Curator's Take
This research tackles a crucial challenge for near-term quantum computers simulating fermionic systems like molecules and materials: how different ways of encoding fermions onto qubits affect their resilience to noise. The findings reveal that local encoding schemes maintain stable results even as system size grows, while popular non-local methods like Jordan-Wigner mapping become increasingly unreliable with noise in higher dimensions. This has immediate practical implications for quantum chemistry and condensed matter simulations, suggesting researchers should prioritize local fermionic encodings when designing algorithms for today's noisy quantum devices. The work provides valuable design principles for extracting meaningful results from quantum simulations before we achieve full fault tolerance.
— Mark Eatherly
Summary
Quantum simulations before fault tolerance suffer from the intrinsic noise present in quantum computers. In this regime, extracting meaningful results greatly benefits from stability against that noise. This stability, defined as an error in observables that is independent of the system's size, is expected in local systems under local noise. In fermionic systems, the encoding of the fermionic degrees of freedom into qubits can introduce non-locality, making stability more delicate. Here, we investigate the stability to noise of fermion-to-qubit mappings. We consider noisy quantum circuits in $D$ dimensions modeled by alternating layers of local unitaries and general, single-qubit Pauli noise. We show that, when using local fermionic encodings, expectation values of quadratic fermionic observables are stable to noise in states with spatially decaying correlations: a power-law decay with exponent $μ>D$ is sufficient for stability. By contrast, we show that this stability cannot be achieved by non-local encodings such as Jordan-Wigner in $2D$, or quasi-local ones such as the Bravyi-Kitaev transform. Our findings formalize the intuition that decaying correlations of the physical systems under study provide protection against noise for local fermionic encodings, and help inform design principles in near-term quantum simulations.