Quantum Error Correction (QEC) has the potentialto reduce errors in quantum logic by orders of magnitude when encoding quantuminformation nonlocally and detecting local errors with an error decoder. Thiscapability positions QEC as the leading, and arguably the only, viablecandidate for achieving useful quantum computation. As quantum hardware scalesfrom a few qubits to hundreds without compromising physical gate fidelities,experimental demonstrations have begun to reach critical QEC milestones. These includeconnecting the wires and running gate sequences [1], suppressing idle errorswhen increasing the number of qubits [2], initializing magic-states [3], andrunning shallow Clifford circuits with QEC [4].

In these experiments, control requirements wereprimarily focused on pulse-sequence optimization, with error decoding appliedonly in post-processing. However, real-time decoding is essential for executingnon-Clifford circuits and achieving quantum advantage. In this seminar, I willbreak down the quantum control requirements necessary to reach the next majorQEC milestone: running shallow non-Clifford circuits. Using the factorizationcircuit of the number 21 as a case study, I will demonstrate why classicalhardware is pivotal for these circuits and outline the high-level requirementsfor the control system. I will then translate these high-level requirementsinto specific numerical metrics derived from a pulse-level simulation of thefactorization circuit with thousands of physical qubits. Finally, I willdiscuss our strategy to meet these requirements and enable the nextbreakthroughs in QEC once quantum hardware is matured.

[1] Krinner et al., “Realizing Repeated Quantum Error Correction in aDistance-Three Surface Code,” Nature, vol. 605, no. 7911, pp. 669–674,May 2022, doi: 10.1038/s41586-022-04566-8.

[2] Google Quantum AI et al., “Suppressing quantum errorsby scaling a surface code logical qubit,” Nature, vol. 614, no. 7949,pp. 676–681, Feb. 2023, doi: 10.1038/s41586-022-05434-1.

[3] Gupta et al. , “Encoding a magic state with beyondbreak-even fidelity,” Nature, vol. 625, no. 7994, pp. 259–263, Jan.2024, doi: 10.1038/s41586-023-06846-3.

[4] D. Bluvstein et al., “Logical quantum processor basedon reconfigurable atom arrays,” Nature, Dec. 2023, doi:10.1038/s41586-023-06927-3.