Local Quantum Encodings Maintain Stability Despite Increasing Computer Noise

Guillermo González-García and colleagues at Phasecraft Ltd. have shown that the stability of quantum simulations, defined as an error in observable results independent of system size, is strongly influenced by how fermionic systems are mapped onto qubits. The work reveals that local fermionic encodings maintain stability against noise in states exhibiting spatially decaying correlations, specifically with a power-law decay exponent greater than the system’s dimensionality. Commonly used non-local and quasi-local encodings, including the Jordan-Wigner and Bravyi-Kitaev transforms, cannot achieve the same level of noise resilience. These findings offer key insight into designing more resilient near-term quantum simulations by using the protective qualities of decaying correlations within physical systems. Stability in quantum simulations emerges with spatially decaying correlations and local fermionic Error rates in quantum simulations utilising local fermionic encodings remained independent of system size when a power-law decay exponent, μ, exceeds the dimensionality of the system, D, for the first time. A threshold of μ > D now guarantees this stability for quadratic fermionic observables under Pauli noise, contrasting with previous limitations where stability against noise in fermion-to-qubit mappings was unproven. Researchers at University College London and the University of Oxford found that commonly used non-local encodings, including the Jordan-Wigner and Bravyi-Kitaev transforms, cannot achieve this level of durability, highlighting the importance of encoding choice. This result is particularly significant because fermionic systems are ubiquitous in modelling materials science, high-energy physics, and quantum chemistry, and accurately simulating their behaviour is a central goal of quantum computation. These findings formalise the protective effect of spatially decaying correlations in physical systems, offering important design principles for near-term quantum simulations and paving the way for more robust calculations. Simulations revealed that an exponent greater than the system’s dimensionality, μ > D, ensures a consistent error rate regardless of system size for quadratic fermionic observables impacted by Pauli noise, which represents errors arising from single-qubit operations. Pauli noise is a realistic model of errors present in current quantum hardware, stemming from imperfections in qubit control and measurement. The quadratic fermionic observables represent fundamental properties of the system being simulated, such as energy or particle density. Further analysis showed that the Jordan-Wigner encoding fails to achieve this durability in two-dimensional systems, and the Bravyi-Kitaev transform, a quasi-local encoding, also falls short; this reinforces theoretical understanding of noise mitigation strategies. The Jordan-Wigner transform, while conceptually simple, introduces long-range qubit interactions, making it susceptible to noise propagation. The Bravyi-Kitaev transform attempts to improve locality but still exhibits limitations in maintaining stability as system size increases. The concept of ‘locality’ is crucial here. Local encodings map fermionic degrees of freedom to qubits in a way that preserves the short-range interactions inherent in many physical systems. This means that a change to one qubit primarily affects its immediate neighbours, limiting the spread of errors. Non-local encodings, conversely, can create long-range dependencies between qubits, allowing errors to propagate more easily throughout the system. The power-law decay exponent, μ, quantifies how quickly the spatial correlations between fermions diminish. A larger μ indicates slower decay and stronger correlations, which, when combined with a local encoding, contribute to enhanced stability. The dimensionality, D, of the system defines the spatial extent of the simulation; for example, D=1 represents a one-dimensional chain, D=2 a two-dimensional lattice, and D=3 a three-dimensional volume. Error mitigation versus computational cost in fermionic quantum simulations A fundamental trade-off remains despite this breakthrough in understanding how to encode stability into quantum simulations. While local encodings offer durability against noise, the resulting error scaling, though independent of system size, is demonstrably steeper than that achieved by directly simulating fermionic systems on dedicated hardware. This presents a practical challenge, requiring researchers to weigh the benefits of error mitigation against the increased computational cost of qubit encoding. The ‘steeper’ error scaling implies that, for a given level of accuracy, a local encoding may require significantly more qubits than a direct fermionic simulation, increasing the demands on quantum hardware resources. This is because local encodings often require more qubits to represent the same fermionic system, effectively increasing the complexity of the quantum circuit. Acknowledging that steeper error scaling exists when directly simulating fermionic systems presents a genuine hurdle, this research remains vital for near-term quantum computing. Carefully chosen methods of converting the behaviour of electrons, known as fermions, into quantum bits, or qubits, can sharply improve stability against the inherent errors in today’s machines. The establishment of a key link between the method of encoding fermionic systems into qubits and the durability of quantum simulations to noise is a significant advancement. Locally-encoded systems, when modelling physical systems with naturally diminishing interactions, maintain a consistent level of accuracy regardless of size, addressing a significant obstacle to near-term quantum computation. This confirms that spatial correlations offer inherent protection against errors when using appropriate encoding strategies, and moves beyond simply mitigating errors by revealing how the choice of encoding directly impacts stability, with non-local methods like the widely-used Jordan-Wigner transform proving inadequate in higher dimensions. The implications extend to the development of quantum algorithms for materials discovery, where accurate simulations of electronic structure are crucial for predicting material properties. Furthermore, the findings have implications for the design of quantum error correction codes. While full fault-tolerance remains a distant goal, understanding how to encode systems to minimise error propagation can inform the development of more effective error mitigation strategies in the interim. The research highlights the importance of considering the underlying physical properties of the system being simulated when choosing a fermionic encoding. By leveraging the natural decay of correlations, researchers can potentially reduce the burden on error correction and achieve more reliable results with near-term quantum computers. Future work could explore the application of these principles to other types of quantum simulations and investigate the interplay between encoding choice, noise models, and error correction techniques. The research demonstrated that locally-encoded fermionic systems, representing particles with decaying spatial interactions, exhibited stability against noise in quantum simulations regardless of system size. This matters because it suggests a pathway to more reliable results from current, imperfect quantum computers, potentially accelerating fields like materials discovery which rely on accurate electronic structure modelling. Specifically, the team showed power-law decay with an exponent greater than the system’s dimensions ensured stability, unlike non-local encodings such as the Jordan-Wigner transform. These findings may lead to the development of improved error mitigation strategies and inform the design of more effective quantum algorithms for near-term devices. 👉 More information 🗞 On the stability to noise of fermion-to-qubit mappings 🧠 ArXiv: https://arxiv.org/abs/2603.22141 Tags: