Clifford Circuits Augmented Grassmann Matrix Product States

• URL: http://arxiv.org/abs/2510.04164v1
• Date: Sun, 05 Oct 2025 11:42:28 GMT
• Title: Clifford Circuits Augmented Grassmann Matrix Product States
• Authors: Atis Yosprakob, Wei-Lin Tu, Tsuyoshi Okubo, Kouichi Okunishi, Donghoon Kim,
• Abstract summary: Recent advances in combining Clifford circuits with tensor network (TN) states have shown that classically simulable disentanglers can significantly reduce entanglement.<n>We develop a variational TN framework based on Grassmann tensor networks, which encode fermionic statistics while preserving locality.<n>Our results show that Clifford disentangling removes the classically simulable component of entanglement, leading to a reduced bond dimension and improved accuracy in ground-state energy estimates.
• Score: 2.7892067588273517
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent advances in combining Clifford circuits with tensor network (TN) states have shown that classically simulable disentanglers can significantly reduce entanglement, mitigating the bond-dimension bottleneck in TN simulations. In this work, we develop a variational TN framework based on Grassmann tensor networks, which natively encode fermionic statistics while preserving locality. By incorporating locally defined Clifford circuits within the fermionic formalism, we simulate benchmark models including the tight-binding and $t$-$V$ models. Our results show that Clifford disentangling removes the classically simulable component of entanglement, leading to a reduced bond dimension and improved accuracy in ground-state energy estimates. Interestingly, imposing the natural Grassmann-evenness constraint on the Clifford circuits significantly reduces the number of disentangling gates, from 720 to just 32, yielding a far more efficient implementation. These findings highlight the potential of Clifford-augmented Grassmann TNs as a scalable and accurate tool for studying strongly correlated fermionic systems, particularly in higher dimensions.

