相关论文: Exact and Approximate Unitary 2-Designs: Construct…

The purpose of this paper is to give explicit constructions of unitary $t$-designs in the unitary group $U(d)$ for all $t$ and $d$. It seems that the explicit constructions were so far known only for very special cases. Here explicit…

This paper explores artificial intelligence (AI) methods for the approximate compiling of unitaries, focusing on the use of fixed two-qubit gates and arbitrary single-qubit rotations typical in superconducting hardware. Our approach…

Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state…

We present an algorithm for building a circuit that approximates single qubit unitaries with precision {\epsilon} using O(log(1/{\epsilon})) Clifford and T gates and employing up to two ancillary qubits. The algorithm for computing our…

The accessible information and the informational power quantify the amount of information extractable from a quantum ensemble and by a quantum measurement, respectively. So-called spherical quantum 2-designs constitute a class of ensembles…

A powerful tool emerging from the study of many-body quantum dynamics is that of dual-unitary circuits, which are unitary even when read `sideways', i.e., along the spatial direction. Here, we show that this provides the ideal framework to…

The accurate identification of faulty hardware is a fundamental requirement for reliable quantum information processing. We address this problem in a quantum setting, where a series of $n$ devices is intended to apply the same unitary…

Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…

Imperfect measurement can degrade a quantum error correction scheme. A solution that restores fault tolerance is to add redundancy to the process of syndrome extraction. In this work, we show how to optimize this process for an arbitrary…

The use of quantum processing units (QPUs) promises speed-ups for solving computational problems. Yet, current devices are limited by the number of qubits and suffer from significant imperfections, which prevents achieving quantum…

We consider the problem of mapping a logical quantum circuit onto a given hardware with limited two-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes…

The Haar measure plays a vital role in quantum information, but its study often requires a deep understanding of representation theory, posing a challenge for beginners. This tutorial aims to provide a basic introduction to Haar measure…

Operator controllability refers to the ability to implement an arbitrary unitary in SU(N) and is a prerequisite for universal quantum computing. Controllability tests can be used in the design of quantum devices to reduce the number of…

We show how to directly and efficiently approximate arbitrary one-qubit unitaries, bypassing the Euler decomposition and the magnitude approximation problem, at the cost of one ancillary qubit. Our technique also applies to approximating…

We present a technique for derandomising large deviation bounds of functions on the unitary group. We replace the Haar distribution with a pseudo-random distribution, a k-design. k-designs have the first k moments equal to those of the Haar…

In this Letter we make progress on a longstanding open problem of Aaronson and Ambainis [Theory of Computing 1, 47 (2005)]: we show that if A is the adjacency matrix of a sufficiently sparse low-dimensional graph then the unitary operator…

Distributed quantum computing represents at present one of the most promising approaches to scaling quantum processors. Current implementations typically partition circuits into multiple cores, each composed of several qubits, with…

Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…

In this short review we describe the process of designing a superconducting circuit device for quantum information applications. We discuss the factors that must be considered to implement a desired effective Hamiltonian on a device. We…

We study measurements on various subsystems of the output of a universal 1 to 2 cloning machine, and establish a correspondence between these measurements at the output and effective measurements on the original input. We show that one can…