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Physical Review A

Some implications of the quantum nature of laser fields for quantum computations

Julio R. Gea-Banacloche

Published Jan 4, 2002• 60 citations
Publisher

Abstract

The quantum nature of the laser fields used in many proposed schemes for the manipulation of quantum information may have important consequences for some very large scale quantum computations. Some of these consequences are explored here, focusing especially on phase errors and their effects on error-correction schemes. Depending on the way the logical gates are performed, constraints are found on either the required number of photons per coherence time put out by the laser source, or the source's power

DOI
10.1103/physreva.65.022308

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The quantum nature of the laser fields used in many proposed schemes for the manipulation of quantum information may have important consequences for some very large scale quantum computations. Some of these consequences are explored here, focusing especially on phase errors and their effects on error-correction schemes. Depending on the way the logical gates are performed, constraints are found on either the required number of photons per coherence time put out by the laser source, or the source's power
Quantum information is very fragile to environmentally and operationally induced imperfections. Therefore, the construction of practical quantum computers requires quantum error-correction techniques to protect quantum information. In particular, encoding a logical qubit into the large Hilbert space of an oscillator is a hardware-efficient way of correcting quantum errors. In this strategy, selective number-dependent arbitrary phase (SNAP) gates are vital for universal quantum control. However, the quality of SNAP gates is considerably limited by the small coupling-induced nonlinearity of the oscillator. Here, to resolve this limitation, we propose a robust scheme based on quantum optimal control via functional theory, by designing an appropriate trajectory for a target operation. Besides, we combine the geometric phase approach with our trajectory design scheme to minimize the decoherence effect, by shortening the gate time. Numerical simulation shows that both errors can be significantly mitigated and that the robustness of the geometric gate against both XXX and ZZZ errors can be maintained. Therefore, our scheme provides a promising alternative for fault-tolerant quantum computation.
Topological quantum computing has recently proven itself to be a very powerful model when considering large-scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven method of error corrected computation, with the hardware responsible for only creating a generic quantum resource (the topological lattice). Computation in this scheme is achieved by the geometric manipulation of holes (defects) within the lattice. Interactions between logical qubits (quantum gate operations) are implemented by using particular arrangements of the defects, such as braids and junctions. We demonstrate that junction-based topological quantum gates allow highly regular and structured implementation of large CNOT (controlled-not) gate networks, which ultimately form the basis of the error corrected primitives that must be used for an error corrected algorithm. We present a number of heuristics to optimise the area of the resulting structures and therefore the number of the required hardware resources.
Abstract—Topological quantum computing has recently proven itself to be a very powerful model when considering large-scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven method of error corrected computation, with the hardware responsible for only creating a generic quantum resource (the topological lattice). Computation in this scheme is achieved by the geometric manipulation of holes (defects) within the lattice. Interactions between logical qubits (quantum gate operations) are implemented by using particular arrangements of the defects, such as braids and junctions. We demonstrate that junction-based topological quantum gates allow highly regular and structured implementation of large CNOT (controlled-not) gate networks, which ultimately form the basis of the error corrected primitives that must be used for an error corrected algorithm. We present a number of heuristics to optimise the area of the resulting structures and therefore the number of the required hardware resources. I.