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We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…
In the emerging domain of quantum algorithms, the Grover's quantum search is certainly one of the most significant. It is relatively simple, performs a useful task and more importantly, does it in an optimal way. However, due to the success…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
The simplest technique for simulating a quantum algorithm - QA described based on the direct matrix representation of the quantum operators. Using this approach, it is relatively simple to simulate the operation of a QA and to perform…
Quantum algorithms for unstructured search problems rely on the preparation of a uniform superposition, traditionally achieved through Hadamard gates. However, this incidentally creates an auxiliary search space consisting of nonsensical…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of…
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…
Quantum query complexity is typically characterized in terms of XOR queries |x,y> to |x,y+f(x)> or phase queries, which ensure that even queries to non-invertible functions are unitary. When querying a permutation, another natural model is…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
Quantum mechanical search induces polynomial speed up in an unsorted database search process. In case of classical linear search the computational time increases with the dimensionality of the query. However, quantum parallelism, inherent…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
Solving hard problems is one of the most important issues in computing to be addressed by a quantum computer. Previously, we have shown that the H-SEARCH; which is the problem of finding a Hadamard matrix (H-matrix) among all possible…
We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post application of the oracle. The standard…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
Matrix inversion problems are often encountered in experimental physics, and in particular in high-energy particle physics, under the name of unfolding. The true spectrum of a physical quantity is deformed by the presence of a detector,…
Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry and statistics. Traditional solution methods such as Gaussian elimination become very time…