The Solovay-Kitaev algorithm
TLDR
The algorithm can be used to compile Shor's algorithm into an efficient fault-tolerant form using only Hadamard, controlled-not, and π/8 gates, and is generalized to apply to multi-qubit gates and togates from SU(d).Abstract:
This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form ofan efficient classical algorithm for compiling an arbitrary single-qubit gate into a sequenceof gates from a fixed and finite set. The algorithm can be used, for example, to compileShor's algorithm, which uses rotations of π/2k, into an efficient fault-tolerant form usingonly Hadamard, controlled-not, and π/8 gates. The algorithm runs in O(log2.71(1/e))time, and produces as output a sequence of O(log3.97(1/e)) quantum gates which isguaranteed to approximate the desired quantum gate to an accuracy within e > 0. Wealso explain how the algorithm can be generalized to apply to multi-qubit gates and togates from SU(d).read more
Citations
More filters
Journal ArticleDOI
A quantum engineer's guide to superconducting qubits
Philip Krantz,Philip Krantz,Morten Kjaergaard,Fei Yan,Terry P. Orlando,Simon Gustavsson,William D. Oliver +6 more
TL;DR: In this paper, the authors provide an introductory guide to the central concepts and challenges in the rapidly accelerating field of superconducting quantum circuits, including qubit design, noise properties, qubit control and readout techniques.
Journal ArticleDOI
Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions
TL;DR: A scheme of fault-tolerant quantum computation for a local architecture in two spatial dimensions with error threshold 0.75% for each source in an error model with preparation, gate, storage, and measurement errors.
Journal ArticleDOI
Error bounds for approximations with deep ReLU networks.
TL;DR: It is proved that deep ReLU networks more efficiently approximate smooth functions than shallow networks and adaptive depth-6 network architectures more efficient than the standard shallow architecture are described.
Journal ArticleDOI
Quantum error correction for beginners.
TL;DR: The basic aspects of quantum error correction and fault-tolerance are examined largely through detailed examples, which are more relevant to experimentalists today and in the near future.
Journal ArticleDOI
A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits
TL;DR: An algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speedup over simple brute force algorithms is presented.
References
More filters
Book
Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Journal ArticleDOI
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms on a quantum computer and gave an efficient randomized algorithm for these two problems, which takes a number of steps polynomial in the input size of the integer to be factored.
Book
Topics in Matrix Analysis
TL;DR: The field of values as discussed by the authors is a generalization of the field of value of matrices and functions, and it includes singular value inequalities, matrix equations and Kronecker products, and Hadamard products.
Proceedings ArticleDOI
Algorithms for quantum computation: discrete logarithms and factoring
TL;DR: Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.
Proceedings ArticleDOI
A fast quantum mechanical algorithm for database search
TL;DR: In this paper, it was shown that a quantum mechanical computer can solve integer factorization problem in a finite power of O(log n) time, where n is the number of elements in a given integer.