Date & time: Friday March 9 @ 12pm

Who: Peter Rohde

Seminar type: Research Seminar

Where: Interaction Room

Abstract:
Qubit loss and gate failure are a significant problem in many quantum computing architectures. Most notably this is the case in optical QC where photon loss, inefficient detection, inefficient state preparation, and non-determinsitic gates are a given. To combat these problems several authors have proposed schemes for tolerating qubit loss and/or gate failure. These include Nielsen’s cluster state approach to optical QC, Varnava et al’s ‘horticultural’ approach to loss tolerance, and Ralph et al’s parity encoding scheme. We demonstrate that while such schemes are very effective at tolerating qubit loss, they have the undesirable side-effect that they magnify the effects of other noise types, namely depolarizing noise. We show that there is a tradeoff relationship between the error- and loss-tolerance of such schemes. This places fundamental limitations on the degree of loss tolerance that is achievable in practise.

These observations motivate the question ‘can we say anything about the tradeoff between loss- and error-tolerance in a general scenario, rather than just for these specific protocols?’. We examine this question for the general case of non-degenerate codes, by deriving a generalization of the quantum Hamming bound. We derive the Hamming bound to explicitly include separate parameters for loss and depolarizing errors. From this follows an upper bound on the tradeoff between the number of loss and depolarizing errors a non-degenerate code can correct against.

References:

• Upper bounds on the tradeoff between loss and error rates in non-degenerate quantum error correcting codes, Peter Rohde, quant-ph/0605183
• Error tolerance and tradeoffs in loss- and failure-tolerant quantum computing schemes, Peter Rohde, Timothy Ralph, William Munro, quant-ph/0603130

Date & time: Friday March 9 @ 12pm

Who: Peter Rohde

Seminar type: Research Seminar

Where: Interaction Room

Abstract:
Qubit loss and gate failure are a significant problem in many quantum computing architectures. Most notably this is the case in optical QC where photon loss, inefficient detection, inefficient state preparation, and non-determinsitic gates are a given. To combat these problems several authors have proposed schemes for tolerating qubit loss and/or gate failure. These include Nielsen’s cluster state approach to optical QC, Varnava et al’s ‘horticultural’ approach to loss tolerance, and Ralph et al’s parity encoding scheme. We demonstrate that while such schemes are very effective at tolerating qubit loss, they have the undesirable side-effect that they magnify the effects of other noise types, namely depolarizing noise. We show that there is a tradeoff relationship between the error- and loss-tolerance of such schemes. This places fundamental limitations on the degree of loss tolerance that is achievable in practise.

These observations motivate the question ‘can we say anything about the tradeoff between loss- and error-tolerance in a general scenario, rather than just for these specific protocols?’. We examine this question for the general case of non-degenerate codes, by deriving a generalization of the quantum Hamming bound. We derive the Hamming bound to explicitly include separate parameters for loss and depolarizing errors. From this follows an upper bound on the tradeoff between the number of loss and depolarizing errors a non-degenerate code can correct against.

References:

• Upper bounds on the tradeoff between loss and error rates in non-degenerate quantum error correcting codes, Peter Rohde, quant-ph/0605183
• Error tolerance and tradeoffs in loss- and failure-tolerant quantum computing schemes, Peter Rohde, Timothy Ralph, William Munro, quant-ph/0603130