Cost-effective Quantum Error Mitigation Scales for Molecular Simulations with up to 6 Qubits

Quantum computation promises revolutionary advances, but building practical quantum computers requires overcoming the challenges posed by noise and errors. Oskar Graulund Lentz Rasmussen, Erik Kjellgren, and Peter Reinholdt, all from University of Southern Denmark, alongside Stephan P. A. Sauer from University of Copenhagen, Sonia Coriani from Technical University of Denmark, and Karl Michael Ziems from University of Southampton, now present a significant step towards reliable quantum calculations. Their research introduces a new, cost-effective method for mitigating these errors, specifically designed for a class of quantum circuits known as tiled Ansätze. This technique dramatically reduces the computational resources needed to correct errors, paving the way for more complex and accurate simulations on near-term quantum hardware, as demonstrated through successful molecular energy calculations on systems including lithium hydride and benzene.

This work introduces a cost-effective quantum error mitigation technique building on the Ansatz-based gate and readout error mitigation method, M0. The technique, termed tiled M0, leverages the unique structure of tiled Ansätze, such as tUPS, QNP, and hardware-efficient circuits, to apply a locality approximation to M0, resulting in an exponential reduction in the quantum processing unit (QPU) cost of noise characterisation.

Variational Quantum Eigensolver with Tiled Noise Mitigation

Scientists have demonstrated a new approach to improving the accuracy of quantum computations for molecular systems. They investigated tiled M0, a method for mitigating errors that arise from noise in quantum processors, focusing on calculations using the tUPS Ansatz. The team performed calculations on molecules including lithium hydride, hydrogen, water, butadiene, and benzene, using systems with up to twelve qubits, and validated their approach using both real quantum hardware from IBM and simulations of noisy quantum processors. The research involved optimizing quantum circuits to find the lowest energy state of each molecule, using 100,000 repetitions of each circuit to obtain statistically reliable results.

Comparing energies obtained with and without tiled M0, the results demonstrate that the technique generally improves accuracy, although its effectiveness can be limited by the level of noise present in the quantum hardware. Detailed analysis revealed that accuracy depends on both the molecule and the noise level, with excessive noise potentially overwhelming the error mitigation technique. The team meticulously calculated the exact energies of each molecule using ideal simulations, providing a benchmark for evaluating the quantum computations. They also identified cases where tiled M0 failed due to excessive noise, providing valuable insights into the method’s limitations. By analyzing fluctuations in the quantum computations, they gained a deeper understanding of the impact of noise on the accuracy of the results.

Tiled M0 Lowers Noise Characterization Costs

Scientists have developed a new quantum error mitigation technique, tiled M0, that significantly reduces the computational cost of characterizing noise in quantum processors. This work builds upon existing methods by leveraging the unique structure of tiled Ansätze, specifically the tUPS Ansatz, to apply a locality approximation. This approximation dramatically lowers the QPU cost needed for noise characterization, achieving a constant cost independent of system size. The core achievement lies in efficiently characterizing noise by focusing on individual tiles within the tUPS Ansatz, rather than the entire system simultaneously.

Experiments and simulations demonstrate the effectiveness of tiled M0 in calculating molecular ground state energies. Researchers performed calculations on LiH, molecular hydrogen, water, butadiene, and benzene, utilizing the tUPS Ansatz with qubit counts ranging from 2 to 12. Results show little to no loss in accuracy compared to the original M0 method, despite the substantial reduction in computational cost. The team successfully implemented tiled M0 on IBM quantum computers and in noisy simulations, validating its performance in real-world conditions. The technique’s ability to maintain accuracy while drastically reducing computational demands positions it as a promising solution for near-term quantum applications, and its independence from layer depth in tiled Ansätze further enhances its practicality and scalability.

Tiled M0 Boosts Accuracy and Efficiency

This work presents a new quantum error mitigation technique, tiled M0, designed to reduce errors in calculations using tiled Ansätze, a class of quantum circuits commonly employed in molecular simulations. The technique builds upon existing methods by incorporating aspects of the quantum chemical Ansatz into the noise characterization process and, crucially, introducing a locality approximation that dramatically reduces the computational cost of identifying and correcting errors. This cost reduction is significant, achieving a constant characterization time regardless of the number of qubits or circuit complexity for systems studied. Results from both noisy simulations and quantum experiments demonstrate that tiled M0 reliably improves the accuracy of ground state energy calculations for molecules ranging in size from four to twelve qubits.

The technique achieved substantial reductions in energy error, reaching chemical accuracy for certain simulations of lithium hydride. While performance was strong across several molecular systems, including hydrogen and butadiene, improvements were more limited for water and benzene in quantum experiments, likely due to fluctuations and drifts in the quantum hardware’s noise. The authors acknowledge that noise instability poses a challenge for the technique’s effectiveness on current hardware, and future research will focus on further investigating these effects. Despite these limitations, the team anticipates that tiled M0 will be particularly valuable as quantum hardware improves and noise levels decrease, offering a scalable and cost-effective approach to error mitigation in near-term quantum computing applications.