English
Related papers

Related papers: Unitary synthesis with fewer T gates

200 papers

We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation…

Quantum Physics · Physics 2016-08-30 Vadym Kliuchnikov , Dmitri Maslov , Michele Mosca

Among the cost metrics characterizing a quantum circuit, the $T$-count stands out as one of the most crucial as its minimization is particularly important in various areas of quantum computation such as fault-tolerant quantum computing and…

Quantum Physics · Physics 2025-09-17 Vivien Vandaele

A popular universal gate set for quantum computing with qubits is Clifford+T, as this can be readily implemented on many fault-tolerant architectures. For qutrits, there is an equivalent T gate, that, like its qubit analogue, makes…

Quantum Physics · Physics 2022-09-05 Andrew Glaudell , Neil J. Ross , John van de Wetering , Lia Yeh

Before executing a quantum algorithm, one must first decompose the algorithm into machine-level instructions compatible with the architecture of the quantum computer, a process known as quantum compiling. There are many different quantum…

Quantum Physics · Physics 2018-06-08 Luke Heyfron , Earl T. Campbell

We study the resources required to achieve universal quantum computing via the gate sets that provide the fundamental instructions from which quantum algorithms are built. While single-gate universal sets are known, they rely on precisely…

Quantum Physics · Physics 2026-02-24 Robin Kaarsgaard

We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate…

Quantum Physics · Physics 2022-08-24 Sahel Ashhab , Naoki Yamamoto , Fumiki Yoshihara , Kouichi Semba

We propose a method of compiling that permits to identify quantum circuits able to simulate arbitrary $n$-qubit unitary operations via the adjustment of angles in single-qubit gates therein. The method of compiling itself extends older…

Quantum Physics · Physics 2021-01-06 Rahul P. Singh , A. Mandilara

Multi-controlled unitary gates have been a subject of interest in quantum computing since its inception, and are widely used in quantum algorithms. The current state-of-the-art approach to implementing n-qubit multi-controlled gates…

We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…

Quantum Physics · Physics 2013-05-29 Vivek V. Shende , Igor L. Markov , Stephen S. Bullock

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

We present pygridsynth, an open-source Python library for ancilla-free approximate Clifford+$T$ synthesis that runs in $O(\log(1/\epsilon))$ for precision $\epsilon$. For $n=1, 2$ qubits, the library builds upon established efficient and…

Quantum Physics · Physics 2026-04-24 Shuntaro Yamamoto , Nobuyuki Yoshioka

Exact synthesis is a tool used in algorithms for approximating an arbitrary qubit unitary with a sequence of quantum gates from some finite set. These approximation algorithms find asymptotically optimal approximations in probabilistic…

Quantum Physics · Physics 2015-04-17 Vadym Kliuchnikov , Jon Yard

Quantum circuits for basic image processing functions such as bilinear interpolation are required to implement image processing algorithms on quantum computers. In this work, we propose quantum circuits for the bilinear interpolation of…

Quantum Physics · Physics 2018-10-31 Edgard Muñoz-Coreas , Himanshu Thapliyal

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

Recent research in generalizing quantum computation from 2-valued qudits to d-valued qudits has shown practical advantages for scaling up a quantum computer. A further generalization leads to quantum computing with hybrid qudits where two…

Quantum Physics · Physics 2007-05-23 Faisal Shah Khan , Marek Perkowski

Unitary synthesis is the process of decomposing a target unitary transformation into a sequence of quantum gates. This is a challenging task, as the number of possible gate combinations grows exponentially with the circuit depth. In this…

Quantum Physics · Physics 2025-09-01 Xavier Valcarce , Bastien Grivet , Nicolas Sangouard

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

Quantum circuits of a general quantum gate acting on multiple $d$-level quantum systems play a prominent role in multi-valued quantum computation. We first propose a new recursive Cartan decomposition of semi-simple unitary Lie group…

Quantum Physics · Physics 2024-05-29 Gui-Long Jiang , Wen-Qiang Liu , Hai-Rui Wei

Prior work of Beverland et al. has shown that any exact Clifford+$T$ implementation of the $n$-qubit Toffoli gate must use at least $n$ $T$ gates. Here we show how to get away with exponentially fewer $T$ gates, at the cost of incurring a…

Quantum Physics · Physics 2025-10-09 David Gosset , Robin Kothari , Chenyi Zhang

Using error correcting codes and fault tolerant techniques, it is possible, at least in theory, to produce logical qubits with significantly lower error rates than the underlying physical qubits. Suppose, however, that the gates that act on…

Quantum Physics · Physics 2016-12-06 M. B. Hastings