Melvin Mathews

Placing and Routing Non-Local Quantum Error Correcting Codes in Multi-Layer Superconducting Qubit Hardware

  1. Melvin Mathews,
  2. Lukas Pahl,
  3. David Pahl,
  4. Vaishnavi L. Addala,
  5. Catherine Tang,
  6. William D. Oliver,
  7. and Jeffrey A. Grover
Quantum error correcting codes (QECCs) with asymptotically lower overheads than the surface code require non-local connectivity. Leveraging multi-layer routing and long-range coupling
capabilities in superconducting qubit hardware, we develop Hardware-Aware Layout, HAL: a robust, runtime-efficient heuristic algorithm that automates and optimizes the placement and routing of arbitrary QECCs. Using HAL, we perform a comparative study of hardware cost across various families of QECCs, including the bivariate bicycle codes, the open-boundary tile codes, and the constant-depth-decodable radial codes. The layouts produced by HAL confirm that open boundaries significantly reduce the hardware cost, while incurring reductions in logical efficiency. Among the best-performing codes were low-weight radial codes, despite lacking topological structure. Overall, HAL provides a valuable framework for evaluating the hardware feasibility of existing QECCs and guiding the discovery of new codes compatible with realistic hardware constraints.
arxiv pdf

Efficient Qubit Calibration by Binary-Search Hamiltonian Tracking

  1. Fabrizio Berritta,
  2. Jacob Benestad,
  3. Lukas Pahl,
  4. Melvin Mathews,
  5. Jan A. Krzywda,
  6. Réouven Assouly,
  7. Youngkyu Sung,
  8. David K. Kim,
  9. Bethany M. Niedzielski,
  10. Kyle Serniak,
  11. Mollie E. Schwartz,
  12. Jonilyn L. Yoder,
  13. Anasua Chatterjee,
  14. Jeffrey A. Grover,
  15. Jeroen Danon,
  16. William D. Oliver,
  17. and Ferdinand Kuemmeth
We present a real-time method for calibrating the frequency of a resonantly driven qubit. The real-time processing capabilities of a controller dynamically compute adaptive probing
sequences for qubit-frequency estimation. Each probing time and drive frequency are calculated to divide the prior probability distribution into two branches, following a locally optimal strategy that mimics a conventional binary search. We show the algorithm’s efficacy by stabilizing a flux-tunable transmon qubit, leading to improved coherence and gate fidelity. By feeding forward the updated qubit frequency, the FPGA-powered control electronics also mitigates non-Markovian noise in the system, which is detrimental to quantum error correction. Our protocol highlights the importance of feedback in improving the calibration and stability of qubits subject to drift and can be readily applied to other qubit platforms.
arxiv pdf