Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series

• URL: http://arxiv.org/abs/2605.21597v1
• Date: Wed, 20 May 2026 18:00:49 GMT
• Title: Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series
• Abstract summary: We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians.<n>The MPO construction can be made accurate up to arbitrary order in the time step, it can be applied to both finite and infinite systems, and it can handle long-range interactions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians. The MPO construction can be made accurate up to arbitrary order in the time step, it can be applied to both finite and infinite systems, and it can handle long-range interactions. The resulting MPO can be combined with state-of-the-art time evolution algorithms based on matrix product states, allowing for drastic improvements in simulating evolution under time-dependent Hamiltonians. Our MPO construction can also be used for the optimization of quantum circuits in the context of quantum simulation of time-dependent Hamiltonians.

Related papers

• Time evolution of controlled many-body quantum systems with matrix product operators [0.0]
  We present a method for describing the time evolution of many-body controlled quantum systems using matrix product operators (MPOs)<n>We apply this technique to quantum optimal control, specifically for a gate problem synthesis.
  arXiv  Detail & Related papers  (2025-09-08T21:13:27Z)
• A unifying framework for quantum simulation algorithms for time-dependent Hamiltonian dynamics [27.781524610367782]
  We show how Sambe-Howland's clock can serve as a unifying framework for simulating time-dependent Hamiltonian dynamics. We also illustrate how this framework, combined with time-independent methods, can facilitate the development of efficient algorithms for simulating time-dependent dynamics.
  arXiv  Detail & Related papers  (2024-11-05T15:26:44Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators [0.7799708033005247]
  Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics.<n>The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle.<n>We show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude.
  arXiv  Detail & Related papers  (2024-03-20T18:01:27Z)
• Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations [31.223649540164928]
  We propose an alternative formalism that turns any non-autonomous unitary dynamical system into an autonomous unitary system. This makes the simulation with time-dependent Hamiltonians not much more difficult than that of time-independent Hamiltonians. We show how our new quantum protocol for time-dependent Hamiltonians can be performed in a resource-efficient way and without measurements.
  arXiv  Detail & Related papers  (2023-12-05T14:59:23Z)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• Temporal Entanglement in Chaotic Quantum Circuits [62.997667081978825]
  The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. We show that temporal entanglement always follows a volume law in time. This unexpected structure in the temporal entanglement spectrum might be the key to an efficient computational implementation of the space evolution.
  arXiv  Detail & Related papers  (2023-02-16T18:56:05Z)
• Optimal/Nearly-optimal simulation of multi-periodic time-dependent Hamiltonians [0.0]
  We establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time-periodicity. Overcoming the difficulty of time-dependency, our protocol can simulate the dynamics under multi-periodic time-dependent Hamiltonians.
  arXiv  Detail & Related papers  (2023-01-16T01:53:09Z)
• Time Dependent Hamiltonian Simulation Using Discrete Clock Constructions [42.3779227963298]
  We provide a framework for encoding time dependent dynamics as time independent systems. First, we create a time dependent simulation algorithm based on performing qubitization on the augmented clock system. Second, we define a natural generalization of multiproduct formulas for time-ordered exponentials.
  arXiv  Detail & Related papers  (2022-03-21T21:29:22Z)
• 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)
• 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)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)

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.