Related papers

• Hyperparameter Trajectory Inference with Conditional Lagrangian Optimal Transport [51.56484100374058]
  Post-deployment, user preferences can evolve, making initial settings undesirable.<n>We learn, from observed data, how a NN's conditional output distribution changes with its hyper parameters.<n>We construct a surrogate model that approximates the NN at unobserved hyper parameters.
  arXiv  Detail & Related papers  (2026-03-02T11:55:02Z)
• Limits of Clifford Disentangling in Tensor Network States [0.27998963147546146]
  We study the disentangling power of Clifford transformations acting on tensor networks.<n>We prove that no Clifford operation can universally disentangle even a single qubit from an arbitrary non-Clifford rotation.
  arXiv  Detail & Related papers  (2026-02-17T19:01:26Z)
• FALCON: Few-step Accurate Likelihoods for Continuous Flows [78.37361800856583]
  We propose Few-step Accurate Likelihoods for Continuous Flows (FALCON), which allows for few-step sampling with a likelihood accurate enough for importance sampling applications.<n>We show FALCON outperforms state-of-the-art normalizing flow models for molecular Boltzmann sampling and is two orders of magnitude faster than the equivalently performing CNF model.
  arXiv  Detail & Related papers  (2025-12-10T18:47:25Z)
• Disentangling Kitaev Quantum Spin Liquid [3.9186557599917293]
  We investigate the Kitaev honeycomb model employing the recently developed Clifford Circuits Augmented Matrix Product States ( CAMPS) method.<n>We demonstrate that the very different gapless quantum spin liquid (QSL) phase can also be significantly disentangled with Clifford circuits.<n> CAMPS simulations reveal that approximately two-thirds of the entanglement entropy in the isotropic point arises from Clifford-circuit contributions.
  arXiv  Detail & Related papers  (2025-11-25T12:42:06Z)
• Symmetry-accelerated classical simulation of Clifford-dominated circuits [0.0]
  We exploit symmetries in the computation of the stabilizer extent, proving that for real, diagonal, and real-diagonal unitaries, the optimization can be restricted to the corresponding subgroups of the Clifford group without loss of optimality.<n>This strong symmetry reduction'' drastically reduces computational cost, enabling optimal decompositions of unitaries on up to seven qubits using a standard laptop.
  arXiv  Detail & Related papers  (2025-10-21T18:01:14Z)
• When Clifford benchmarks are sufficient; estimating application performance with scalable proxy circuits [0.0]
  We show that for a broad class of error models these concerns are unwarranted.<n>We show that for error models that admit noise tailoring by Pauli twirling, the diamond norm and fidelity of any generic circuit is well approximated by the fidelities of proxy circuits composed only of Clifford gates.
  arXiv  Detail & Related papers  (2025-03-07T21:18:59Z)
• Disentangling unitary dynamics with classically simulable quantum circuits [0.0]
  We show that states obtained from deep random Clifford circuits doped with non-Clifford phase gates can be disentangled completely.<n>This implies that Pauli expectation values of such states can be efficiently simulated classically.<n>We show that this result implies a novel representation of approximate state designs that can also facilitate their efficient generation.
  arXiv  Detail & Related papers  (2024-10-11T17:18:26Z)
• Clifford Circuits Augmented Time-Dependent Variational Principle [0.49157446832511503]
  Recently proposed Clifford Circuits Augmented Matrix Product States (CA-MPS) seamlessly augments Density Matrix Renormalization Group with Clifford circuits. We generalize CA-MPS to the framework of Time-Dependent Variational Principle (TDVP) for time evolution simulations. We show that the Clifford circuits augmented TDVP method can reduce the entanglement entropy in the time evolution process.
  arXiv  Detail & Related papers  (2024-07-03T15:34:15Z)
• Extending Classically Simulatable Bounds of Clifford Circuits with Nonstabilizer States via Framed Wigner Functions [3.9482012852779085]
  Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability.<n>We propose a novel classical simulation method for qubit Clifford circuits based on the framed Wigner function.
  arXiv  Detail & Related papers  (2023-07-31T14:02:33Z)
• Iterative Qubit Coupled Cluster using only Clifford circuits [36.136619420474766]
  An ideal state preparation protocol can be characterized by being easily generated classically. We propose a method that meets these requirements by introducing a variant of the iterative qubit coupled cluster (iQCC) We demonstrate the algorithm's correctness in ground-state simulations and extend our study to complex systems like the titanium-based compound Ti(C5H5)(CH3)3 with a (20, 20) active space.
  arXiv  Detail & Related papers  (2022-11-18T20:31:10Z)
• Clifford Neural Layers for PDE Modeling [61.07764203014727]
  Partial differential equations (PDEs) see widespread use in sciences and engineering to describe simulation of physical processes as scalar and vector fields interacting and coevolving over time. Current methods do not explicitly take into account the relationship between different fields and their internal components, which are often correlated. This paper presents the first usage of such multivector representations together with Clifford convolutions and Clifford Fourier transforms in the context of deep learning. The resulting Clifford neural layers are universally applicable and will find direct use in the areas of fluid dynamics, weather forecasting, and the modeling of physical systems in general.
  arXiv  Detail & Related papers  (2022-09-08T17:35:30Z)
• Simulating quench dynamics on a digital quantum computer with data-driven error mitigation [62.997667081978825]
  We present one of the first implementations of several Clifford data regression based methods which are used to mitigate the effect of noise in real quantum data. We find in general Clifford data regression based techniques are advantageous in comparison with zero-noise extrapolation. This is the largest systems investigated so far in a study of this type.
  arXiv  Detail & Related papers  (2021-03-23T16:56:14Z)
• A Fully Tensorized Recurrent Neural Network [48.50376453324581]
  We introduce a "fully tensorized" RNN architecture which jointly encodes the separate weight matrices within each recurrent cell. This approach reduces model size by several orders of magnitude, while still maintaining similar or better performance compared to standard RNNs.
  arXiv  Detail & Related papers  (2020-10-08T18:24:12Z)
• Optimizing Mode Connectivity via Neuron Alignment [84.26606622400423]
  Empirically, the local minima of loss functions can be connected by a learned curve in model space along which the loss remains nearly constant. We propose a more general framework to investigate effect of symmetry on landscape connectivity by accounting for the weight permutations of networks being connected.
  arXiv  Detail & Related papers  (2020-09-05T02:25:23Z)
• Rewiring the Transformer with Depth-Wise LSTMs [55.50278212605607]
  We present a Transformer with depth-wise LSTMs connecting cascading Transformer layers and sub-layers. Experiments with the 6-layer Transformer show significant BLEU improvements in both WMT 14 English-German / French tasks and the OPUS-100 many-to-many multilingual NMT task.
  arXiv  Detail & Related papers  (2020-07-13T09:19:34Z)

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.