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The simulation of physical phenomena is one of the main applications of computation. In this key area quantum computers are expected to become useful long before they will become capable to solve large-scale problems such as integer factorisation. The EDIQIP project developed new efficient quantum algorithms for the simulation of complex classical and quantum dynamics, including phenomena such as dynamical localization, Anderson metal-insulator transitions, strange attractors in classical dissipative systems and information spreading in small-world systems. NMR(Nuclear Magnetic Resonance)-based quantum computation of dynamical localization has been recently implemented by the group of D.Cory at MIT.
Quantum computers, relying on the weird logics of the quantum world, can be much faster than any classical machine, since they perform, so to speak, all the calculations at once. However, their construction is rather challenging, since they are prone to errors and decoherence. The EDIQIP project addressed an important question: what is the influence of static imperfections in computer hardware (parasitic coupling between qubits, imperfections in qubit energies). It determined a universal law, based on random matrix theory invented by Wigner for complex nuclei and atoms, for the computation fidelity decay induced by internal static imperfections.
The theoretical predictions were confirmed by extensive numerical simulations of a quantum algorithms. The decay law provides a transition between exponential and Gaussian behaviours and is characterized by two time-scales analogous to the Thouless and Heisenberg times for probability decay in mesoscopic systems. These studies establish the universal accuracy bounds for quantum computation in presence of residual static couplings between qubits. They are essential to estimate the individual gates fidelity required for a large scale quantum computation. The universal fidelity decay law induced by dissipative effects have also been determined and compared with the effects of static imperfections.
Quantum computing and quantum information processing can be simulated with the given codes on a classical computer for a moderate number of qubits (20) in presence of realistic internal imperfections and external decoherence. The Quatware Library was established in the framework of the EC IST-FET project EDIQIP ("Effects of decoherence and imperfections for quantum information processing"). It provides a diversified code basis for the classical simulation of realistic quantum computations. It can be useful to test the effects of various realistic noise sources on the stability of quantum information processing, thus optimising quantum hardware design.
A general quantum error correction method is presented which is capable of correcting coherent errors originating from static residual inter-qubit couplings in a quantum computer. It is based on a randomisation of static imperfections in a many-qubit system by the repeated application of Pauli operators, which change the computational basis. This Pauli-Random-Error-Correction (PAREC)-method eliminates coherent errors produced by static imperfections and increases significantly the maximum time over which realistic quantum computations can be performed reliably. Furthermore, it does not require redundancy so that all physical qubits involved can be used for logical purposes. We expect that in the future this general-purpose code will be used to improve the accuracy of quantum computation.
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