New Technique Reduces Noise in Quantum Simulations for Complex Systems

Scientists are tackling the challenge of accurately simulating the behaviour of complex chemical systems using quantum computers. Xeno De Vriendt from Next Generation Computing, BASF SE, Jacob Bringewatt of The Volgenau Department of Physics, United States Naval Academy, and Nik O. Gjonbalaj, Stefan Ostermann, Johannes Borregaard, Susanne F. Yelin and colleagues from the Department of Physics, Harvard University, present a novel approach to subspace diagonalization, a technique used to estimate the energy levels of these systems. This research, conducted in collaboration between Next Generation Computing, BASF SE, the United States Naval Academy, and Harvard University, introduces a new thresholding method designed to mitigate the impact of noise on calculations, a significant hurdle in applying these techniques to real-world problems. Their findings, demonstrated on systems including the industrially important Fe(III)-NTA chelate complex, suggest a potential reduction in computational resources, up to a factor of 100 in certain scenarios, and pave the way for more robust and efficient quantum simulations.

Scientists have developed a new technique to enhance the accuracy of quantum computations used for simulating molecules and materials, addressing a critical limitation of emerging quantum algorithms, their sensitivity to noise, and offering a pathway towards practical applications on near-term quantum computers. Researchers focused on quantum subspace diagonalization and Krylov algorithms, methods offering a potential alternative to the demanding requirements of quantum phase estimation for determining the energy levels of quantum systems, but these algorithms are hampered by their vulnerability to errors from quantum hardware and the measurement process. To overcome this challenge, the study introduces a novel thresholding method for solving generalised eigenvalue problems, a key step in subspace diagonalization, employing eigenvector-preserving transformations, specifically rotations, applied to the problem before thresholding, effectively filtering out noise and improving the stability of the calculation. By applying this rotation thresholding scheme to an iterative quantum Krylov algorithm, the team demonstrated significant improvements in estimating the ground state energy of several chemical systems, including the complex Fe(III)-NTA chelate. A carefully designed heuristic determines the optimal rotation angle from noisy data, leading to reductions in the number of samples needed to achieve a target error. For certain systems and noise conditions, researchers observed a remarkable decrease in sample requirements, up to a factor of 100, and simulations with access to the ideal transformation revealed even more substantial gains, with sample reductions reaching up to 104, suggesting a clear path for future optimisation. While the work centres on quantum chemistry, the improved thresholding scheme has broader implications for any application requiring the solution of noisy, ill-conditioned generalised eigenvalue problems, potentially impacting fields beyond quantum simulation. This magnitude of reduction underscores the potential of refined thresholding techniques to unlock practical quantum advantages in near-term quantum computing, as the study measured the impact of these rotations on the accuracy of ground state estimation, quantifying the reduction in samples needed to reach a predefined error tolerance. These gains are particularly significant given the challenges posed by intrinsic noise sources, such as sampling noise, which commonly plague quantum computations, and the developed thresholding scheme addresses the ill-conditioning often found in generalised eigenvalue problems arising from quantum subspace diagonalization. Ill-conditioning leads to large perturbations of eigenvalues due to noise, compromising the reliability of results, and is especially problematic for current and near-future quantum devices. By leveraging eigenvector-preserving transformations, the research mitigates these perturbations, enhancing the robustness of the algorithm, and while developed within the context of quantum subspace diagonalization, the improved thresholding scheme is broadly applicable to any scenario requiring the solution of noisy, ill-conditioned generalised eigenvalue problems. The research directly addresses the sensitivity of subspace diagonalization and Krylov algorithms to noise, a significant barrier to applying these methods to complex, real-world systems, offering a potential pathway to estimating the low-lying spectra of quantum systems without the need for fully fault-tolerant quantum computers. To counteract this, the study implemented eigenvector-preserving transformations, specifically rotations, applied to the generalised eigenvalue problem before thresholding, aiming to improve the conditioning of the problem and make it less susceptible to errors. This pre-processing step was integrated into an iterative quantum Krylov algorithm, a technique that builds a Krylov subspace by repeatedly applying the Hamiltonian to an initial state vector, allowing for a systematic refinement of the estimated ground state energy. The algorithm was tested on several chemical systems, including the Fe(III)-NTA chelate complex, to demonstrate its applicability to practical problems, and a key methodological innovation involved developing a heuristic to determine the optimal rotation angle directly from the noisy data. This adaptive approach avoids the need for prior knowledge of the noise characteristics, enhancing the robustness of the method. The study’s focus on generalised eigenvalue problems acknowledges the inherent ill-conditioning that arises when using non-orthogonal bases in quantum algorithms, and consequently, the improved thresholding scheme developed is potentially valuable beyond quantum subspace diagonalization, offering a general solution for solving noisy, ill-conditioned eigenvalue problems across various scientific disciplines. Scientists pursuing more efficient quantum simulations have long grappled with the problem of noise, as theoretical algorithms promise exponential speedups over classical methods for modelling complex systems, but these gains are often swamped by errors arising from imperfect quantum hardware or numerical approximations inherent in even classical simulations of quantum phenomena. The challenge isn’t simply to find the lowest energy states of a molecule or material, but to do so reliably when the calculations are riddled with uncertainty, and this new work offers a clever refinement to existing techniques, specifically those relying on subspace diagonalization and Krylov algorithms. By strategically rotating the mathematical problem before applying a thresholding procedure, the researchers demonstrate a significant reduction in the sensitivity to noise, with improvements, particularly for complex chemical systems like the iron-NTA chelate, potentially decreasing the computational effort required to achieve accurate results by a factor of one hundred in certain scenarios. However, the true power of this approach hinges on knowing the optimal rotation angle, a parameter currently estimated using a heuristic. While the method’s current practicality is tied to the development of algorithms capable of determining this optimal rotation in real-time and with minimal computational overhead. Looking ahead, this work could spur a broader re-evaluation of thresholding techniques across various scientific computing domains, and beyond quantum simulation, any field dealing with noisy or ill-conditioned eigenvalue problems, from structural mechanics to data analysis, might benefit from these eigenvector-preserving transformations. The immediate next step is likely to focus on refining the heuristic, perhaps incorporating machine learning to predict the optimal rotation angle, and exploring whether similar rotation strategies can be applied to other noise reduction techniques.