Related papers: Quantum Latin squares and unitary error bases
We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure which has been shown to relate the…
Latin squares are interesting combinatorial objects with many applications. When working with Latin squares, one is sometimes led to deal with partial Latin squares, a generalization of Latin squares. One of the problems regarding partial…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
The main thrust of the article is to provide interesting example, useful for students of using bitwise operations in the programming languages C ++ and Java. As an example, we describe an algorithm for obtaining a Latin square of arbitrary…
We introduce Unitaria, a Python library that brings the simplicity of classical linear algebra toolkits such as NumPy and SciPy to the implementation of quantum algorithms based on block encodings, a general-purpose abstraction in which a…
The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the…
Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications…
The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the…
Quantum computing as a promising technology can utilize stochastic solutions instead of deterministic approaches for complicated scenarios for which classical computing is inefficient, provided that both the concerns of the error-prone…
Most quantum computing architectures can be realized as two-dimensional lattices of qubits that interact with each other. We take transmon qubits and transmission line resonators as promising candidates for qubits and couplers; we use them…
Quantum simulation of materials is a promising application area of quantum computers. To practically realize this promise, we must reduce quantum resources while maintaining accuracy. In electronic structure calculations on classical…
We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of…
This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field…
Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. This "encoded universality"…
A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates…
We show how to construct a universal set of quantum logic gates using control over exchange interactions and single- and two-spin measurements only. Single-spin unitary operations are teleported instead of being executed directly, thus…
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…
Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary…
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…
We consider the notion of unitary transformations forming bases for subspaces of $M(d,\mathbb{C})$ such that the square of Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case,…