Related papers: Demonstration of Optimal Fixed-Point Quantum Searc…
We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the…
Generating a test suite for a quantum program such that it has the maximum number of failing tests is an optimization problem. For such optimization, search-based testing has shown promising results in the context of classical programs. To…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
Quantum computing (QC) emulators, which simulate quantum algorithms on classical hardware, are indispensable platforms for testing quantum algorithms before scalable quantum computers become widely available. A critical challenge in QC…
We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of…
Quantum computing has advanced rapidly in recent years and has shown advantages in a variety of domains. In this paper, we investigate its potential for discrete simulation optimization in the fixed-confidence setting, a fundamental problem…
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot…
A new method for simulation of a binary homogeneous Markov process using a quantum computer was proposed. This new method allows using the distinguished properties of the quantum mechanical systems -- superposition, entanglement and…
Benchmarking the performance of quantum optimization algorithms is crucial for identifying utility for industry-relevant use cases. Benchmarking processes vary between optimization applications and depend on user-specified goals. The…
Quantum algorithms on the noisy intermediate-scale quantum (NISQ) devices are expected to simulate quantum systems that are classically intractable to demonstrate quantum advantages. However, the non-negligible gate error on the NISQ…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching…
A novel simulation strategy is proposed to search for semiconductor quantum devices which are optimized with respect to required performances. Based on evolutionary programming, a tecnique implementing the paradigm of genetic algorithms to…
Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of n items and we would like to find a marked item. We consider a new variant of this problem in which…
Consider a database most of whose entries are marked but the precise fraction of marked entries is not known. What is known is that the fraction of marked entries is 1-X, where X is a random variable that is uniformly distributed in the…
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…
Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime. In the paper "Quantum…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…