# Publications

## Scheduling error correction operations for a quantum computer

Phillips, Cynthia A.; Carr, Robert D.; Ganti, Anand G.; Landahl, Andrew J.

In a (future) quantum computer a single logical quantum bit (qubit) will be made of multiple physical qubits. These extra physical qubits implement mandatory extensive error checking. The efficiency of error correction will fundamentally influence the performance of a future quantum computer, both in latency/speed and in error threshold (the worst error tolerated for an individual gate). Executing this quantum error correction requires scheduling the individual operations subject to architectural constraints. Since our last talk on this subject, a team of researchers at Sandia National Labortories has designed a logical qubit architecture that considers all relevant architectural issues including layout, the effects of supporting classical electronics, and the types of gates that the underlying physical qubit implementation supports most naturally. This is a two-dimensional system where 2-qubit operations occur locally, so there is no need to calculate more complex qubit/information transportation. Using integer programming, we found a schedule of qubit operations that obeys the hardware constraints, implements the local-check code in the native gate set, and minimizes qubit idle periods. Even with an optimal schedule, however, parallel Monte Carlo simulation shows that there is no finite error probability for the native gates such that the error-correction system would be benecial. However, by adding dynamic decoupling, a series of timed pulses that can reverse some errors, we found that there may be a threshold. Thus finding optimal schedules for increasingly-refined scheduling problems has proven critical for the overall design of the logical qubit system. We describe the evolving scheduling problems and the ideas behind the integer programming-based solution methods. This talk assumes no prior knowledge of quantum computing.