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Related papers: Simulating quantum circuits with ZX-calculus reduc…

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Bravyi and Gosset recently gave classical simulation algorithms for quantum circuits dominated by Clifford operations. These algorithms scale exponentially with the number of T-gate in the circuit, but polynomially in the number of qubits…

Quantum Physics · Physics 2019-05-15 Yifei Huang , Peter Love

The development of a framework for quantifying "non-stabiliserness" of quantum operations is motivated by the magic state model of fault-tolerant quantum computation, and by the need to estimate classical simulation cost for noisy…

Quantum Physics · Physics 2019-08-05 James R. Seddon , Earl T. Campbell

We employed the techniques from [Phys. Rev. A \textbf{70}, 052328 (2004)/arXiv:0406196] to analytically study two set of quantum circuits containing one $T$ gate/magic $|T\rangle = \frac{|0\rangle+\sqrt{i}|1\rangle}{\sqrt{2}}$ state. These…

Quantum Physics · Physics 2025-02-25 Kwok Ho Wan

Improving the simulation of quantum circuits on classical computers is important for understanding quantum advantage and increasing development speed. In this paper, we explore a new way to express stabilizer states and further improve the…

Quantum Physics · Physics 2022-09-12 Alexander Tianlin Hu , Andrey Boris Khesin

This work augments the recently introduced Stabilizer Tensor Network (STN) protocol with magic state injection, reporting a new framework with significantly enhanced ability to simulate circuits with an extensive number of non-Clifford…

Quantum Physics · Physics 2025-05-19 Azar C. Nakhl , Ben Harper , Maxwell West , Neil Dowling , Martin Sevior , Thomas Quella , Muhammad Usman

The ZX-calculus is an intuitive but also mathematically strict graphical language for quantum computing, which is especially powerful for the framework of quantum circuits. Completeness of the ZX-calculus means any equality of matrices with…

Quantum Physics · Physics 2023-05-18 Quanlong Wang

The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…

Quantum Physics · Physics 2025-01-09 Nadish de Silva , Wilfred Salmon , Ming Yin

The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be simulated efficiently on a classical computer. This paper improves that theorem in…

Quantum Physics · Physics 2009-11-10 Scott Aaronson , Daniel Gottesman

Stabilizer circuits play an important role in quantum error correction protocols, and will be vital for ensuring fault tolerance in future quantum hardware. While stabilizer circuits are defined on the Clifford generating set, {H, S, CX},…

Quantum Physics · Physics 2024-05-01 Brendan Reid

We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the…

Quantum Physics · Physics 2020-03-10 Robert Raussendorf , Juani Bermejo-Vega , Emily Tyhurst , Cihan Okay , Michael Zurel

We present a system of equations between Clifford circuits, all derivable in the ZX-calculus, and formalised as rewrite rules in the Quantomatic proof assistant. By combining these rules with some non-trivial simplification procedures…

Quantum Physics · Physics 2019-01-30 Andrew Fagan , Ross Duncan

The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics.The language is sound and complete: a stabilizer ZX-diagram can be transformed into another one if and only if these two diagrams represent…

Quantum Physics · Physics 2017-01-04 Miriam Backens , Simon Perdrix , Quanlong Wang

We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a…

Quantum Physics · Physics 2021-08-09 Andrey Boris Khesin , Kevin Ren

Quantum computing promises significant speed-ups for certain algorithms but the practical use of current noisy intermediate-scale quantum (NISQ) era computers remains limited by resources constraints (e.g., noise, qubits, gates, and circuit…

Quantum Physics · Physics 2026-03-31 Tobias Fischbach , Pierre Talbot , Pascal Bouvry

We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces…

We find a scaling reduction in the stabilizer rank of the twelve-qubit tensored $T$ gate magic state. This lowers its asymptotic bound to $2^{\sim 0.463 t}$ for multi-Pauli measurements on $t$ magic states, improving over the best…

Quantum Physics · Physics 2022-06-08 Lucas Kocia

Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…

Quantum Physics · Physics 2021-03-23 James R. Seddon , Bartosz Regula , Hakop Pashayan , Yingkai Ouyang , Earl T. Campbell

Quantum circuits are considered more powerful than classical circuits and require exponential resources to simulate classically. Clifford circuits are a special class of quantum circuits that can be simulated in polynomial time but still…

Quantum Physics · Physics 2025-12-09 Yuchen Pang , Edgar Solomonik

We propose several methods for optimizing the number of qubits in a quantum circuit while preserving the number of non-Clifford gates. One of our approaches consists in reversing, as much as possible, the gadgetization of Hadamard gates,…

Quantum Physics · Physics 2024-07-16 Vivien Vandaele

In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of $m$…

Quantum Physics · Physics 2021-12-22 Hammam Qassim , Hakop Pashayan , David Gosset