Related papers: On an implementation of the Solovay-Kitaev algorit…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its…
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…
This paper presents a quantum algorithm for the solution of prototypical second-order linear elliptic partial differential equations discretized by $d$-linear finite elements on Cartesian grids of a bounded $d$-dimensional domain. An…
We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to…
We propose a new Kalikow decomposition for continuous time multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation…
The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank $k$ approximation of a matrix $A$ using matrix-vector products with standard Gaussian vectors. Here, we generalize the…
For several computational problems in homotopy theory, we obtain algorithms with running time polynomial in the input size. In particular, for every fixed k>1, there is a polynomial-time algorithm that, for a 1-connected topological space X…
We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…
An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…
Product formula approximations of the time-evolution operator on quantum computers are of great interest due to their simplicity, and good scaling with system size by exploiting commutativity between Hamiltonian terms. However, product…
Imaginary-time evolution is fundamental for analyzing quantum many-body systems, yet classical simulation requires exponentially growing resources in both system size and evolution time. While quantum approaches reduce the system-size…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
We study a quantum algorithm that consists of a simple quantum Markov process, and we analyze its behavior on restricted versions of Quantum 2-SAT. We prove that the algorithm solves this decision problem with high probability for n qubits,…
We consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers. We start by providing a hybrid numeric-symbolic…