Matrix Product Evolution: A Method for Simulating Quantum Circuits Using Tensor Networks

• URL: http://arxiv.org/abs/2608.03472v1
• Date: Tue, 04 Aug 2026 11:07:41 GMT
• Title: Matrix Product Evolution: A Method for Simulating Quantum Circuits Using Tensor Networks
• Abstract summary: We introduce a tensor-train representation of quantum circuits constructed along the circuit depth rather than along the qubit index.<n>Within this formulation, the simulation of a quantum circuit is modeled as the contraction of multiple MPE tensors.<n>We investigate the numerical behavior of this MPE-based contraction framework through simulations of random quantum circuits and the time evolution of a quantum many-body state.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Classical simulation of quantum circuits is an essential tool in quantum information science, but its applicability is constrained by the exponential growth of the Hilbert space and the entanglement structure of quantum states. In this work, we introduce Matrix Product Evolution (MPE), a tensor-train representation of quantum circuits constructed along the circuit depth rather than along the qubit index. Within this formulation, the simulation of a quantum circuit is modeled as the contraction of multiple MPE tensors. We develop an efficient contraction strategy based on a zip-up procedure to carry out this contraction in practice. We investigate the numerical behavior of this MPE-based contraction framework through simulations of random quantum circuits and the time evolution of a quantum many-body state. Our results characterize the growth of temporal bond dimensions, clarify how post-selection modifies the contraction cost and approximation accuracy, and identify regimes in which depth-oriented tensor-network contractions provide a useful complement to standard MPS-based simulation approaches.

Related papers

• Quantum-inspired classical simulation through randomized time evolution [0.0]
  We build on recently introduced randomized quantum algorithms for time evolution (TE-PAI)<n>We adapt them to the classical simulation context with the purpose of enabling massive parallelisation.<n>We numerically observe that MPS TE-PAI is substantially more robust against severe bond-dimension truncation than product formulas.
  arXiv  Detail & Related papers  (2026-04-14T15:09:29Z)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [50.95799256262098]
  Variational quantum circuits (VQCs) hold promise for quantum machine learning but face challenges in expressivity, trainability, and noise resilience.<n>We propose VQC-MLPNet, a hybrid architecture where a VQC generates the first-layer weights of a classical multilayer perceptron during training, while inference is performed entirely classically.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Fully optimised variational simulation of a dynamical quantum phase transition on a trapped-ion quantum computer [0.039583175274885335]
  We time-evolve a translationally invariant quantum state on the Quantinuum H1-1 trapped-ion quantum processor.<n>This physics requires a delicate cancellation of phases in the many-body wavefunction and presents a tough challenge for current quantum devices.<n>Our results demonstrate the feasibility of variational quantum time-evolution and reveal a hitherto hidden simplicity of the evolution of the transverse-field Ising model.
  arXiv  Detail & Related papers  (2025-02-10T19:01:28Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [62.46800898243033]
  Recent progress in quantum learning theory prompts a question: can linear properties of a large-qubit circuit be efficiently learned from measurement data generated by varying classical inputs?<n>We prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.<n>We propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• Decomposition of Matrix Product States into Shallow Quantum Circuits [62.5210028594015]
  tensor network (TN) algorithms can be mapped to parametrized quantum circuits (PQCs) We propose a new protocol for approximating TN states using realistic quantum circuits. Our results reveal one particular protocol, involving sequential growth and optimization of the quantum circuit, to outperform all other methods.
  arXiv  Detail & Related papers  (2022-09-01T17:08:41Z)
• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer [0.11744028458220425]
  We simulate the groundstate of the quantum Ising model through its quantum critical point on a superconducting quantum device. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states.
  arXiv  Detail & Related papers  (2022-05-25T18:05:53Z)
• Low-rank tensor decompositions of quantum circuits [14.531461873576449]
  We show how MPOs can be used to express certain quantum states, quantum gates, and entire quantum circuits as low-rank tensors. This enables the analysis and simulation of complex quantum circuits on classical computers.
  arXiv  Detail & Related papers  (2022-05-19T22:09:15Z)
• Reducing circuit depth in adaptive variational quantum algorithms via effective Hamiltonian theories [8.24048506727803]
  We introduce a new transformation in the form of a product of a linear combination of excitation operators to construct the effective Hamiltonian with finite terms. The effective Hamiltonian defined with this new transformation is incorporated into the adaptive variational quantum algorithms to maintain constant-size quantum circuits.
  arXiv  Detail & Related papers  (2022-01-23T09:38:46Z)
• 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)
• Fast Swapping in a Quantum Multiplier Modelled as a Queuing Network [64.1951227380212]
  We propose that quantum circuits can be modeled as queuing networks. Our method is scalable and has the potential speed and precision necessary for large scale quantum circuit compilation.
  arXiv  Detail & Related papers  (2021-06-26T10:55:52Z)
• Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale [57.84751206630535]
  We present a modernized version of the Quantum Virtual Machine (TNQVM) which serves as a quantum circuit simulation backend in the e-scale ACCelerator (XACC) framework. The new version is based on the general purpose, scalable network processing library, ExaTN, and provides multiple quantum circuit simulators. By combining the portable XACC quantum processors and the scalable ExaTN backend we introduce an end-to-end virtual development environment which can scale from laptops to future exascale platforms.
  arXiv  Detail & Related papers  (2021-04-21T13:26:42Z)

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.