Related papers: Stable factorization for phase factors of quantum …
In this work we demonstrate the use of adapted classical phase retrieval algorithms to perform control-free quantum phase estimation. We eliminate the costly controlled time evolution and Hadamard test commonly required to access the…
We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…
Variational algorithm using Quantum Approximate Optimization Algorithm (QAOA) can solve the prime factorization problem in near-term noisy quantum computers. Conventional Variational Quantum Factoring (VQF) requires a large number of…
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues and eigenvectors. In this article we propose a new method for…
This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…
The quantum singular value transformation has revolutionised quantum algorithms. By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms. However, polynomials are restricted to definite parity…
New algorithms for prime factorization that outperform the existing ones or take advantage of particular properties of the prime factors can have a practical impact on present implementations of cryptographic algorithms that rely on the…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
We study numerically the effects of static imperfections and residual couplings between qubits for the quantum phase estimation algorithm with two qubits. We show that the success probability of the algorithm is affected significantly more…
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…
We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring"…
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…
A factor-graph representation of quantum-mechanical probabilities is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables.
Quantum signal processing provides an optimal procedure for simulating Hamiltonian evolution on a quantum computer using calls to a block encoding of the Hamiltonian. In many situations it is possible to control between forward and reverse…
We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
We present a quantum process-tomography protocol based on a low-degree ansatz for the quantum channel, i.e. when it can be expressed as a fixed-degree polynomial in terms of Pauli operators. We demonstrate how to perform tomography of such…
Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new…
Two steps phase shifting interferometry has been a hot topic in the recent years. We present a comparison study of 12 representative self--tunning algorithms based on two-steps phase shifting interferometry. We evaluate the performance of…
We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wavefunction by a branching random walk in an over-complete basis space of Slater determinants. By…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…