Related papers: Path Integration on a Quantum Computer
The scalability, error correction and practical problem solving are important challenges for quantum computing (QC) as more emphasized by quantum supremacy (QS) experiments. Quantum path computing (QPC), recently introduced for linear optic…
Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
Quantum image processing (QIP) means the quantum based methods to speed up image processing algorithms. Many quantum image processing schemes claim that their efficiency are theoretically higher than their corresponding classical schemes.…
Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
Path integrals developed by Richard Feynman have been an important tool in Physics in studying quantum field theory. In mathematics, it has also been widely used in providing formal proofs in the study of Index theorem and asymptotic…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…
Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…
In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
A computational problem fed into a gate-model quantum computer identifies an objective function with a particular computational pathway (objective function connectivity). The solution of the computational problem involves identifying a…
The exact evaluation of the molecular ground state in quantum chemistry requires an exponentially increasing computational cost. Quantum computation is a promising way to overcome the exponential problem using polynomial-time quantum…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…
Using the path integral measure factorization method based on the nonlinear filtering equation from the stochastic process theory, we consider the reduction procedure in Wiener path integrals for a mechanical system with symmetry that…
Quantum computing is fast evolving as a technology due to recent advances in hardware, software, as well as the development of promising applications. To use this technology for solving specific problems, a suitable quantum algorithm has to…
The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical…
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to…