Quantum Derivative Estimation Accelerated with Approximate Parameter Shift Rules.

Researchers developed an approximate generalised parameter shift rule (aGPSR) for estimating derivatives in quantum algorithms. Testing on variational eigensolvers with 3-6 qubits demonstrated a reduction in computational cost – specifically, expectation value calls – by a factor of 7 to 504, without compromising accuracy.

Accurate calculation of derivatives is fundamental to many computational algorithms, particularly within the rapidly developing field of quantum machine learning. However, realising these calculations on current quantum hardware presents significant challenges due to inherent noise and limitations in qubit connectivity. Researchers at Pasqal – Vytautas Abramavicius, Evan Philip, Kaonan Micadei, Charles Moussa, Mario Dagrada, Vincent E. Elfving, Panagiotis Barkoutsos, and Roland Guichard – detail in their paper, ‘Evaluation of derivatives using approximate generalized parameter shift rule’, a novel method for derivative estimation. Their approach, the approximate generalized parameter shift rule (aGPSR), demonstrably reduces the computational demands of these calculations, achieving comparable accuracy to existing methods with a substantial reduction – a factor of 7 to 504 – in the number of required quantum circuit executions, as validated through simulations on systems ranging from 3 to 6 qubits.

Efficient Gradient Estimation Accelerates Variational Quantum Algorithms

Variational Quantum Algorithms (VQAs) require optimisation of parameters to minimise a cost function, a process demanding accurate gradient calculations. Traditional methods for gradient estimation, such as parameter-shift rules, become computationally expensive as system size increases, particularly on Noisy Intermediate-Scale Quantum (NISQ) hardware where device limitations and qubit interactions complicate calculations. Researchers now present the approximate Generalized Quantum Circuit Differentiation Rule (aGPSR), a method demonstrably reducing the computational burden of gradient estimation without sacrificing accuracy and enabling more complex quantum simulations.

The aGPSR method addresses the limitations of existing generalised parameter-shift rules by approximating the derivative estimation process, allowing for a significant reduction in the number of expectation value calls – essentially, the number of times the quantum circuit must be executed – required to achieve accurate gradient calculations. This technique accommodates arbitrary device Hamiltonians, meaning it functions effectively across diverse quantum hardware configurations and expands the possibilities for tackling complex optimisation problems. Experiments utilising both digital and analog ansatze – representing circuits built from standard quantum gates and those employing continuous-time evolution respectively – validate the efficiency of aGPSR and demonstrate its broad applicability.

The research team implemented aGPSR within a robust computational framework, leveraging the ARPACK library to efficiently solve the large-scale eigenvalue problems inherent in the gradient calculation process. This integration, facilitated by the differentiable programming interface Qadence, streamlines the incorporation of aGPSR into existing quantum computing workflows and accelerates the development of new quantum algorithms. The observed performance gains are particularly relevant for noisy intermediate-scale quantum (NISQ) devices, where minimising the number of quantum circuit executions is crucial to mitigate the impact of errors and achieve meaningful results.

Researchers validated aGPSR’s efficacy through comprehensive experiments employing the Variational Quantum Eigensolver (VQE), a prominent VQA used for finding the ground state energy of molecules. These experiments spanned systems ranging from three to six qubits, demonstrating a substantial reduction in expectation value calls while maintaining accuracy.

The research team plans to investigate the potential of combining aGPSR with other advanced techniques, such as adaptive optimisation algorithms and error mitigation strategies, to further improve the performance and robustness of variational quantum algorithms. This collaborative approach will accelerate the development of practical quantum applications and unlock the full potential of quantum computing.

The development of aGPSR represents a significant step towards realising the promise of quantum computing, enabling the development of more efficient and scalable quantum algorithms for a wide range of applications. By addressing the computational challenges associated with gradient estimation, this research paves the way for tackling increasingly complex problems in fields such as drug discovery, materials science, and financial modelling.

The research team acknowledges the support of funding agencies and collaborators who contributed to this work, highlighting the importance of collaborative research in advancing the field of quantum computing. They also express their gratitude to the open-source community for providing valuable tools and resources that facilitated this research. The team is committed to sharing their findings with the broader scientific community and fostering collaboration to accelerate the development of quantum technologies.

The successful implementation of aGPSR demonstrates the power of combining theoretical insights with practical implementation, showcasing the importance of interdisciplinary research in advancing the field of quantum computing. The team’s commitment to developing user-friendly software and sharing their findings with the broader scientific community will undoubtedly accelerate the adoption of this technology and unlock its full potential.

Future work should focus on extending the scalability of aGPSR to larger qubit numbers and more complex quantum circuits, exploring new approximation strategies and optimisation techniques to further enhance its performance. Investigating the performance of aGPSR with different optimisation algorithms and problem Hamiltonians will further establish its robustness and general applicability. Additionally, exploring methods to dynamically adjust the approximation parameters within aGPSR could optimise the trade-off between accuracy and computational cost, tailoring the method to specific hardware constraints and algorithmic requirements.