The solovay-kitaev algorithm
WebJun 24, 2024 · Solovay – Kitaev algorithm is explainable using the following. lemma. Lemma 6 [23]. Suppose V, W, ~ V, and ~ W are unitaries such. that k V ... WebIt was introduced by Alexei Kitaev. The toric code gets its name from its periodic boundary conditions, ... The most well-used algorithm is minimum weight perfect matching. When applied to the noise model with independent bit and flip errors, a threshold of around 10.5% is achieved. This falls only a little short of the 11% maximum.
The solovay-kitaev algorithm
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WebThe Solovay-Kitaev algorithm is the standard method used for approximating arbitrary single-qubit gates for fault-tolerant quantum computation. In this paper we introduce a technique called search space expansion, which modi es the initial stage of the Solovay-Kitaev algorithm, increasing
WebThe Solovay-Kitaev algorithm is the standard method used for approximating arbitrary single-qubit gates for fault-tolerant quantum computation. In this paper we introduce a … WebDec 3, 2024 · The Solovay-Kitaev (S-K) algorithm is a central result in quantum compilation. It shows how to approximate arbitrary unitary operations using elements from a finite, universal gate set. In particular, it gives an explicit algorithm which, given an inverse-closed universal gate set G and a target unitary U, ϵ -approximates U using merely ...
WebDec 3, 2024 · The Solovay-Kitaev algorithm is a fundamental result in quantum computation. It gives an algorithm for efficiently compiling arbitrary unitaries using … In quantum information and computation, the Solovay–Kitaev theorem says, roughly, that if a set of single-qubit quantum gates generates a dense subset of SU(2), then that set can be used to approximate any desired quantum gate with a relatively short sequence of gates. This theorem is considered one of the most significant results in the field of quantum computation and was first announced by Robert M. Solovay in 1995 and independently proven by Alexei Kitaev in 1997. Micha…
WebThe Solovay–Kitaev theorem guarantees the existence of such that such that . By Lemma 2, . Since is a homomorphism, . That is, ,where . 3. Approximations in Now we describe how …
WebDec 16, 2015 · Then, we explain the Solovay–Kitaev algorithm, which provides a way to decompose an arbitrary single-qubit unitary operation into an elementary set of single-qubit gates. Using multi-qubit gates, we construct an arbitrary n -qubit unitary operation from an elementary universal set of gates, which we call universal quantum computation. christian eduard franke bambergWebThe Solovay-Kitaev algorithm is the standard method used for approximating arbitrary single-qubit gates for fault-tolerant quantum computation. In this paper we introduce a technique called search space expansion, which modifies the initial stage of the Solovay-Kitaev algorithm, increasing the length of the possible approximating sequences but ... christian educational consortium louisvilleWebthe Solovay-Kitaev Theorem states that a change of a gate set only increases the complexity of the algorithms in a polylogarithmic factor, so they can be well de ned. However, there are certain details of the exact statement of the theorem that have to be improved (see [Kup15]). The aim of this work is to introduce the Solovay Kitaev theorem ... georgetown seattle garden tour 2022WebLet’s examine each of these lines in detail. The first line: function Solovay-Kitaev (Gate U, depth n) indicates that the algorithm is a function with two inputs: an arbitrary single-qubit quantum gate, U, which we desire to approximate, and a non-negative integer, n, which controls the accuracy of the approximation. georgetown seattle restaurantsWebMay 30, 2013 · The Solovay-Kitaev algorithm is the standard method used for approximating arbitrary single-qubit gates for fault-tolerant quantum computation. In this … georgetown seattle mapWebApr 4, 2024 · Approximately decompose 1q gates to a discrete basis using the Solovay-Kitaev algorithm. The Solovay-Kitaev theorem [1] states that any single qubit gate can be approximated to arbitrary precision by a set of fixed single-qubit gates, if the set generates a dense subset in S U ( 2). georgetown seattle hotelsWebThe Solovay-Kitaev algorithm. This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form of an efficient classical algorithm for compiling an arbitrary … georgetown seattle breakfast