Towards Large-Scale Quantum Computation

Abstract

This thesis deals with a series of quantum computer implementation issues from the Kane 31P in 28Si architecture to Shor's integer factoring algorithm and beyond. The discussion begins with simulations of the adiabatic Kane CNOT and readout gates, followed by linear nearest neighbor implementations of 5-qubit quantum error correction with and without fast measurement. A linear nearest neighbor circuit implementing Shor's algorithm is presented, then modified to remove the need for exponentially small rotation gates. Finally, a method of constructing optimal approximations of arbitrary single-qubit fault-tolerant gates is described and applied to the specific case of the remaining rotation gates required by Shor's algorithm.

PhD thesis, 185 pages, 59 figures, combination of articles quant-ph/0207103, quant-ph/0306018, quant-ph/0311116, quant-ph/0402077, quant-ph/0402196, quant-ph/0411206 and other research together with additional discussion and review material

References in corpus (11)

• Fast Quantum Modular Exponentiation
• Local Fault-tolerant Quantum Computation
• Fault-Tolerant Postselected Quantum Computation: Schemes
• Fault-Tolerant Postselected Quantum Computation: Threshold Analysis
• Threshold Error Penalty for Fault Tolerant Computation with Nearest Neighbour Communication
• Improved ancilla preparation scheme increases fault-tolerant threshold
• Electrical readout of a spin qubit without double occupancy
• Stabilizer Codes for Continuous-variable Quantum Error Correction
• Generalization of the Deutsch algorithm using two qudits
• Qubiter Algorithm Modification, Expressing Unstructured Unitary Matrices with Fewer CNOTs
• The Continuous Variable Quantum Teleportation Controversy