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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 construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-qubit measurements in any basis. Our results apply to…

Quantum Physics · Physics 2026-01-09 Jon Nelson , Joel Rajakumar , Dominik Hangleiter , Michael J. Gullans

To approximate arbitrary unitary transformations on one or more qubits, one must perform transformations which are outside of the Clifford group. The gate most commonly considered for this purpose is the T = diag(1, exp(i \pi/4)) gate. As T…

Quantum Physics · Physics 2020-05-04 Niel de Beaudrap , Xiaoning Bian , Quanlong Wang

We present optimized quantum circuits for GF$(2^m)$ multiplication and division operations, which are essential computing primitives in various quantum algorithms. Our ancilla-free GF multiplication circuit has the gate count complexity of…

Quantum Physics · Physics 2026-03-25 Noureldin Yosri , Dmytro Gavinsky , Dmitri Maslov

A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e.,…

With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation -- magic state preparation. Using an…

Quantum Physics · Physics 2025-10-30 Nicholas Fazio , Mark Webster , Zhenyu Cai

The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete…

Quantum Physics · Physics 2020-04-09 Yunseong Nam , Yuan Su , Dmitri Maslov

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

Fault-tolerant quantum computation enables reliable quantum computation but incurs a significant overhead from both time and resource perspectives. To reduce computation time, Austin G. Fowler proposed time-optimal quantum computation by…

Quantum Physics · Physics 2024-05-02 Taewan Kim , Kyunghyun Baek , Yongsoo Hwang , Jeongho Bang

We present two new constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T =…

Quantum Physics · Physics 2013-03-18 Cody Jones

We present improved quantum circuit for modular exponentiation of a constant, which is the most expensive operation in Shor's algorithm for integer factorization. While previous work mostly focuses on minimizing the number of qubits or the…

Quantum Physics · Physics 2023-11-28 Xia Liu , Huan Yang , Li Yang

In this work, we introduce a new circuit optimization technique to reduce the number of T gates in Clifford+T circuits by treating T gates conjugated by Clifford gates as $\frac{\pi}{4}$-rotations around Pauli operators. The tested…

Quantum Physics · Physics 2019-04-01 Fang Zhang , Jianxin Chen

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

A scalable and programmable quantum computer holds the potential to solve computationally intensive tasks that classical computers cannot accomplish within a reasonable time frame, achieving quantum advantage. However, the vulnerability of…

Quantum Physics · Physics 2025-03-04 Younghun Kim , Martin Sevior , Muhammad Usman

Transversal gates are logical gate operations on encoded quantum information that are efficient in gate count and depth, and are designed to minimize error propagation. Efficient encoding circuits for quantum codes that admit transversal…

Quantum Physics · Physics 2024-05-24 Praveen Jayakumar , Priya J. Nadkarni , Shayan Srinivasa Garani

We investigate quantum circuits built from arbitrary single-qubit operations combined with programmable all-to-all multiqubit entangling gates that are native to, among other systems, trapped-ion quantum computing platforms. We report a…

Quantum Physics · Physics 2025-10-24 Jonathan Nemirovsky , Lee Peleg , Amit Ben Kish , Yotam Shapira

Quantum computers are expected to bring drastic acceleration to several computing tasks against classical computers. Noisy intermediate-scale quantum (NISQ) devices, which have tens to hundreds of noisy physical qubits, are gradually…

Quantum Physics · Physics 2024-08-28 Yutaro Akahoshi , Kazunori Maruyama , Hirotaka Oshima , Shintaro Sato , Keisuke Fujii

In this research, we create a scalable version of the quantum Fourier transform-based arithmetic circuit to perform addition and subtraction operations on N n-bit unsigned integers encoded in quantum registers, and it is compatible with…

Quantum Physics · Physics 2024-11-04 Murat Kurt , Ayda Kaltehei , Azmi Gençten , Selçuk Çakmak

For a number of useful quantum circuits, qudit constructions have been found which reduce resource requirements compared to the best known or best possible qubit construction. However, many of the necessary qutrit gates in these…

Quantum Physics · Physics 2022-09-05 Lia Yeh , John van de Wetering

We present a simple algorithm that implements an arbitrary $n$-qubit unitary operator using a Clifford+T circuit with T-count $O(2^{4n/3} n^{2/3})$. This improves upon the previous best known upper bound of $O(2^{3n/2} n)$, while the best…

Quantum Physics · Physics 2025-10-01 Xinyu Tan