Related papers: A Theory for Valiant's Matchcircuits (Extended Abs…

Any non-affine one-to-one binary gate can be wired together with suitable inputs to give AND, OR, NOT and fan-out gates, and so suffices to construct a general-purpose computer.

The Cayley-Hamilton problem of expressing functions of matrices in terms of only their eigenvalues is well-known to simplify to finding the inverse of the confluent Vandermonde matrix. Here, we give a highly compact formula for the inverse…

An alternating sign matrix is a square matrix with entries 1, 0 and -1 such that the sum of the entries in each row and each column is equal to 1 and the nonzero entries alternate in sign along each row and each column. To some of the…

We propose a theory of characterizing quantum circuits with qubit functional configurations. Any quantum circuit can be decomposed into alternating sequences of 1-qubit unitary gates and CNOT gates. Each CNOT sequence prepares the current…

An $n\times n$ matrix $M=[m_{ij}]$ with $m_{ij}\in U_n=\{1,2,\ldots,n\}$ will be called a cycle matrix if $(U_n,\cdot)$ is a cycle set, where $i\cdot j=m_{ij}$. We study these matrices in this article. Using these matrices, we give some…

We investigate the special class of formulas made up of arbitrary but finite com- binations of addition, multiplication, and exponentiation gates. The inputs to these formulas are restricted to the integral unit 1. In connection with such…

For a Lie algebra L over an algebraically closed field of non-zero characteristic, every finite-dimensional L-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character.…

This article gives a new matrix function named "twisted immanant," which can be regarded as an analogue of the immanant. This is defined for each self-conjugate partition through a "twisted" analogue of the irreducible character of the…

We present a new class of sparse and easily invertible circulant matrices that can have a sparse inverse though not being permutation matrices. Their study is useful in the design of quasi-cyclic low-density generator matrix codes, that are…

Implementing a scalable quantum information processor using polar molecules in optical lattices requires precise control over the long-range dipole-dipole interaction between molecules in selected lattice sites. We present here a scheme…

We prove a computable version of the Hall Harem Theorem where the matching realizes a unary function with controlled sizes of cycles. We apply it to non-amenable computable coarse spaces. As a result, we obtain a computable version of the…

This note introduces a family of circulant quantum channels -- a subclass of the mixed-permutation channels -- and investigates its key structural and operational properties. We show that the image of the circulant quantum channel is…

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…

In [R. Jozsa, B. Kraus, A. Miyake, J. Watrous, Proc. R. Soc. A {\bf 466}, 809-830 (2010)] it has been shown that a match gate circuit running on n qubits can be compressed to a universal quantum computation on \log(n)+3 qubits. Here, we…

Learning an unknown quantum process is a central task for validation of the functioning of near-term devices. The task is generally hard, requiring exponentially many measurements if no prior assumptions are made on the process. However, an…

The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be…

This work presents closed formulas for determinant, permanent, inverse, and Drazin inverse of circulant matrices with two non-zero coefficients.

In 2010, B. Rhoades proved that promotion together with the fake-degree polynomial associated with rectangular standard Young tableaux give an instance of the cyclic sieving phenomenon. We extend this result to all skew standard Young…

We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT gates within the context of the Single Cooper Pair Box (SCB) approach to quantum computing. Such gates are sufficient to support universal quantum computation.…

We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be…