[quantum-info] Next week's PIQuDos

[Markus Mueller]

Hi all,

next week, we have a talk by Dan Browne on Wednesday at 4pm in the Time 
Room.

Best wishes,
Markus



Title: *Quantum Reed-Muller codes and Magic State distillation in all 
prime dimensions*
Speaker: Dan Browne (University College London)

Abstract:

Joint work with Earl Campbell (FU-Berlin) and Hussain Anwar (UCL)

Magic state distillation is a key component of some high-threshold 
schemes for fault-tolerant quantum computation [1], [2]. Proposed by 
Bravyi and Kitaev [3] (and implicitly by Knill [4]), and improved by 
Reichardt [4], Magic State Distillation is a method to broaden the 
vocabulary of a fault-tolerant computational model, from a limited set 
of gates (e.g. the Clifford group or a sub-group[2])  to full 
universality, via the preparation of mixed ancilla qubits which may be 
prepared without fault tolerant protection.

Magic state distillation schemes have a close relation with quantum 
error correcting codes, since a key step in such protocols [5] is the 
projection onto a code subspace. Bravyi and Kitaev proposed two 
protocols; one based upon the 5-qubit code, the second derived from a 
punctured Reed-Muller code. Reed Muller codes are a very important 
family of classical linear code. They gained much interest [6] in the 
early years of quantum error correction theory, since their properties 
make them well-suited to the formation of quantum codes via the 
CSS-construction [7]. Punctured Reed-Muller codes (loosely speaking, 
Reed-Muller codewords with a bit removed) in particular lead to quantum 
codes with an unusual property, the ability to implement non-Clifford 
gates transversally [8].

Most work in fault-tolerant quantum computation focuses on qubits, 
but fault tolerant constructions can be generalised to higher dimensions 
[9]  - particularly readily for prime dimensions. Recently, we presented 
the first magic state distillation protocols [10] for non-binary 
systems, providing explicit protocols for the qutrit case (complementing 
a recent no-go theorem demonstrating bound states for magic state 
distillation in higher dimensions [11]). In this talk, I will report on 
more recent work [12], where the properties of punctured Reed-Muller 
codes are employed to demonstrate Magic State distillation protocols for 
all prime dimensions. In my talk, I will give a technical account of 
this result and present numerical investigations of the performance of 
such a protocol in the qutrit case. Finally, I will discuss the 
potential for application of these results to fault-tolerant quantum 
computation.


This will be a technical talk, and though some concepts of linear codes 
and quantum codes will be briefly revised, I will assume that listeners 
are familiar with quantum error correction theory (e.g. the stabilizer 
formalism and the CSS construction) for qubits.

[1] E. Knill. Fault-tolerant postselected quantum computation: schemes, 
quant-ph/0402171
[2] R. Raussendorf, J. Harrington and K. Goyal, Topological 
fault-tolerance in cluster state quantum computation, 
arXiv:quant-ph/0703143v1
[3] S. Bravyi and A. Kitaev. Universal quantum computation based on a 
magic states distillation, quant- ph/0403025
[4] B. W. Reichardt, Improved magic states distillation for quantum 
universality, arXiv:quant-ph/0411036v1
[5] E.T. Campbell and D.E. Browne, On the Structure of Protocols for 
Magic State Distillation, arXiv:0908.0838
[6] A. Steane, Quantum Reed Muller Codes, arXiv:quant-ph/9608026[7] 
Nielsen and Chuang, Quantum Information and Computation, chapter 10
[8] E. Knill, R. Laflamme, and W. Zurek, Threshold accuracy for 
quantum computation, quant-ph/9610011
[9] D. Gottesman, Fault-Tolerant Quantum Computation with 
Higher-Dimensional Systems, quant-ph/9802007
[10] H. Anwar, E.T Campbell and D.E. Browne, Qutrit Magic State 
Distillation, arXiv:1202.2326
[11] V. Veitch, C. Ferrie, J. Emerson, Negative Quasi-Probability 
Representation is a Necessary Resource for Magic State 
Distillation, arXiv:1201.1256v3
[12] H. Anwar, E.T Campbell and D.E. Browne, in preparation



Date: May 02, 2012 - 4:00 pm
Series: Perimeter Institute Quantum Discussions
Location: Time Rm


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