Google Research

Majorana Loop Stabilizer Codes for Error Correction of Fermionic Quantum Simulations

Abstract

Locality-preserving fermion-to-qubit mappings are especially useful to simulating lattice fermion models (e.g., the Hubbard model) on a quantum computer. They avoid the overhead associated with non-local parity terms in mappings such as the Jordan-Wigner transformation. As a result, they often provide solutions with lower circuit depth and gate complexity. Interestingly, these locality-preserving mappings encode the fermionic state in the common +1 eigenstate of a set of stabilizers, akin to quantum error-correcting codes. Here, we discuss a couple of known locality-preserving mappings and their abilities to correct/detect single-qubit errors. We also introduce a locality-preserving map, whose stabilizers are products of Majorana operators on closed paths of the fermionic hopping graph. The code can correct all single-qubit errors on a 2-dimensional square lattice, while previous locality-preserving codes can only detect single-qubit errors on the same lattice. Our code also has the advantage of having lower-weight logical operators. We expect that error-mitigating schemes with low overhead to be useful to the success of near-term quantum algorithms such as the variational quantum eigensolver.

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