Preprocessing for correlated topological quantum error correction

#The present disclosure relates generally to algorithms for quantum error correction for quantum computing systems.

#Quantum computing is a computing method that takes advantage of quantum effects, such as superposition of basis states and entanglement to perform certain computations more efficiently than a classical digital computer. In contrast to a digital computer, which stores and manipulates information in the form of bits, e.g., a “1” or “0,” quantum computing systems can manipulate information using quantum bits (“qubits”). A qubit can refer to a quantum device that enables the superposition of multiple states, e.g., data in both the “0” and “1” state, and/or to the superposition of data, itself, in the multiple states. In accordance with conventional terminology, the superposition of a “0” and “1” state in a quantum system may be represented, e.g., as a|0+b|1 The “0” and “1” states of a digital computer are analogous to the |0 and |1 basis states, respectively of a qubit.

#Aspects and advantages of embodiments of the present disclosure will be set forth in part in the following description, or can be learned from the description, or can be learned through practice of the embodiments.

#Detailed discussion of embodiments directed to one of ordinary skill in the art is set forth in the specification, which refers to the appended figures, in which:

#FIG. 1 depicts an example embodiment of a quantum computing system according to example aspects of the present disclosure;

#FIG. 2A depicts a time-layer visualization of a set of error detection measurements for an example embodiment of a quantum computing system according to example aspects of the present disclosure;

#Example aspects of the present disclosure are directed to systems, devices, and computer-implemented methods for error detection in quantum computing systems. More particularly, example aspects are directed to reweighting a detection graph based at least in part on correlations in an underlying error model for a quantum error correction process. For example, a quantum error correction process may include reducing the error rate of logical qubits of a quantum computing system by detecting and correcting physical errors within the system. Uncorrected physical errors can generate errors in the logical qubit, but the quantum computing system may be configured to permit identification and correction of the physical errors. Advantageously, embodiments according to example aspects of the present disclosure leverage correlations between physical errors to identify likely physical errors with improved computational efficiency.

#For instance, in some embodiments, each logical qubit may be encoded in a plurality of physical qubits. For instance, a code (e.g., a topological code, such as a surface code) may encode a logical qubit using data qubits and ancilla qubits. The ancilla qubits may be configured such that their respective states can be measured to detect physical errors (e.g., errors of the physical qubits and/or of their measurement). These error detection measurements may be combined to build a weighted detection graph, with the weights of the graph links corresponding to an associated error probability. Embodiments according to example aspects of the present disclosure provide for the efficient reweighting of the detection graph based on correlations between physical errors, advantageously lowering the computational cost of achieving a desired logical error rate.

#Prior techniques for leveraging error correlations have often proved to be computationally expensive. For example, some prior techniques required processing all error detection measurements to determine a first set of results, adjusting the probabilities of certain error detection measurements according to known correlations among the first set of results, and then re-processing all error detection measurements with the adjusted probabilities. For real-time tracking of quantum errors, intervals between subsequent error detection measurements are generally on the scale of microseconds, and the iterative global processing of the entire set of error detection measurements can result in substantial computational overhead.