Addressing fidelity decay in quantum computations
Recent progress in quantum computation has increasingly attracted the interest of the scientific community. Due to the massive parallelism of many-body quantum mechanics forming its basis, quantum algorithms promise unprecedented information processing performances. As a consequence, quantum computers will have the potential to simulate complex mechanical behaviours ranging from quantum systems to models describing electrons movement within crystals. Research pursued within the interdisciplinary and transnational EDIQIP project network of universities and research centres focused on decoherence barriers. Quantum information processing relies upon the ability to ensure and control the unitary evolution of an array of coupled qubits for long periods of time. The term 'decoherence' includes the degradation of superposition states, which essentially leads to the loss of stored information and causes failures in computation. Decoherence induced by unavoidable couplings to the surrounding environment is one of the main obstacles to the experimental implementation of a quantum computer. Even if there were no external couplings, internal static imperfections remain inside a quantum computer. These static imperfections generate residual couplings between qubits and variations of energy level-spacing from one qubit to another. The aim of researchers at the Université Paul Sabatier was to investigate their effect on the accuracy of quantum computations. Extensive numerical and analytical studies were conducted on a well-defined quantum algorithm, describing dynamics in a mixed phase space with chaotic and integrable motion. On the basis of Random matrix theory (RMT) a scaling law for universal fidelity decay was established and extended to include dissipative effects. In addition to the exponential decay, imperfections were shown to cause a Gaussian decrease limiting siginificantly the maximum reliable computation times. In the next phase of research, the EDIQIP project partners will exploit knowledge and expertise gained in developing a general correcting method to overcome disastrous effects of static imperfections.
