Related papers: Challenges for quantum computation of nonlinear dy…
We propose an explicit algorithm based on the Linear Combination of Hamiltonian Simulations technique to simulate both the advection-diffusion equation and a nonunitary discretized version of the Koopman-von Neumann formulation of nonlinear…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
Using a quantumlike description for light propagation in nonhomogeneous optical fibers, quantum information processing can be implemented by optical means. Quantum-like bits (qulbits) are associated to light modes in the optical fiber and…
It is well known in quantum optics that any process involving the preparation of a multimode gaussian state, followed by a gaussian operation and gaussian measurements, can be efficiently simulated by classical computers. Here, we provide…
Reachability analysis of nonlinear dynamical systems is a challenging and computationally expensive task. Computing the reachable states for linear systems, in contrast, can often be done efficiently in high dimensions. In this paper, we…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
While experimental advancements continue to expand the capabilities to control and probe non-equilibrium quantum matter at an unprecedented level, the numerical simulation of the dynamics of correlated quantum systems remains a pivotal…
The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite its ease of implementation of one-qubit gates. Two-qubit gates necessarily need a nonlinear…
Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…