Implementation Schemes for the Factorized Quantum Lattice-Gas Algorithm for the One Dimensional Diffusion Equation using Persistent-Current Qubits

J. Phys. A: Math. Theor.

Colburn

2007

The controlled-NOT (CNOT) gate is widely used in quantum circuits and in current and proposed quantum computing technologies. We investigate the feasibility and minimal implementation of CNOT from specific model Hamiltonian operators that have appeared in the literature. We follow an algebraic approach that provides an analytic solution. Our results are relevant to effective two-qubit Hamiltonians currently being considered for spin-based, superconductivity-based and other implementations of quantum computing.

Section: Alternative Techniques For the Matrix Exponentialmentioning

confidence: 99%

“…The collision operator for the most part has been based upon the SWAP 1/2 gate. Besides current NMR implementation [15], superconducting qubits [16][17][18][19][20] and optical qubits appear promising.…”

Section: Introductionmentioning

confidence: 99%

Feasibility of the controlled-NOT gate from certain model Hamiltonians

J. Phys. A: Math. Theor.

Colburn

2007

“…Many further avenues for physical implementations of type II QCs should exist. These include other spin-based systems, coupled ion or neutral atom traps and flux-, charge-or phase-based superconducting qubit systems (Berns & Orlando 2005). An attraction of the type II approach is the possibility of realization significantly prior to large-scale type I quantum computers.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional linear diffusion for image enhancement on a type II quantum computer

Colburn

2007

Proc. R. Soc. A.

We describe how multidimensional linear diffusion with application to image processing could be carried out on a hybrid classical–quantum computer. We present the quantum-lattice-gas-based algorithms, their effective finite difference approximations and representative simulation results. The methods for two-dimensional diffusion processing are particularly relevant to image enhancement tasks. We additionally demonstrate an extension to constrained linear diffusion that provides for non-uniform image smoothing. The simulation results and accompanying analysis support the utility of both classical and classical–quantum lattice gases for image enhancement. The diffusion modelling has applicability to many other fields including biological and physical science.

Quantum lattice gas approach for the Maxwell equations

2008

Quantum Inf Process

We show that a quantum lattice gas approach can provide a viable means for numerically solving the classical Maxwell equations. By casting the Maxwell equations in Dirac form, the propagator may be discretized, and we describe how the accuracy relative to the time step may be systematically increased. The quantum lattice gas form of the discretization is suitable for implementation on hybrid classical-quantum computers. We discuss a number of extensions, including application to inhomogeneous media.