Quon Classical Simulation: Unifying Cliffords, Matchgates and Entanglement

• URL: http://arxiv.org/abs/2505.07804v2
• Date: Fri, 08 Aug 2025 16:08:20 GMT
• Title: Quon Classical Simulation: Unifying Cliffords, Matchgates and Entanglement
• Authors: Zixuan Feng, Zhengwei Liu, Fan Lu, Ningfeng Wang,
• Abstract summary: We establish the Quon Classical Simulation (QCS) for hybrid Clifford-Matchgate circuits.<n>This framework is built upon the Quon language, a 2+1D topological quantum field theory with space-time boundary and defects.
• Score: 1.1584392437481228
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new framework of topological complexity to study the computational complexity of quantum circuits and tensor networks. Within this framework, we establish the Quon Classical Simulation (QCS) for hybrid Clifford-Matchgate circuits, which is efficient for both Clifford circuits and Matchgate circuits, therefore answering a long standing open question on unifying efficient classical simulations. This framework is built upon the Quon language, a 2+1D topological quantum field theory with space-time boundary and defects. Its exponential computation complexity is captured by Magic holes, a topological feature capturing the global long-range entanglement. Both Clifford circuits and Matchgate circuits are free of Magic holes. Efficient classical simulations of Cliffords and Matchgates are implemented by two parallel operations, generalized surgery theory of 3-manifolds and Yang-Baxter relations on the 2D boundary respectively, with additional binary arithmetic properties.

Related papers

• 2D Quon Language: Unifying Framework for Cliffords, Matchgates, and Beyond [4.886638121226719]
  We make progress toward the unified understanding of the Clifford and matchgate.<n>We introduce the 2D Quon language, which combines Majorana worldlines with their underlying spacetime topology.<n>We discuss a range of applications of our approach, from recovering well-known results such as the Kramers-Wannier duality.
  arXiv  Detail & Related papers  (2025-05-09T18:00:00Z)
• Classical simulation of parity-preserving quantum circuits [0.0]
  We present a classical simulation method for fermionic quantum systems without loss of generality.<n>We map such circuits to a fermionic tensor network and introduce a novel decomposition of non-Matchgate gates.<n>Our algorithm significantly lowers resource requirements for simulating parity-preserving circuits while retaining high accuracy.
  arXiv  Detail & Related papers  (2025-04-27T17:42:39Z)
• Clifford and Non-Clifford Splitting in Quantum Circuits: Applications and ZX-Calculus Detection Procedure [49.1574468325115]
  We propose and analyze use cases that come from quantum circuits that can be written as product between a Clifford and a Non-Clifford unitary.<n>We make use of ZX-Calculus and its assets to detect a limiting border of these circuits that would allow for a separation between a Clifford section and a Non-Clifford section.
  arXiv  Detail & Related papers  (2025-04-22T16:10:34Z)
• Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states [0.6580655899524989]
  One approach to classical simulation is to represent the output of a quantum circuit as a Clifford-augmented Matrix Product State ( CAMPS)<n>We develop an optimization-free disentangling algorithm for Clifford circuits either doped with multi-qubit gates of the form $alpha I+beta P$.<n>This work establishes a versatile framework for understanding classical simulatability of Clifford+$T$ circuits and explores the interplay between quantum entanglement and quantum magic in quantum systems.
  arXiv  Detail & Related papers  (2024-12-23T01:26:40Z)
• Efficient quantum-enhanced classical simulation for patches of quantum landscapes [0.0]
  We show that it is always possible to generate a classical surrogate of a sub-region of an expectation landscape produced by a parameterized quantum circuit.<n>We provide a quantum-enhanced classical algorithm which, after simple measurements on a quantum device, allows one to classically simulate approximate expectation values of a subregion of a landscape.
  arXiv  Detail & Related papers  (2024-11-29T18:00:07Z)
• Disentangling unitary dynamics with classically simulable quantum circuits [0.0]
  We study both quantum circuit and Hamiltonian dynamics. We find that expectations of Pauli operators can be simulated efficiently even for deep Clifford circuits. For the Hamiltonian dynamics we find that the classical simulation generically quickly becomes inefficient.
  arXiv  Detail & Related papers  (2024-10-11T17:18:26Z)
• QuCLEAR: Clifford Extraction and Absorption for Quantum Circuit Optimization [8.043057448895343]
  Currently available quantum devices suffer from noisy quantum gates, which degrade the fidelity of executed quantum circuits.<n>We present QuCLEAR, a compilation framework designed to optimize quantum circuits.
  arXiv  Detail & Related papers  (2024-08-23T18:03:57Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Hybrid Quantum-Classical Machine Learning with String Diagrams [49.1574468325115]
  This paper develops a formal framework for describing hybrid algorithms in terms of string diagrams. A notable feature of our string diagrams is the use of functor boxes, which correspond to a quantum-classical interfaces.
  arXiv  Detail & Related papers  (2024-07-04T06:37:16Z)
• Lie-algebraic classical simulations for quantum computing [0.3774866290142281]
  We present a framework for classical simulations, dubbed "$mathfrakg$-sim"<n>We show that $mathfrakg$-sim enables new regimes for classical simulations.<n>We report large-scale noiseless and noisy simulations on benchmark problems.
  arXiv  Detail & Related papers  (2023-08-02T21:08:18Z)
• Tensor Networks or Decision Diagrams? Guidelines for Classical Quantum Circuit Simulation [65.93830818469833]
  tensor networks and decision diagrams have independently been developed with differing perspectives, terminologies, and backgrounds in mind. We consider how these techniques approach classical quantum circuit simulation, and examine their (dis)similarities with regard to their most applicable abstraction level. We provide guidelines for when to better use tensor networks and when to better use decision diagrams in classical quantum circuit simulation.
  arXiv  Detail & Related papers  (2023-02-13T19:00:00Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• A graph-state based synthesis framework for Clifford isometries [2.048226951354646]
  We tackle the problem of synthesizing a Clifford isometry into an executable quantum circuit.<n>We propose a simple framework for synthesis that exploits the elementary properties of the Clifford group and one equation of the symplectic group.<n>We also propose practical synthesis algorithms for Clifford isometries with a focus on Clifford operators, graph states and codiagonalization of Pauli rotations.
  arXiv  Detail & Related papers  (2022-12-13T22:50:24Z)
• Crystalline Quantum Circuits [0.0]
  Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics. Motivated by an interest in deterministic circuits with similar applications, we construct classes of textitnonrandom unitary Clifford circuits. A full classification on the square lattice reveals, of particular interest, a "nonfractal good scrambling class" with dense operator spreading.
  arXiv  Detail & Related papers  (2022-10-19T18:00:57Z)
• Classical circuits can simulate quantum aspects [0.0]
  This study introduces a method for simulating quantum systems using electrical networks. By synthesizing interaction networks, we accurately simulate quantum systems of varying complexity, from $2-$state to $n-$state systems.
  arXiv  Detail & Related papers  (2022-09-19T18:42:06Z)
• A single $T$-gate makes distribution learning hard [56.045224655472865]
  This work provides an extensive characterization of the learnability of the output distributions of local quantum circuits. We show that for a wide variety of the most practically relevant learning algorithms -- including hybrid-quantum classical algorithms -- even the generative modelling problem associated with depth $d=omega(log(n))$ Clifford circuits is hard.
  arXiv  Detail & Related papers  (2022-07-07T08:04:15Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• 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)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)

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.