On the feasibility of self-correcting quantum memory

Beni Yoshida

Wolfgang Tittel, Mikael Afzelius, Nicolas Gisin +2 more

Sergey B. Bravyi, Jeongwan Haah

A big open question in the quantum information theory concerns the feasibility of a self-correcting quantum memory. A quantum state recorded in such memory can be stored reliably for a macroscopic time without need for active error correction, if the memory is in contact with a cold enough thermal bath. Here we report analytic and numerical evidence for self-correcting behavior in the quantum spin lattice model known as the 3D cubic code. We prove that its memory time is at least L(cβ), where L is the lattice size, β is the inverse temperature of the bath, and c>0 is a constant coefficient. However, this bound applies only if the lattice size L does not exceed a critical value which grows exponentially with β. In that sense, the model can be called a partially self-correcting memory. We also report a Monte Carlo simulation indicating that our analytic bounds on the memory time are tight up to constant coefficients. To model the readout step we introduce a new decoding algorithm, which can be implemented efficiently for any topological stabilizer code. A longer version of this work can be found in Bravyi and Haah, arXiv:1112.3252.

Cécile Grèzes

David Poulin, Roger G. Melko, Matthew B. Hastings

Motivated by the growing interest in self-correcting quantum memories, we study the feasibility of self-correction in classical lattice systems composed of bounded degrees of freedom with local interactions. We argue that self-correction, including a requirement of stability against external perturbation, cannot be realized in system with broken global symmetries such as the two-dimensional Ising model, but that systems with local, i.e., gauge symmetries, have the required properties. Previous work identified a three-dimensional (3D) quantum system which realizes a self-correcting classical memory [E. Dennis et al., J. Math. Phys. 43, 4452 (2002)]. Here, we show that a purely classical 3D system, Wegner's Ising lattice gauge model [F. J. Wegner, J. Math. Phys. 12, 2259 (1971)], can also realize this self-correction despite having an extensive ground-state degeneracy. We give a detailed numerical study to support the existence of a self-correcting phase in this system, even when the gauge symmetry is explicitly broken. More generally, our results obtained by studying the memory lifetime of the system are in quantitative agreement with the phase diagram obtained from conventional analysis of the system's specific heat [I. S. Tupitsyn et al., Phys. Rev. B 82, 085114 (2010)], except that self-correction extends beyond the topological phase, past the lower critical temperature.

Yong Hui Yu