[Paper Review] Physical qubit calibration on a directed acyclic graph

J. Kelly, P. O’Malley+3 more|arXiv (Cornell University)|Mar 8, 2018

Quantum and electron transport phenomena19 citations

TL;DR

This paper introduces Optimus, a framework that models quantum qubit calibration as a directed acyclic graph (DAG) to automate and optimize calibration workflows. By structuring calibrations as interdependent nodes in a DAG, the system enables efficient graph traversal for forward and backward calibration, reducing redundant experiments and enabling scalable, autonomous operation of multi-qubit quantum processors.

ABSTRACT

High-fidelity control of qubits requires precisely tuned control parameters. Typically, these parameters are found through a series of bootstrapped calibration experiments which successively acquire more accurate information about a physical qubit. However, optimal parameters are typically different between devices and can also drift in time, which begets the need for an efficient calibration strategy. Here, we introduce a framework to understand the relationship between calibrations as a directed graph. With this approach, calibration is reduced to a graph traversal problem that is automatable and extensible.

Motivation & Objective

• To address the challenge of efficiently calibrating physical qubits in quantum processors, where control parameters are device-specific and prone to drift over time.
• To replace manual, sequential calibration workflows with an automated, extensible framework that supports dynamic navigation through calibration dependencies.
• To reduce calibration time and experimental overhead by modeling calibrations as a DAG and using intelligent graph traversal strategies.
• To enable robust handling of parameter drift, errors, and system reconfiguration through modular state-checking and diagnostic procedures.

Proposed method

• Model calibration procedures as nodes in a directed acyclic graph (DAG), where each node represents a calibration (cal) with defined parameters, scans, and analysis functions.
• Define three core operational modes: 'maintain' (verify and update parameters), 'diagnose' (identify and correct mismatches between system state and knowledge), and 'check_state' (validate system state based on dependencies).
• Use graph traversal algorithms to minimize redundant experiments: start from the lowest-level out-of-spec nodes and propagate upward, avoiding unnecessary tuning of higher-level dependencies.
• Implement a layered approach to handle cyclic dependencies by unwrapping them into precision layers (e.g., coarse, mid, fine) to enable iterative convergence.
• Integrate error handling via DiagnoseError when unexpected inconsistencies arise, such as a node failing despite its dependencies being in spec.
• Extend the framework to multi-qubit calibrations by ensuring that a multi-qubit node fails check_state if any of its constituent qubits fail, preserving system-wide consistency.

Experimental results

Research questions

• RQ1 How can calibration workflows in quantum processors be modeled to support both forward and backward traversal while minimizing redundant experiments?
• RQ2 What graph-based structure enables scalable, autonomous calibration of multi-qubit systems with drifting parameters?
• RQ3 How can system state knowledge be dynamically validated and corrected when discrepancies arise between expected and actual behavior?
• RQ4 What strategies can reduce calibration time and experimental overhead in the presence of parameter drift or system reconfiguration?
• RQ5 How can cyclic dependencies between calibrations be resolved without compromising convergence or increasing complexity?

Key findings

• The DAG-based calibration framework enables efficient, automated calibration by reducing the number of required experiments through intelligent graph traversal.
• The 'maintain' and 'diagnose' modes allow the system to dynamically respond to parameter drift and data inconsistencies without restarting from the beginning of the calibration sequence.
• By starting traversal from the lowest-level out-of-spec nodes, the framework minimizes unnecessary work on higher-level dependencies.
• Cyclic dependencies can be resolved by unwrapping them into layered precision stages, enabling iterative convergence without violating acyclicity.
• The framework successfully supports multi-qubit calibrations by enforcing system-wide consistency through dependency checks.
• The system has been deployed and used to automate calibration of multi-qubit quantum processors, demonstrating scalability and robustness in real-world operation.