Fermion-to-qubit mappings and their error mitigating properties
As we move towards the era of quantum computers with 1000+ qubits, the most promising application able to harness the potential of such devices is quantum simulation. Simulating fermionic systems is both a well-formulated problem with clear real-world applications and a computationally challenging task. In order to simulate a system of fermions on a quantum computer, one has to map the fermionic Hamiltonian to a qubit Hamiltonian. The most popular such mapping is the Jordan-Wigner encoding, which suffers from inefficiencies caused by the non-locality of the encoded operators. As a result, alternative local mappings have been proposed that solve the problem of long encoded operators at the expense of constant factor of qubits. Some of these alternative mappings end up possessing non-trivial stabilizer structure akin to popular quantum error correction (QEC) codes.
In this talk, I will introduce the problem of mapping fermionic operators to qubit operators and how the selection of an encoding could affect resource requirements in near-term simulations. I will also talk about error mitigation approaches utilizing the stabilizer structure of certain encodings as well as using stabilizer simulation to assess the effectiveness of such approaches.
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