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arXiv:quant-ph/0301105 · Physical Review A

Quantum computing in the presence of spontaneous emission by a combined dynamical decoupling and quantum-error-correction strategy

Kaveh Khodjasteh, Daniel A. Lidar

Published Aug 28, 2003• 32 citations
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Abstract

A method for quantum computation in the presence of spontaneous emission is proposed. The method combines strong and fast (dynamical decoupling) pulses and a quantum error correcting code that encodes n logical qubits into only $n+1$ physical qubits. Universal, fault-tolerant, quantum computation is shown to be possible in this scheme using Hamiltonians relevant to a range of promising proposals for the physical implementation of quantum computers.

DOI
10.1103/physreva.68.022322

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A method for quantum computation in the presence of spontaneous emission is proposed. The method combines strong and fast (dynamical decoupling) pulses and a quantum error correcting code that encodes n logical qubits into only n+1n+1n+1 physical qubits. Universal, fault-tolerant, quantum computation is shown to be possible in this scheme using Hamiltonians relevant to a range of promising proposals for the physical implementation of quantum computers.
Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and control of effective exchange interactions and possibly a global magnetic field. This "encoded universality" paradigm offers potential simplifications in quantum computer design since it does away with the need to control physical qubits individually. Here we show how encoded universality schemes can be combined with fault-tolerant quantum error correction, thus establishing the scalability of such schemes.
Decoherence is the main obstacle to the realization of quantum computers. Until recently it was thought that quantum error correcting codes are the only complete solution to the decoherence problem. Here we present an alternative that is based on a combination of a decoherence-free subspace encoding and the application of strong and fast pulses: ``encoded recoupling and decoupling'' (ERD). This alternative has the advantage of lower encoding overhead (as few as two physical qubits per logical qubit suffice), and direct application to a number of promising proposals for the experimental realization of quantum computers.
We present a universal fault-tolerant quantum computing architecture based on identical particle qubits (IPQs), where we find that the first-order IPQ - bath interaction fundamentally differs from the conventional first-order qubit-bath interaction. This key distinction necessitates a redesign of existing strategies to fight decoherence. We propose that the simplest quantum error correction code can be realized directly within the physical qubit, provided that conventional correction and restoration are generalized beyond unitary operations to employ physically implementable reversal operations -- naturally placing logical and physical qubits on equal footing. We further demonstrate that dynamical decoupling (DD) remains effective within this unified framework, and that a decoherence-free subspace (DFS) -- like structure emerges. Unlike previous approximate treatments, our analytically solvable IPQ-Bath model enables rigorous testing of these strategies, with numerical simulations validating their effectiveness.
Quantum computers now show the promise of surpassing any possible classical machine. However, errors limit this ability and current machines do not have the ability to implement error correcting codes due to the limited number of qubits and limited control. Therefore, dynamical decoupling (DD) and encodings that limit noise with fewer qubits are more promising. For these reasons, we put forth a model of universal quantum computation that has many advantages over strategies that require a large overhead such as the standard quantum-error correcting codes. First, we separate collective noise from individual noises on physical qubits and use a decoherence-free subspace that uses just two qubits for its encoding to eliminate collective noise. Second, our bath model is very general as it uses a spin-boson-type bath but without any Markovian assumption. Third, we are able to either use a steady global magnetic field or to devise a set of DD pulses that remove much of the remaining noise and commute with the logical operations on the encoded qubit. This allows removal of noise while implementing gate operations. Numerical support is given for this hybrid protection strategy which provides an efficient approach to deal with the decoherence problems in quantum computation and is experimentally viable for several current quantum computing systems. This is emphasized by a recent experiment on superconducting qubits which shows promise for increasing the number of gates that can be implemented reliably with some realistic parameter assumptions.
Quantum control and fault-tolerant quantum computing (FTQC) are two of the cornerstones on which the hope of realizing a large-scale quantum computer is pinned, yet only preliminary steps have been taken towards formalizing the interplay between them. Here we explore this interplay using the powerful strategy of dynamical decoupling (DD), and show how it can be seamlessly and optimally integrated with FTQC. To this end we show how to find the optimal decoupling generator set (DGS) for various subspaces relevant to FTQC, and how to simultaneously decouple them. We focus on stabilizer codes, which represent the largest contribution to the size of the DGS, showing that the intuitive choice comprising the stabilizers and logical operators of the code is in fact optimal, i.e., minimizes a natural cost function associated with the length of DD sequences. Our work brings hybrid DD-FTQC schemes, and their potentially considerable advantages, closer to realization.