相关论文: The Solovay-Kitaev algorithm

For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary…

Quantum algorithms offer a dramatic speedup for computational problems in machine learning, material science, and chemistry. However, any near-term realizations of these algorithms will need to be heavily optimized to fit within the finite…

Compilation of unitaries into a sequence of physical quantum gates is a critical prerequisite for execution of quantum algorithms. This work introduces STOQ, a stochastic search protocol for approximate unitary compilation into a sequence…

A canonical result about satisfiability theory is that the 2-SAT problem can be solved in linear time, despite the NP-hardness of the 3-SAT problem. In the quantum 2-SAT problem, we are given a family of 2-qubit projectors $\Pi_{ij}$ on a…

We formulate and numerically simulate the single control qubit Shor algorithm for the case of static imperfections induced by residual couplings between qubits. This allows us to study the accuracy of Shor's algorithm with respect to these…

Controlled gates are key components in various quantum algorithms. Improving on the prior work of Gosset et al., we show that, for an allowed error $\varepsilon$, $3\log_2(1/\varepsilon) + o(\log(1/\varepsilon))$ $T$ gates are sufficient to…

With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type.…

Quantum algorithms require a universal set of gates that can be implemented in a physical system. For these, an optimal decomposition into a sequence of available operations is desired. Here, we present a method to find such sequences for a…

We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…

We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…

We present a simple method for constructing optimal fault-tolerant approximations of arbitrary unitary gates using an arbitrary discrete universal gate set. The method presented is numerical and scales exponentially with the number of gates…

The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era.…

Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze…

In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker{\aa} so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one…

We show how, given any set of generators of the stabilizer of a quantum code, an efficient gate array that computes the codewords can be constructed. For an n-qubit code whose stabilizer has d generators, the resulting gate array consists…

Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum…

The creation of composite quantum gates that implement quantum response functions $\hat{U}(\theta)$ dependent on some parameter of interest $\theta$ is often more of an art than a science. Through inspired design, a sequence of $L$…

Spin qubits in quantum dots define an attractive platform for scalable quantum information because of their compatibility with semiconductor manufacturing, their long coherence times, and the ability to operate at temperatures exceeding one…

Periodic functions are of special importance in quantum computing, particularly in applications of Shor's algorithm. We explore methods of creating circuits for periodic functions to better understand their properties. We introduce a method…

We propose a new quantum circuit for the quantum search problem. The quantum circuit is superior to Grover's algorithm in some realistic cases. The reasons for the superiority are in short as follows: In the quantum circuit proposed in this…