Mitigating Errors in Local Fermionic Encodings

• URL: http://arxiv.org/abs/2003.07125v2
• Date: Mon, 15 Jun 2020 18:32:08 GMT
• Title: Mitigating Errors in Local Fermionic Encodings
• Authors: Johannes Bausch, Toby Cubitt, Charles Derby, Joel Klassen
• Abstract summary: We show that fermionic encodings with low-weight representations of local fermionic operators can still exhibit error mitigating properties. In particular when undetectable errors correspond to "natural" fermionic noise. This suggests that even when employing low-weight fermionic encodings, error rates can be suppressed in a similar fashion to high distance codes.
• Score: 6.0409040218619685
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum simulations of fermionic many-body systems crucially rely on mappings from indistinguishable fermions to distinguishable qubits. The non-local structure of fermionic Fock space necessitates encodings that either map local fermionic operators to non-local qubit operators, or encode the fermionic representation in a long-range entangled code space. In this latter case, there is an unavoidable trade-off between two desirable properties of the encoding: low weight representations of local fermionic operators, and a high distance code space. Here it is argued that despite this fundamental limitation, fermionic encodings with low-weight representations of local fermionic operators can still exhibit error mitigating properties which can serve a similar role to that played by high code distances. In particular when undetectable errors correspond to "natural" fermionic noise. We illustrate this point explicitly for two fermionic encodings: the Verstraete-Cirac encoding, and an encoding appearing in concurrent work by Derby and Klassen. In these encodings many, but not all, single-qubit errors can be detected. However we show that the remaining undetectable single-qubit errors map to local, low-weight fermionic phase noise. We argue that such noise is natural for fermionic lattice models. This suggests that even when employing low-weight fermionic encodings, error rates can be suppressed in a similar fashion to high distance codes, provided one is willing to accept simulated natural fermionic noise in their simulated fermionic system.

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