Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session N64: Quantum Error Correction Foundations and Theory I
11:30 AM–2:18 PM,
Wednesday, March 8, 2023
Room: Room 415
Sponsoring
Unit:
DQI
Chair: Michael Vasmer, Perimeter Inst for Theo Phys
Abstract: N64.00008 : Homomorphic Logical Measurements*
1:18 PM–1:30 PM
Presenter:
Shilin Huang
(Duke University)
Authors:
Shilin Huang
(Duke University)
Tomas Jochym-O'Connor
(IBM TJ Watson Research Center)
Theodore J Yoder
(IBM TJ Watson Research Center)
which are successful on small codes and their concatenations. On large quantum low-density-parity-
check (LDPC) codes, however, Shor and Steane measurements have impractical time and space over-
head respectively. In this work, we widen the choice of ancilla codes by unifying Shor and Steane
measurements into a single framework, called homormophic measurements. As an example, we utilize
the theory of covering spaces to construct homomorphic measurement protocols for arbitrary X- or
Z-type logical Pauli measurements on surface codes in general, including the toric code and hyper-
bolic surface codes. These protocols do not require repetitive measurements or complicated ancilla
state preparation procedures such as distillation, which overcomes the difficulties of both Shor and
Steane methods. In contrast to other existing methods such as lattice surgery, conventional surface
code decoders can be directly applied to our constructions. The conceptual idea of our framework can
be extended to other quantum LDPC codes, which presents a new direction of fault-tolerant logical
operation design.
*S.H. is supported by IARPA (W911NF-16-1-0082), ARO (W911NF-21-1-0005) and NSF (CCF-1832377).
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