Pulse-optimised circuit elements for scalable and noise-resilient quantum chemistry

Abstract: Useful chemistry calculations on near-term quantum processors are hindered by current algorithmic runtimes. We develop a methodology to significantly reduce these runtimes. Typically, variational quantum eigensolver (VQE) algorithms are implemented as sequences of primitive gates. Our methodology instead relies on gradient-ascent pulse engineering to construct hardware-tailored pulses for the direct implementation of VQEs. As problem sizes increase, it quickly becomes intractable to optimise a pulse that implements an entire VQE ansatz circuit. However, leading VQEs are constructed in a modular fashion. A problem-tailored VQE is assembled from parameterised circuit elements that simulate hopping between two or four electronic spin orbitals. We show that these circuit elements can be implemented more efficiently using hardware-tailored pulses. We numerically demonstrate our methodology on a silicon spin-qubit quantum processor. We find that common circuit elements, known as single- and double-qubit excitations, can be implemented in less than 289 ns and 927 ns, respectively. Compared with conventional gate-based implementations, our pulse-accelerated qubit excitations provide a scalable approach for faster and therefore more noise-robust quantum chemistry simulations by reducing VQE runtimes by up to a factor of 15.3.

• The paper demonstrates a pulse optimization methodology using GRAPE to implement qubit-excitation elements with improved fidelity and speed.
• Numerical benchmarks reveal up to a 15.3× speedup for double-qubit excitations and high fidelity (>99%), even in the presence of hardware variations.
• The approach simplifies hardware requirements by eliminating the need for microwave drives, paving the way for scalable quantum chemistry on silicon spin-qubit devices.

Pulse-Optimised Circuit Elements for Quantum Chemistry: Methodologies and Implications

Motivation and Background

Quantum computational chemistry seeks to leverage quantum hardware to simulate electronic structure problems that are intractable for classical computers, especially in the regime of strongly correlated systems with $50$–$200$ spin orbitals. The leading hybrid quantum-classical algorithms, particularly the Variational Quantum Eigensolver (VQE), offer a pragmatic approach for noisy intermediate-scale quantum (NISQ) hardware. Traditional VQE implementations rely on gate-based circuits transpiled into sequences of primitive gates—an approach that becomes increasingly inefficient as circuit depth and system size grow, due to decoherence and temporal constraints inherent to current hardware.

A central paradigm shift addressed in this paper is the transition from gate-based to pulse-engineered implementations, specifically focusing on the modular circuit elements that constitute scalable VQE ansätze: single- and double-qubit excitations mimicking spin-orbital transitions. The authors develop and numerically validate a methodology for constructing hardware-tailored pulses using gradient-ascent pulse engineering (GRAPE) to directly implement these elements on silicon spin-qubit quantum processors, targeting substantial reductions in execution time and improved noise resilience.

Technical Contributions and Methodology

The pulse optimisation framework is built upon several foundational steps:

1. Modular Circuit Decomposition: The VQE circuit is decomposed into parameterised qubit-excitation elements, each representing single or double electronic hopping terms under Jordan-Wigner encoding. These elements are physically motivated and have demonstrated scalability in adaptive VQE algorithms.
2. Pulse Construction: Rather than optimising pulses for an entire circuit, which is computationally intractable for large problems, the authors optimise pulses for individual circuit elements. Using GRAPE with piecewise-constant exchange-only control, they tailor pulses to the silicon spin-qubit Hamiltonian, omitting the need for microwave-based single-qubit drives.
3. Benchmarking and Numerical Simulation: The methodology is applied to a linear silicon array of Loss-DiVincenzo qubits. By numerically integrating the device Hamiltonian and minimising gate infidelity, the authors determine minimal evolution times (METs) required for high-fidelity implementation of qubit excitations, finding single- and double-qubit excitations can be executed in $\leq 289$ ns and $\leq 927$ ns, respectively.
4. Interpolation and Parameter Robustness: The authors address the practical challenge of continuous excitation strengths in VQE by demonstrating that pre-optimised pulses for discrete strengths can be interpolated—yielding intermediate pulses with infidelities $\sim10^{-6}$, so experimental error is limited chiefly by hardware decoherence.
5. Device Parametric Dependence: The robustness of METs with respect to Zeeman-energy detuning is investigated. The methodology yields substantially flat METs across a broad detuning range—indicating generality and stability for realistic hardware variations.

Numerical Results and Claims

Strong numerical evidence is provided for the acceleration factor achieved by pulse-based versus gate-based implementations: up to $15.3\times$ for double-qubit excitations and $11.1\times$ for single-qubit excitations. This reduces total VQE circuit runtime and, consequently, susceptibility to noise and decoherence. The METs remain largely independent of excitation strength and detuning parameters, suggesting the efficacy of this pulse engineering approach is not limited by specific circuit configurations or minor hardware variation.

The authors also claim that:

• Microwave control channels, typically essential for single-qubit operations, are unnecessary for efficient qubit-excitation elements in quantum chemistry applications, potentially simplifying hardware design.
• Pulse-based qubit-excitation elements achieve high-fidelity (>99%) for a broad set of strengths via simple interpolation, providing continuous tuneability without additional optimisation overhead.

Practical and Theoretical Implications

Practical Implications

• Accelerated Algorithm Runtime: By reducing circuit execution times by an order of magnitude, larger and more chemically relevant molecules become accessible on NISQ hardware before decoherence dominates.
• Noise Resilience: Shorter execution times directly translate to reduced accumulated errors, advancing the prospect of practical quantum computational chemistry.
• Simplified Hardware Requirements: The elimination of microwave drives for single-qubit operations suggests future silicon spin-qubit devices for quantum chemistry can be optimised with simpler architectures.

Theoretical Implications

• Scalability: The modular pulse optimisation framework retains the scalability benefits of adaptive gate-based VQE algorithms while circumventing the traditional bottlenecks of circuit transpilation and compilation.
• Generalizability: The methodology is not restricted to silicon electron-spin qubits or qubit-excitation elements; it can be readily adapted for other circuit elements and hardware platforms, presenting a generic path for Hamiltonian-engineered quantum algorithms.
• Limitations of Control Fields: The flat METs for varying excitation strengths highlight intrinsic limitations of silicon control fields in exploiting circuit structure for further speedup, motivating future exploration of alternative platforms.

Future Perspectives

Advancement of this methodology toward full VQE circuits (beyond individual elements) and extension to more diverse quantum architectures remains an open problem. Further, the integration with advanced numerical optimisers and more complex circuit element families could yield additional runtime reductions and efficiency gains. The approach is well-positioned to influence the development of quantum hardware tailored for chemistry, as well as the theoretical design of quantum algorithms that exploit pulse-level control over gate abstraction.

Conclusion

This paper establishes a robust methodology for pulse-based acceleration of modular circuit elements in variational quantum chemistry, combining the noise resilience and runtime efficiency of pulse-engineered implementations with the scalability of adaptive, modular VQE circuits. The demonstrated execution time reductions and fidelity results on silicon spin-qubit arrays represent a significant advancement toward practical quantum chemistry on near-term devices, with broad implications for both hardware design and algorithmic development in quantum computing (2606.17357).