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SUMMARY:Sparse Quantum Codes from Quantum Circuits - Aram Harrow (MIT)
DTSTART:20141023T131500Z
DTEND:20141023T141500Z
UID:TALK54908@talks.cam.ac.uk
CONTACT:William Matthews
DESCRIPTION:We describe a general method for turning quantum circuits into
  sparse quantum subsystem codes. Using this prescription\, we can map an a
 rbitrary stabilizer code into a new subsystem code with the same distance 
 and number of encoded qubits but where all the generators have constant we
 ight\, at the cost of adding some ancilla qubits. With an additional overh
 ead of ancilla qubits\, the new code can also be made spatially local.\n\n
 Applying our construction to certain concatenated stabilizer codes yields 
 families of subsystem codes with constant-weight generators and with minim
 um distance d = n<sup>1 - &epsilon\;</sup> for any &epsilon\;>0. For spati
 ally local codes in D dimensions we nearly saturate a bound due to Bravyi 
 and Terhal and achieve d = n<sup>(1-&epsilon\;-1/D)</sup>. Previously the 
 best code distance achievable with constant-weight generators in any dimen
 sion\, due to Freedman\, Meyer and Luo\, was O(sqrt(n log(n))) for a stabi
 lizer code.\n\nJoint work with Dave Bacon\, Steve Flammia and Jonathan Shi
LOCATION:MR3\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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