Superconducting quantum computation

Abstract

Quantum computers have the potential to solve certain problems with a significant reduction in resources from their classical counterparts. For this reason, quantum information science has grown into an extremely active field of physics with constant theoretical and experimental development. Superconducting devices provide the functionality necessary to store and process quantum information in a large-scale quantum computer. In this dissertation, a survey of existing and proposed superconducting quantum bits (qubits) is given while demonstrating the mathematical formalism that is necessary to treat superconducting circuits quantum mechanically.

High fidelity demonstration of universal gates is one of the current focuses of both theoretical and experimental work in quantum computation. Of the established universal two qubit logic gates, the most well-known and useful in algorithm design is the controlled-NOT (CNOT). Protocols for performing the CNOT gate are surveyed here and generalized to a protocol that applies to any configuration of weakly coupled two-level system. In this context, a technique for quantum gate design is described.

A certain superconducting quantum computing architecture is focused on, that of a large-area, current-biased Josephson-junction phase qubit coupled to the dilatational mode of a nanomechanical resonator. While the Josephson phase qubit has proven repeatedly to have the functionality to store and process quantum information, certain other quantum devices, like mechanical or $LC$ oscillators, can store information longer with less interaction from the environment. However, quantum state prepared in a superconducting qubit can be stored and later retrieved from an attached high-Q resonator. Here the memory capabilities of a such a qubit-resonator system are studied.

Quantum logic gates are the building blocks of quantum algorithms, an important class of which are quantum simulation algorithms. Here, we introduce an alternative approach to quantum simulation that does not involve logic gate decomposition. Alternatively, a direct mapping is given between the control parameters of a tunable quantum computer and the matrix element of $H_{rm s}(t)$, an arbitrary, real, time-dependent $ntimes n$ dimensional Hamiltonian that is simulated in the $n$-dimensional `single excitation' subspace of the quantum computer. Simulation of a molecular collison with three Josephson phase qubits is demonstrated and the fidelity of the simulation is studied.