Related papers: Quantum Circuits for the Unitary Permutation Probl…
We construct quantum circuits for measuring the commuting set of vertex and plaquette operators that appear in the Levin-Wen model for doubled Fibonacci anyons. Such measurements can be viewed as syndrome measurements for the quantum…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…
Higher-order transformations acting on input quantum channels in an indefinite causal order, such as the quantum switch, cannot be described by quantum circuits using the same number of calls to the input channels. A natural question is…
We propose a method of compiling that permits to identify quantum circuits able to simulate arbitrary $n$-qubit unitary operations via the adjustment of angles in single-qubit gates therein. The method of compiling itself extends older…
We present a quantum variational algorithm based on a novel circuit that generates all permutations that can be spanned by one- and two-qubits permutation gates. The construction of the circuits follows from group-theoretical results, most…
A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all one-qubit…
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly…
We extend the work in New J. Phys. 19, 103015 (2017) by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields.…
It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type…
Quantum circuit complexity-a measure of the minimum number of gates needed to implement a given unitary transformation-is a fundamental concept in quantum computation, with widespread applications ranging from determining the running time…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many…
We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the…
Universal quantum computation may be realized based on quantum walk, by formulating it as a scattering problem on a graph. In this paper, we simulate quantum gates through electric circuits, following a recent report that a one-dimensional…
This paper addresses quantum circuit mapping for Noisy Intermediate-Scale Quantum (NISQ) computers. Since NISQ computers constraint two-qubit operations on limited couplings, an input circuit must be transformed into an equivalent output…
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis…
We study a variant of quantum circuit complexity, the binding complexity: Consider a $n$-qubit system divided into two sets of $k_1$, $k_2$ qubits each ($k_1\leq k_2$) and gates within each set are free; what is the least cost of two-qubit…