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arXiv:2309.17391 · ACS Physical Chemistry Au

Singular Value Decomposition Quantum Algorithm for Quantum Biology

E. Oh, Timothy J. Krogmeier, Anthony W. Schlimgen, Kade Head-Marsden

Published May 17, 2024• 9 citations
arXivHTMLPDF

Abstract

There has been a recent interest in quantum algorithms for the modeling and prediction of nonunitary quantum dynamics using current quantum computers. The field of quantum biology is one area where these algorithms could prove to be useful as biological systems are generally intractable to treat in their complete form but amenable to an open quantum systems approach. Here, we present the application of a recently developed singular value decomposition (SVD) algorithm to two systems in quantum biology: excitonic energy transport through the Fenna-Matthews-Olson complex and the radical pair mechanism for avian navigation. We demonstrate that the SVD algorithm is capable of capturing accurate short- and long-time dynamics for these systems through implementation on a quantum simulator and conclude that while the implementation of this algorithm is beyond the reach of current quantum computers, it has the potential to be an effective tool for the future study of systems relevant to quantum biology.

DOI
10.1021/acsphyschemau.4c00018

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The simulation of open quantum dynamics on quantum circuits has attracted wide interests recently with a variety of quantum algorithms developed and demonstrated. Among these, one particular design of a unitary-dilation-based quantum algorithm is capable of simulating general and complex physical systems. In this paper, we apply this quantum algorithm to simulating the dynamics of the radical pair mechanism in the avian compass. This application is demonstrated on the IBM QASM quantum simulator. This work is the first application of any quantum algorithm to simulating the radical pair mechanism in the avian compass, which not only demonstrates the generality of the quantum algorithm but also opens new opportunities for studying the avian compass with quantum computing devices.
The theory of open quantum systems has many applications ranging from simulating quantum dynamics in condensed phases to better understanding quantum-enabled technologies. At the center of theoretical chemistry are the developments of methodologies and computational tools for simulating charge and excitation energy transfer in solutions, biomolecules, and molecular aggregates. As a variety of these processes display non-Markovian behavior, classical computer simulation can be challenging due to exponential scaling with existing methods. With quantum computers holding the promise of efficient quantum simulations, in this paper, we present a new quantum algorithm based on Kraus operators that capture the exact non-Markovian effect at a finite temperature. The implementation of the Kraus operators on the quantum machine uses a combination of singular value decomposition (SVD) and optimal Walsh operators that result in shallow circuits. We demonstrate the feasibility of the algorithm by simulating the spin-boson dynamics and the exciton transfer in the Fenna-Matthews-Olson (FMO) complex. The NISQ results show very good agreement with the exact ones.
This research paper explores the application of singular value decomposition (SVD) in quantum image processing (QIP), specifically focusing on the computation of eigenvalues using variational quantum algorithms. SVD is a powerful mathematical tool in image processing, used for tasks such as image compression, noise reduction, and feature extraction. In this study, we propose quantum variational singular value decomposition (QVSVD) based on the variational quantum deflation (VQD) algorithm to determine the eigenvalues that contributes in calculating the singular values of the image matrix and eventually doing the SVD. This facilitates the extraction of eigenvalues with exponential speedup on real hardware compared to classical methods. We detail the implementation of this quantum algorithm within the framework of QIP, highlighting its advantages in terms of computational efficiency and accuracy on a Fault-Tolerant Quantum Computing (FTQC). Furthermore, we present a comparative analysis of the quantum and the classical method of SVD, demonstrating the accuracy of the image data. The simulation results validate the theoretical advantages of using quantum algorithms for SVD in image processing. This work not only underscores the potential of quantum computing in enhancing image processing techniques but also sets the stage for future research in the field, exploring more complex image processing tasks and other quantum algorithms. Our findings suggest that quantum image processing can offer unprecedented capabilities, paving the way for advancements in various applications such as medical imaging, remote sensing, and multimedia processing.
Nonautonomous linear ordinary differential equations of the form v˙(t)=A(t) v(t)\dot{v}(t) = A(t)\, v(t)v˙(t)=A(t)v(t), where A(t)A(t)A(t) is non-skew-symmetric, are often used to describe nonunitary dynamics in a variety of fields that range from open quantum system dynamics to economic modeling. Because quantum computing hardware is designed to natively implement unitary transformations, existing algorithms for solving such equations on quantum hardware are based on the assumption that the nonunitary propagator is known, and use dilation techniques to embed the nonunitary dynamics within the unitary dynamics of a larger system. However, with the exception of cases where the nonunitary propagator is known in closed form, it needs to be calculated and manipulated on a classical computer at each time step. In this paper, we propose a quantum algorithm that does not require a priori knowledge of the explicit nonunitary propagator and effectively performs the dilation on the quantum hardware. Our algorithm combines a dilation scheme that uses singular value decomposition (SVD) to write the nonunitary propagator as a sum of unitaries with simulating the dynamics of the SVD factors on the quantum hardware. The population-only time-convolutionless quantum master equation describing photoinduced charge transfer in a solvated molecular triad is used as a demonstrative example of the applicability of the algorithm and its sensitivity to noise.
Using quantum algorithms to simulate complex physical processes and correlations in quantum matter has been a major direction of quantum computing research, towards the promise of a quantum advantage over classical approaches. In this work we develop a generalized quantum algorithm to simulate any dynamical process represented by either the operator sum representation or the Lindblad master equation. We then demonstrate the quantum algorithm by simulating the dynamics of the Fenna-Matthews-Olson (FMO) complex on the IBM QASM quantum simulator. This work represents a first demonstration of a quantum algorithm for open quantum dynamics with a moderately sophisticated dynamical process involving a realistic biological structure. We discuss the complexity of the quantum algorithm relative to the classical method for the same purpose, presenting a decisive query complexity advantage of the quantum approach based on the unique property of quantum measurement.