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Related papers: Unitary Designs from Random Symmetric Quantum Circ…

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We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending single-and multi-qubit URB to single- and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore,…

Quantum Physics · Physics 2024-07-24 Mahnaz Jafarzadeh , Ya-Dong Wu , Yuval R. Sanders , Barry C. Sanders

A quantum unitary gate is realized in this paper by perturbing a free charged particle in a one-dimensional box with a time- and position-varying electric field. The perturbed Hamiltonian is composed of a free particle Hamiltonian plus a…

Quantum Physics · Physics 2023-04-14 Kumar Gautam

Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…

Quantum Physics · Physics 2013-09-16 Bin Li , Zu-Huan Yu , Shao-Ming Fei

A unitary $t$-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general $t$. In this paper, we provide for the first time quantum…

We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive…

Quantum Physics · Physics 2013-08-21 David Gosset , Vadym Kliuchnikov , Michele Mosca , Vincent Russo

This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more…

Quantum Physics · Physics 2021-11-24 Michele Mosca , Priyanka Mukhopadhyay

We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{g_1,\ldots,g_n\}\subset G$ is universal, i.e if the closure $\overline{<\mathcal{S}>}$ is equal to $G$, where $G$ is either the special unitary or the…

Quantum Physics · Physics 2017-11-07 Adam Sawicki , Katarzyna Karnas

We study the problem of constructing strong approximate unitary $k$-designs on $D$-dimensional grids (and more generally on Cartesian products of graphs), building on the work of Schuster et al. arXiv:2509.26310 which establishes strong…

Quantum Physics · Physics 2026-05-06 Marten Folkertsma , Lorenzo Grevink , Jonas Helsen , Alicja Dutkiewicz

We explicitly construct a quantum circuit which exactly generates random three-qubit states. The optimal circuit consists of three CNOT gates and fifteen single qubit elementary rotations, parametrized by fourteen independent angles. The…

Quantum Physics · Physics 2010-05-10 Olivier Giraud , Marko Znidaric , Bertrand Georgeot

From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct a universal quantum circuit. A new analytic construction procedure is presented and shown to be either…

Quantum Physics · Physics 2009-11-10 Jun Zhang , Jiri Vala , Shankar Sastry , K. Birgitta Whaley

This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…

Quantum Physics · Physics 2010-06-29 Richard A. Low

Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary…

Quantum Physics · Physics 2009-04-21 Kaveh Khodjasteh , Lorenza Viola

Implementation of high-dimensional (HD) quantum gates shows very promising perspectives for HD quantum computation. A bipartite quantum system with arbitrary dimensions $n$ and $m$ is termed a quNit-quMit. Here we propose a synthesis scheme…

Quantum Physics · Physics 2026-04-14 Gui-Long Jiang , Hai-Rui Wei

Recent years have enjoyed a strong interest in exploring properties and applications of random quantum circuits. In this work, we explore the ensemble of $t$-doped Clifford circuits on $n$ qubits, consisting of Clifford circuits…

Quantum Physics · Physics 2026-05-06 Lorenzo Leone , Salvatore F. E. Oliviero , Alioscia Hamma , Jens Eisert , Lennart Bittel

In the current framework of Geometric Quantum Machine Learning, the canonical method for constructing a variational ansatz that respects the symmetry of some group action is by forcing the circuit to be equivariant, i.e., to commute with…

Quantum Physics · Physics 2025-06-19 Roeland Wiersema , Alexander F. Kemper , Bojko N. Bakalov , Nathan Killoran

We introduce a model of computation based on quaternions, which is inspired on the quantum computing model. Pure states are vectors of a suitable linear space over the quaternions. Other aspects of the theory are the same as in quantum…

Quantum Physics · Physics 2007-05-23 Jose M. Fernandez , William A. Schneeberger

We consider quantum circuit models where the gates are drawn from arbitrary gate ensembles given by probabilistic distributions over certain gate sets and circuit architectures, which we call stochastic quantum circuits. Of main interest in…

Quantum Physics · Physics 2024-11-08 Linghang Kong , Zimu Li , Zi-Wen Liu

Unitarity randomized benchmarking (URB) is an experimental procedure for estimating the coherence of implemented quantum gates independently of state preparation and measurement errors. These estimates of the coherence are measured by the…

Quantum Physics · Physics 2019-01-17 Bas Dirkse , Jonas Helsen , Stephanie Wehner

A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find…

Combinatorics · Mathematics 2009-08-31 Aidan Roy , A. J. Scott

With improved gate calibrations reducing unitary errors, we achieve a benchmarked single-qubit gate fidelity of 99.95% with superconducting qubits in a circuit quantum electrodynamics system. We present a method for distinguishing between…

Quantum Physics · Physics 2016-01-13 Sarah Sheldon , Lev S. Bishop , Easwar Magesan , Stefan Filipp , Jerry M. Chow , Jay M. Gambetta