Some Publications by Andrew Cross

A. W. Cross, D. P. DiVincenzo, B. M. Terhal "A comparative code study for quantum fault-tolerance," Quantum Physics (2007), quant-ph/0711.1556v1 We study a comprehensive list of quantum codes as candidates of codes to be used at the bottom, physical, level in a fault-tolerant code architecture. Using the Aliferis-Gottesman-Preskill (AGP) ex-Rec method we calculate the pseudo-threshold for these codes against depolarizing noise at various levels of overhead. We estimate the logical noise rate as a function of overhead at a physical error rate of $p_0=1\times 10^{-4}$. The Bacon-Shor codes and the Golay code are the best performers in our study.

A. Cross, G. Smith, J. A. Smolin, B. Zeng, "Codeword stabilized quantum codes," Quantum Physics (2007), quant-ph/0708.1021. We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with superior parameters to any previously known. In particular, we find ((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding circuits for all codes within our framework.

P. Aliferis, A. Cross, " Subsystem Fault Tolerance with the Bacon-Shor Code," Phys. Rev. Lett 98, 220502 (2007)
Quantum Physics (2006), quant-ph/0610063v3 We discuss how the presence of gauge subsystems in the Bacon-Shor code [D. Bacon , Phys. Rev. A 73, 012340 (2006)] leads to remarkably simple and efficient methods for fault-tolerant error correction (FTEC). Most notably, FTEC does not require entangled ancillary states, and it can be implemented with nearest-neighbor two-qubit measurements. By using these methods, we prove a lower bound on the quantum accuracy threshold, 1.94×10-4 for adversarial stochastic noise, that improves previous lower bounds by nearly an order of magnitude.