Related papers: Algorithmic approach to Cosmological Coherent Stat…
Being able to perform explicit computations in a nonperturbative, Planckian regime is key to understanding quantum gravity as a fundamental theory of gravity and spacetime. Rather than a variety of different approaches to quantum gravity,…
It is shown that in the theory of discrete quantum gravity the cosmological constant problem can be solved due to the phenomena of elliptic operators spectrum "loosening" and universe inflation.
The paper is concerned with the coherent quantum Linear Quadratic Gaussian (CQLQG) control problem for time-varying quantum plants governed by linear quantum stochastic differential equations over a bounded time interval. A controller is…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
High order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution $\Delta x$) with only a moderate increase to computational expense. Significant…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an…
Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its…
General Relativity is an extremely successful theory, at least for weak gravitational fields, however, it breaks down at very high energies, such as in correspondence of the initial singularity. Quantum Gravity is expected to provide more…
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…
Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…
This paper is concerned with the Coherent Quantum Linear Quadratic Gaussian (CQLQG) control problem of finding a stabilizing measurement-free quantum controller for a quantum plant so as to minimize an infinite-horizon mean square…
This paper is concerned with linear-quadratic-Gaussian (LQG) control for a field-mediated feedback connection of a plant and a coherent (measurement-free) controller. Both the plant and the controller are multimode open quantum harmonic…
Quantum field theories underlie all of our understanding of the fundamental forces of nature. The are relatively few first principles approaches to the study of quantum field theories [such as quantum chromodynamics (QCD) relevant to the…
This thesis is a study of quantum error-correction codes from an algebraic perspective. We concern ourselves not only with quantum codes but also protocols to perform logical quantum computation using such codes. We derive new methods of…
We design two variational algorithms to optimize specific 2-local Hamiltonians defined on graphs. Our algorithms are inspired by the Quantum Approximate Optimization Algorithm. We develop formulae to analyze the energy achieved by these…
Coherent state functional integral for the minisuperspace model of loop quantum cosmology is studied. By the well-established canonical theory, the transition amplitude in the path integral representation of loop quantum cosmology with…
This study presents a novel quantum algorithm for lattice gas automata simulation with a single time step, demonstrating logarithmic complexity in terms of $CX$ gates. The algorithm is composed of three main steps: collision, mapping, and…
Simulating quantum dynamics of lattice gauge theories (LGTs) is an exciting frontier in quantum science. Programmable quantum simulators based on neutral atom arrays are a promising approach to achieve this goal, since strong Rydberg…