Abstract
We propose a family of local CSS stabilizer codes as possible candidates for self-correcting quantum memories in 3D. The construction is inspired by the classical Ising model on a Sierpinski carpet fractal, which acts as a classical self-correcting memory. Our models are naturally defined on fractal subsets of a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does not imply that these models can be realized with local interactions in , we also discuss this possibility. The X and Z sectors of the code are dual to one another, and we show that there exists a finite temperature phase transition associated with each of these sectors, providing evidence that the system may robustly store quantum information at finite temperature.
Highlights
There is significant interest from both an abstract and practical perspective as to if and how self-correcting quantum memories might be realized
Though we call them codes, fractal product codes (FPCs) should more properly be considered Hamiltonian systems given by a sum of stabilizer generators, and we show that such systems have two phase transitions at finite temperature, one associated with each sector (X or Z) of the codes we present are (CSS) code
C G Brell expect the phase transitions we identify to correspond to the appearance of thermal stability for one preferred encoded qubit associated with global degrees of freedom
Summary
The construction is inspired by the classical Ising model on a Sierpinski carpet fractal, licence. Any further distribution of this work must maintain a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does not imply that these attribution to the author(s) and the title of models can be realized with local interactions in 3, we discuss this possibility. The X and Z the work, journal citation sectors of the code are dual to one another, and we show that there exists a finite temperature phase and DOI. Transition associated with each of these sectors, providing evidence that the system may robustly store quantum information at finite temperature
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