arXiv subjects

C. P. Williams

Publications and source records attributed to C. P. Williams.

2 recordsLinked to original sources

arXiv2001

Universal Quantum Gates for Single Cooper Pair Box Based Quantum Computing

We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT gates within the context of the Single Cooper Pair Box (SCB) approach to quantum computing. Such gates are sufficient to support universal quantum computation. Quantum gate operations are achieved by applying sequences of voltages and magnetic fluxes to single qubits or pairs of qubits. Neither the temporal duration, nor the starting time, of a gate operation is used as a control parameter. As a result, the quantum gates have a constant and known duration, and depend upon standard control parameter sequences regardless of when the gate operation begins. This simplifies the integration of quantum gates into parallel, synchronous, quantum circuits. In addition, we demonstrate the ability to fabricate such gates, and large-scale quantum circuits, using current e-beam lithography technology. These features make the SCB-based scheme a credible contender for practical quantum computer hardware.

quant-ph↗

arXiv1998

Nested quantum search and NP-complete problems

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting this standard search algorithm. The number of iterations required to find the solution of an average instance of a constraint satisfaction problem scales as $\sqrt{d^α}$, with a constant $α<1$ depending on the nesting depth and the problem considered. When applying a single nesting level to a problem with constraints of size 2 such as the graph coloring problem, this constant $α$ is estimated to be around 0.62 for average instances of maximum difficulty. This corresponds to a square-root speedup over a classical nested search algorithm, of which our presented algorithm is the quantum counterpart.

quant-ph↗