Randomised Tests Speed up Quantum Processor Analysis

Researchers are tackling the critical challenge of maintaining coherence in solid-state quantum processors, where unwanted interactions and decoherence limit performance. Rune Thinggaard Birke, Johann Bock Severin, and Malthe A. Marciniak, from the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Denmark, working in collaboration with Emil Hogedal, Andreas Nylander, Irshad Ahmad, Amr Osman, Janka Biznárová, Marcus Rommel, Anita Fadavi Roudsari, Jonas Bylander, Giovanna Tancredi, Daniel Stilck França, Albert Werner, Christopher W. Warren, Jacob Hastrup, Svend Krøjer and Morten Kjaergaard at the Department of Microtechnology and Nanoscience, Chalmers University of Technology, Sweden, present a new approach to efficiently characterise these processors. Their work demonstrates and benchmarks ‘Classical Shadows’ for Lindblad tomography, a technique that significantly accelerates the process of mapping the dynamics of quantum systems. By employing randomised measurements, the team achieved full characterisation of a five-qubit processor in just nine hours, a substantial reduction from the estimated 58 hours required by conventional methods, paving the way for scalable quantum error mitigation strategies.

A new technique promises to dramatically speed up the process of understanding and correcting these flaws, potentially accelerating the development of more stable and powerful quantum processors, bringing practical quantum computation closer to reality.

Scientists are tackling a fundamental challenge in quantum computing: maintaining the delicate quantum states needed for complex calculations. Spurious couplings and decoherence, unwanted interactions and loss of quantum information, plague solid-state quantum processors, demanding increasingly sophisticated calibration and error mitigation strategies.

A new study demonstrates a significant advancement in characterising these processors by accelerating a key technique called Lindblad tomography, which maps out how a quantum system evolves over time. Researchers have successfully implemented and benchmarked a streamlined approach using “shadow” measurements, dramatically reducing the time required to analyse multi-qubit systems.

This work centres on efficiently determining the Lindblad parameters, which describe the rates of energy dissipation and coupling between qubits, the fundamental building blocks of quantum computers. Traditional methods for recovering these parameters scale exponentially with the number of qubits, quickly becoming impractical. The team instead employed randomized measurements, a technique known as shadow tomography, to estimate these parameters with far fewer experimental resources.

By leveraging physically motivated assumptions about the processor’s connectivity, they achieved a substantial speed-up in the characterisation process. The researchers first established a baseline using a standard, exhaustive method called extensible Lindblad tomography, then compared its performance to their new shadow-based approach on small subsystems, verifying that the simplified method accurately reproduced the results while requiring exponentially fewer measurements.

Crucially, this efficiency was extended to a fully functional five-qubit processor, where the team recovered all relevant dissipation and coupling parameters in just nine hours, a significant improvement over the estimated 58 hours that would have been needed with the traditional technique. This breakthrough is enabled by shadow Lindblad tomography, which recycles randomized measurement configurations to extract the same information using fewer resources.

The study confirms that the underlying assumptions about the processor’s limited connectivity hold true, allowing for this efficient data acquisition. Furthermore, the shadow implementation is compatible with standard data analysis techniques, simplifying the process and avoiding the need for complex statistical estimators. These results demonstrate the practical viability of randomized shadow tomography for learning the dynamics of increasingly complex quantum processors, paving the way for more rapid development and optimisation of quantum hardware.

Shadow Lindblad tomography significantly accelerates five-qubit processor characterisation through configuration recycling and locality assumptions

Extensible Lindblad tomography and a novel shadow approach yielded markedly different acquisition times for characterising a five-qubit superconducting processor. Specifically, the shadow Lindblad tomography protocol recovered all single qubit dissipation and two-qubit coupling parameters in just 9 hours, contrasting sharply with an estimated 58 hours required to achieve the same result using extensible Lindblad tomography, demonstrating a greater than six-fold reduction in measurement time.

This efficiency stems from the shadow approach’s ability to recycle randomized configurations, leveraging physically motivated locality assumptions within the processor’s dynamics. Initial verification of these locality assumptions was performed on one- and three-qubit subsystems, where shadow Lindblad tomography reproduced the results of extensible Lindblad tomography within established uncertainties while utilising exponentially fewer configurations.

