Quantum computers are noisy, and Quantum Error Correction (QEC) seeks to insulate quantum information against this reality by redundantly encoding logical information in the correlations between many physical qubits. There is a zoo of QEC codes that demonstrate a threshold - improved decoding performance as the number of physical qubits increases - but this is not the only requirement for reliable quantum computation with NISQ hardware. Fault tolerance further demands that logical information remain protected when stabilizer measurements and decoding operations are noisy, which has led to developments in the design of transversal logical operations and classical decoders for specific codes.
The above is an exceedingly brief summary of the vast field of QEC, which we aim to formulate within a new paradigm. The overwhelming majority of the work discussed above applies only to a gate-based model of quantum computation, which is in truth an approximation of the analog nature of the operations actually performed in hardware. The development of experimental platforms for analog quantum simulation also drives the need for a useful definition of fault tolerance in a continuous time setting.
Inspired by a scheme [1] for protecting logical information against single-qubit errors during time evolution by a logical Hamiltonian, we seek a more general class of such protocols that can protect against correlated noise on a larger number of qubits while obeying a constraint on the locality of the engineered interactions. We are also interested in expressing other components of traditional QEC, such as code concatenation and stabilizer measurements, in an analog setting.
[1] Y. Cao, S. Liu, H. Deng, Z. Xia, X. Wu, and Y.-X. Wang, Robust Analog Quantum Simulators by Quantum Error-Detecting Codes, arXiv:2412.07764.