Related papers: Discrimination of unitary transformations in the D…
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…
In his seminal work on recording quantum queries [Crypto 2019], Zhandry studied interactions between quantum query algorithms and the quantum oracle corresponding to random functions. Zhandry presented a framework for interpreting various…
We report on a performance comparison between physical and logical computations on a prototypical machine-learning application: solving differential equations using quantum kernel methods. The algorithm is implemented on an atom-based…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations…
We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of…
Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…
Schemes of experimental realization of the main two qubit processors for quantum computers and Deutsch-Jozsa algorithm are derived in virtual spin representation. The results are applicable for every four quantum states allowing the…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
A probabilistic version of the Bernstein-Vazirani problem (which is a generalization of the original Bernstein-Vazirani problem) and a quantum algorithm to solve it are proposed. The problem involves finding one or more secret keys from a…
We show that deterministic quantum computing with one qubit (DQC1) can be experimentally implemented with a spatial light modulator, using the polarization and the transverse spatial degrees of freedom of light. The scheme allows the…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation…
We use Deutsch's algorithm as a stand in for more complex quantum algorithms in order to determine how quantum properties of an environment manifest themselves in results that can be obtained on quantum computers. We model pure dephasing in…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
Hoyer has given a generalisation of the Deutsch--Jozsa algorithm which uses the Fourier transform on a group G which is (in general) non-Abelian. His algorithm distinguishes between functions which are either perfectly balanced (m-to-one)…
We report an experimental demonstration of quantum Deutsch's algorithm by using linear-optical system. By employing photon's polarization and spatial modes, we implement all balanced and constant functions for quantum computer. The…