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Related papers: Climbing the Diagonal Clifford Hierarchy

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Recent advances in classical simulation of Clifford+T circuits make use of the ZX calculus to iteratively decompose and simplify magic states into stabiliser terms. We improve on this method by studying stabiliser decompositions of ZX…

Quantum Physics · Physics 2025-09-23 Mark Koch , Richie Yeung , Quanlong Wang

We show that qubit stabilizer states can be represented by non-negative quasi-probability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by…

Quantum Physics · Physics 2018-01-03 Lucas Kocia , Peter Love

Given a quantum error correcting code, an important task is to find encoded operations that can be implemented efficiently and fault-tolerantly. In this Letter we focus on topological stabilizer codes and encoded unitary gates that can be…

Quantum Physics · Physics 2013-10-04 Sergey Bravyi , Robert Koenig

Recently, there has been an emergence of useful applications for noisy intermediate-scale quantum (NISQ) devices notably, though not exclusively, in the fields of quantum machine learning and variational quantum algorithms. In such…

Quantum Physics · Physics 2021-02-26 Ellen Derbyshire , Rawad Mezher , Theodoros Kapourniotis , Elham Kashefi

Twirling noise affecting quantum gates is essential in understanding and controlling errors, but applicable operations to noise are usually restricted by symmetries inherent in quantum gates. In this work, we propose symmetric Clifford…

Quantum Physics · Physics 2025-06-18 Kento Tsubouchi , Yosuke Mitsuhashi , Kunal Sharma , Nobuyuki Yoshioka

Identifying stabilizer codes that admit fault-tolerant implementations of the full logical Clifford group would significantly advance fault-tolerant quantum computation. Motivated by this goal, we study several classes of fault-tolerant…

Quantum Physics · Physics 2026-02-27 Aranya Chakraborty , Daniel Gottesman

Magic states are essential yet resource-intensive components for realizing universal fault-tolerant quantum computation. Preparing magic states within emerging quantum low-density parity-check (qLDPC) codes poses additional challenges, due…

Quantum Physics · Physics 2025-05-13 Guo Zhang , Yuanye Zhu , Xiao Yuan , Ying Li

The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the…

Quantum Physics · Physics 2017-05-26 Benjamin J. Brown , Katharina Laubscher , Markus S. Kesselring , James R. Wootton

The two-dimensional color code is an alternative to the toric code that encodes more logical qubits while maintaining crucial features of the $\mathbb{Z}_2\times\mathbb{Z}_2$ toric code in the long wavelength limit. However its short range…

Fault-tolerant logic gates will consume a large proportion of the resources of a two-dimensional quantum computing architecture. Here we show how to perform a fault-tolerant non-Clifford gate with the surface code; a quantum…

Quantum Physics · Physics 2021-04-20 Benjamin J. Brown

We explore what the integrated use of quantum spatial distribution (QSD), or more specifically, superposition of both spin and position states of particles, and gauge symmetry (GS) within stabilizer formalism provides for quantum error…

Quantum Physics · Physics 2026-05-13 Ryo Asaka

The Clifford group plays a central role in quantum information science. It is the building block for many error-correcting schemes and matches the first three moments of the Haar measure over the unitary group -a property that is essential…

Quantum Physics · Physics 2025-04-17 Lennart Bittel , Jens Eisert , Lorenzo Leone , Antonio A. Mele , Salvatore F. E. Oliviero

Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet. Distillation protocols allows one to overcome this noise at the cost of an increased overhead. We consider here an experimentally relevant…

We propose a Clifford noise reduction (CliNR) scheme that provides a reduction of the logical error rate of Clifford circuit with lower overhead than error correction and without the exponential sampling overhead of error mitigation. CliNR…

Quantum Physics · Physics 2024-07-10 Nicolas Delfosse , Edwin Tham

Determining the best attainable threshold for qudit magic state distillation is directly related to the question of whether or not contextuality is sufficient for universal quantum computation. We show that the performance of a qudit…

Quantum Physics · Physics 2026-03-11 Shiroman Prakash , Rishabh Singhal

We propose two Clifford+$T$ synthesis algorithms that are optimal with respect to $T$-count. The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+$T$ circuit with the minimum…

Quantum Physics · Physics 2025-10-09 Hayata Morisaki , Kaoru Sano , Seiseki Akibue

Fault-tolerant quantum computation (FTQC) schemes using large block codes that encode $k>1$ qubits in $n$ physical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the…

Quantum Physics · Physics 2020-08-04 Yi-Cong Zheng , Ching-Yi Lai , Todd A. Brun , Leong-Chuan Kwek

We propose a protocol to prepare a high-fidelity magic state on a two-dimensional (2D) color code using a three-dimensional (3D) color code. Our method modifies the known code switching protocol with (i) a recently discovered transversal…

Quantum Physics · Physics 2025-04-25 Lucas Daguerre , Isaac H. Kim

This paper presents a deep reinforcement learning approach for synthesizing unitaries into quantum circuits. Unitary synthesis aims to identify a quantum circuit that represents a given unitary while minimizing circuit depth, total gate…

Quantum magic, quantified by nonstabilizerness, measures departures from stabilizer structure and underlies potential quantum speedups. We introduce an efficient classical framework for computing stabilizer R\'enyi entropies and stabilizer…

Quantum Physics · Physics 2026-04-21 Zhenyu Xiao , Shinsei Ryu