This confirms the validity of the underlying principles enabling the accelerated data acquisition. The research demonstrates that the shadow implementation maintains compatibility with conventional Gaussian error propagation, circumventing the need for more complex median-of-means estimators typically employed in similar analyses. The protocols were designed to recover the Lindblad parameters describing the idling dynamics of the five-qubit processor, encompassing both the Hamiltonian and dissipators.

Analysis revealed negligible three-body interactions and correlated decay, further validating the assumptions of k-locality, where interactions are limited to nearest and next-nearest neighbours. This localized structure is crucial for the efficiency gains observed in the shadow tomography approach, allowing for a logarithmic scaling of computational resources with system size.

Furthermore, the study highlights the practical implementation of randomized shadow tomography protocols for learning quantum processor dynamics as qubit counts increase. The ability to extract all single qubit dissipators and two-qubit interactions within a reasonable timeframe represents a significant step towards scalable quantum characterisation and calibration, offering a pathway to more efficient and comprehensive device metrology.

Extensible and shadow Lindblad tomography for characterising 72-qubit dynamics

A 72-qubit superconducting processor underpinned the experimental work detailed herein, enabling precise characterisation of quantum processor dynamics. The study commenced with implementation of extensible Lindblad tomography, a technique for estimating Lindblad parameters using a complete tomographic dataset, establishing a baseline for comparison.

This method relies on exhaustive state preparation and Pauli measurements to map the evolution of the quantum system. Subsequently, researchers introduced shadow Lindblad tomography, a randomized approach designed to accelerate the parameter estimation process under physically motivated locality assumptions. Shadow tomography recycles randomized configurations, significantly reducing the resources needed to estimate Lindblad parameters, a critical advantage when scaling to larger qubit numbers.

The validity of these locality assumptions, specifically, that dissipation and couplings are primarily on-site or between nearest neighbours, was experimentally verified on one- and three-qubit subsystems. By applying both extensible and shadow tomography to these smaller systems, the team confirmed that shadow Lindblad tomography accurately reproduced results while requiring exponentially fewer configurations.

This efficiency was then leveraged to apply shadow Lindblad tomography to the full five-qubit processor, successfully recovering all single-qubit dissipation and two-qubit coupling parameters. The complete parameter recovery on the five-qubit processor was achieved in 9 hours of acquisition time, a substantial improvement over the estimated 58 hours required by extensible Lindblad tomography.

Crucially, the shadow implementation remained compatible with conventional Gaussian error propagation, circumventing the need for more complex median-of-means estimators. The research expanded upon standard Lindblad tomography by representing the Hamiltonian and jump operators in a Pauli basis, allowing for a systematic expansion and quantification of the system’s parameters. This approach facilitated the identification of both coherent and incoherent contributions to the system’s dynamics, ultimately demonstrating the practical implementation of randomized shadow tomography for learning quantum processor dynamics at increasing qubit counts.

Rapid characterisation of five-qubit dynamics via randomised shadow tomography

The relentless pursuit of stable qubits has long been hampered by a fundamental trade-off: thorough characterisation of errors demands exponentially more resources as systems scale up. For years, diagnosing the subtle ways in which quantum information leaks from these fragile states required painstaking, qubit-by-qubit analysis. This new work offers a significant step towards breaking that bottleneck, demonstrating a method for rapidly mapping the dynamics of a five-qubit processor using randomised measurements, a technique known as shadow tomography.

It’s not about faster data acquisition; it’s about shifting the paradigm from exhaustive, resource-intensive diagnostics to a more efficient, scalable approach. The implications extend beyond simply identifying error sources. However, the reliance on assumptions about the locality of interactions, that errors are primarily confined to nearby qubits, remains a crucial caveat. The extent to which these assumptions hold true in larger, more complex architectures needs further investigation.

Future work will likely focus on refining these techniques to handle more intricate error models and exploring the limits of scalability. Ultimately, the goal isn’t just to diagnose errors, but to actively learn from them, building quantum processors that are not merely less prone to failure, but actively resilient.