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Related papers: Qutrit metaplectic gates are a subset of Clifford+…

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We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a…

Quantum Physics · Physics 2023-12-20 Vadym Kliuchnikov , Kristin Lauter , Romy Minko , Adam Paetznick , Christophe Petit

The Clifford hierarchy is a foundational concept for universal quantum computation (UQC). It was introduced to show that UQC can be realized via quantum teleportation, given access to certain standard resources. While the full structure of…

Quantum Physics · Physics 2019-08-12 Narayanan Rengaswamy , Robert Calderbank , Henry D. Pfister

We explore the implementation of pseudo-random single-qubit rotations and multi-qubit pseudo-random circuits constructed only from Clifford gates and the T-gate, a phase rotation of pi/4. Such a gate set would be appropriate for…

Quantum Physics · Physics 2015-06-17 Yaakov S. Weinstein

It is known that the matrices that can be exactly represented by a multiqubit circuit over the Toffoli+Hadamard, Clifford+$T$, or, more generally, Clifford-cyclotomic gate set are precisely the unitary matrices with entries in the ring…

Quantum Physics · Physics 2024-08-13 Andrew N. Glaudell , Neil J. Ross , John van de Wetering , Lia Yeh

In this paper, we show the equivalence of the set of unitaries computable by the circuits over the Clifford and T library and the set of unitaries over the ring $\mathbb{Z}[\frac{1}{\sqrt{2}},i]$, in the single-qubit case. We report an…

Quantum Physics · Physics 2013-03-01 Vadym Kliuchnikov , Dmitri Maslov , Michele Mosca

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…

The use of a few intermediate qutrits for efficient decomposition of 3-qubit unitary gates has been proposed, to obtain an exponential reduction in the depth of the decomposed circuit. An intermediate qutrit implies that a qubit is operated…

Quantum Physics · Physics 2023-09-13 Ritajit Majumdar , Amit Saha , Amlan Chakrabarti , Susmita Sur-Kolay

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

Efficient synthesis of arbitrary quantum states and unitaries from a universal fault-tolerant gate-set e.g. Clifford+T is a key subroutine in quantum computation. As large quantum algorithms feature many qubits that encode coherent quantum…

Quantum Physics · Physics 2024-06-19 Guang Hao Low , Vadym Kliuchnikov , Luke Schaeffer

In fault-tolerant quantum circuit synthesis, T gates supplied via magic states dominate space-time cost, while Clifford gates incur negligible overhead. Conventional flows minimize AND count in an {XOR, AND, NOT} basis as a proxy for T,…

Quantum Physics · Physics 2026-05-18 Hanyu Wang , Mingfei Yu , Xinrui Wu , Jason Cong

We present two deterministic algorithms to approximate single-qutrit gates. These algorithms utilize the Clifford + $\mathbf{R}$ group to find the best approximation of diagonal rotations. The first algorithm exhaustively searches over the…

Quantum Physics · Physics 2025-12-09 Erik J. Gustafson , Henry Lamm , Diyi Liu , Edison M. Murairi , Shuchen Zhu

Recently it has been shown that Repeat-Until-Success (RUS) circuits can approximate a given single-qubit unitary with an expected number of $T$ gates of about $1/3$ of what is required by optimal, deterministic, ancilla-free decompositions…

Quantum Physics · Physics 2015-06-11 Alex Bocharov , Martin Roetteler , Krysta M. Svore

When visualised as an operation on the Bloch sphere, the qubit "pi-over-eight" gate corresponds to one-eighth of a complete rotation about the vertical axis. This simple gate often plays an important role in quantum information theory,…

Quantum Physics · Physics 2012-08-17 Mark Howard , Jiri Vala

Our goal in this paper is to construct optimal topological generators for compact unitary Lie groups, extending the work of a letter of Sarnak and arXiv:1704.02106 on golden and super-golden gates to higher dimensions. To do so we consider…

Number Theory · Mathematics 2025-09-12 Rahul Dalal , Shai Evra , Ori Parzanchevski

Compared with a qubit, a qudit (i.e., $d$-level or $d$-state quantum system) provides a larger Hilbert space to store and process information. On the other hand, qudit-based hybrid quantum computing usually requires performing hybrid…

Quantum Physics · Physics 2022-08-30 Qi-Ping Su , Yu Zhang , Liang Bin , Chui-Ping Yang

While implementing a quantum algorithm it is crucial to reduce the quantum resources, in order to obtain the desired computational advantage. For most fault-tolerant quantum error-correcting codes the cost of implementing the non-Clifford…

Quantum Physics · Physics 2023-02-10 Vlad Gheorghiu , Michele Mosca , Priyanka Mukhopadhyay

The Clifford$+T$ gate set is commonly used to perform universal quantum computation. In such setup the $T$ gate is typically much more expensive to implement in a fault-tolerant way than Clifford gates. To improve the feasibility of…

Quantum Physics · Physics 2024-02-27 Vivien Vandaele , Simon Martiel , Simon Perdrix , Christophe Vuillot

The leading paradigm for performing computation on quantum memories can be encapsulated as distill-then-synthesize. Initially, one performs several rounds of distillation to create high-fidelity magic states that provide one good T gate, an…

Quantum Physics · Physics 2017-02-15 Earl T. Campbell , Mark Howard

There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…

Quantum Physics · Physics 2022-09-05 John van de Wetering

Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations…

Quantum Physics · Physics 2019-10-28 T. Bækkegaard , L. B. Kristensen , N. J. S. Loft , C. K. Andersen , D. Petrosyan , N. T. Zinner