Related papers: A quantum algorithm for estimating the determinant
We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H= \theta H_0$,…
We present an optimized algorithm calculating determinant for multivariate polynomial matrix on GPU. The novel algorithm provides precise determinant for input multivariate polynomial matrix in controllable time. Our approach is based on…
In this paper, we study quantum algorithms of matrix multiplication from the viewpoint of inputting quantum/classical data to outputting quantum/classical data. The main target is trying to overcome the input and output problem, which are…
A projective measurement of energy (PME) on a quantum system is a quantum measurement, determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by…
For matrix $A$, vector $\boldsymbol{b}$ and function $f$, the computation of vector $f(A)\boldsymbol{b}$ arises in many scientific computing applications. We consider the problem of obtaining quantum state $\lvert f \rangle$ corresponding…
We present a protocol that allows the estimation of any density matrix element for continuous-variable quantum states, without resorting to the complete reconstruction of the full density matrix. The algorithm adaptatively discretizes the…
Quantum algorithms speeding up classical counterparts are proposed for the problems: 1. Recognition of eigenvalues with fixed precision. Given a quantum circuit generating unitary mapping $U$ and a complex number the problem is to determine…
We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…
In this paper, a quantum algorithm based on gaussian process regression model is proposed. The proposed quantum algorithm consists of three sub-algorithms. One is the first quantum subalgorithm to efficiently generate mean predictor. The…
We present a new algorithm to rapidly and optimally compute power spectra. This new algorithm is based on a generalization of iterative multigrid, and has computational cost O(N log N), compared to the standard brute force approach which…
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…
We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
We propose a quantum algorithm to compute low-energy expectation values of a quantum Hamiltonian by sampling a partition function associated with the average energy of that Hamiltonian. For any given quantum circuit-Hamiltonian pair, there…
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant…
In this work we consider practical implementations of Kitaev's algorithm for quantum phase estimation. We analyze the use of phase shifts that simplify the estimation of successive bits in the estimation of unknown phase $\varphi$. By using…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…