near Term Quantum Computers [38.860468003121404]
  We study an open quantum system simulation on quantum hardware, which demonstrates robustness to hardware errors even with deep circuits containing up to two thousand entangling gates. We simulate two systems of electrons coupled to an infinite thermal bath: 1) a system of dissipative free electrons in a driving electric field; and 2) the thermalization of two interacting electrons in a single orbital in a magnetic field -- the Hubbard atom. Our results demonstrate that algorithms for simulating open quantum systems are able to far outperform similarly complex non-dissipative algorithms on noisy hardware.
  arXiv  Detail & Related papers  (2021-08-02T21:36:37Z)
• First-Order Trotter Error from a Second-Order Perspective [0.0]
  Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The approximation error of these algorithms is often poorly understood, even in the most basic cases, which are particularly relevant for experiments. Recent studies have reported anomalously low approximation error with unexpected scaling in such cases, which they attribute to quantum interference between the errors from different steps of the algorithm. Our method generalizes state-of-the-art error bounds without the technical caveats of prior studies, and elucidates how each part of the total error arises from the underlying quantum circuit.
  arXiv  Detail & Related papers  (2021-07-16T17:53:44Z)
• 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)
• Boundaries of quantum supremacy via random circuit sampling [69.16452769334367]
  Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling. We examine the constraints of the observed quantum runtime advantage in a larger number of qubits and gates.
  arXiv  Detail & Related papers  (2020-05-05T20:11:53Z)
• Term Grouping and Travelling Salesperson for Digital Quantum Simulation [6.945601123742983]
  Digital simulation of quantum dynamics by evaluating the time evolution of a Hamiltonian is the initially proposed application of quantum computing. The large number of quantum gates required for emulating the complete second quantization form of the Hamiltonian makes such an approach unsuitable for near-term devices. We propose a new term ordering strategy, max-commute-tsp, that simultaneously mitigates both algorithmic and physical errors.
  arXiv  Detail & Related papers  (2020-01-16T18:33:24Z)

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.