Bound on quantum computation time: Quantum error correction in a critical environment

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2010-08-31

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Abstract

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user. © 2010 The American Physical Society.

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10.1103/PhysRevA.82.020303

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Novais, E, ER Mucciolo and HU Baranger (2010). Bound on quantum computation time: Quantum error correction in a critical environment. Physical Review A - Atomic, Molecular, and Optical Physics, 82(2). p. 20303. 10.1103/PhysRevA.82.020303 Retrieved from https://hdl.handle.net/10161/3348.

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Scholars@Duke

Baranger

Harold U. Baranger

Professor of Physics

The broad focus of Prof. Baranger's group is quantum open systems at the nanoscale, particularly the generation of correlation between particles in such systems. Fundamental interest in nanophysics-- the physics of small, nanometer scale, bits of solid-- stems from the ability to control and probe systems on length scales larger than atoms but small enough that the averaging inherent in bulk properties has not yet occurred. Using this ability, entirely unanticipated phenomena can be uncovered on the one hand, and the microscopic basis of bulk phenomena can be probed on the other. Additional interest comes from the many links between nanophysics and nanotechnology. Within this thematic area, our work ranges from projects trying to nail down realistic behavior in well-characterized systems, to more speculative projects reaching beyond regimes investigated experimentally to date.

Correlations between particles are a central issue in many areas of condensed matter physics, from emergent many-body phenomena in complex materials, to strong matter-light interactions in quantum information contexts, to transport properties of single molecules. Such correlations, for either electrons or bosons (photons, plasmons, phonons,…), underlie key phenomena in nanostructures. Using the exquisite control of nanostructures now possible, experimentalists will be able to engineer correlations in nanosystems in the near future. Of particular interest are cases in which one can tune the competition between different types of correlation, or in which correlation can be tunably enhanced or suppressed by other effects (such as confinement or interference), potentially causing a quantum phase transition-- a sudden, qualitative change in the correlations in the system.

My recent work has addressed correlations in both electronic systems (quantum wires and dots) and photonic systems (photon waveguides). We have focused on 3 different systems: (1) qubits coupled to a photonic waveguide, (2) quantum dots in a dissipative environment, and (3) interfaces between graphene and a superconductor, particularly when graphene is in the quantum Hall state. The methods used are both analytical and numerical, and are closely linked to experiments.


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