Dakota Team Simulates Imaginary Time Using Real-Time Data

Imaginary-Time Evolution (ITE) has historically proven comparatively difficult to obtain on quantum computers. A new algorithm now links ITE to more easily implemented real-time simulations by performing analytic continuation of measured correlation functions. The method was demonstrated using both classical diffusion processes and quantum mechanical scattering problems; numerical tests were performed utilising two qubits on IBM hardware. Peng Guo of the University of Birmingham and colleagues have created a computational method allowing determination of Imaginary-Time Evolution, or ITE, a process vital for certain quantum simulations, using capabilities already present in today’s quantum computers. This bypasses previous limitations requiring additional resources or producing unreliable outcomes, linking complex ITE calculations to more readily measurable real-time behaviours. Demonstrations utilising IBM computer hardware suggest this technique expands what near-term devices can achieve without needing further technological improvements.

The team links ITE calculations to real-time simulations via analytic continuation, extending mathematical functions beyond their original range. Obtaining Imaginary-Time Evolution, essentially rewinding and replaying a physical process in reverse to understand its fundamental properties, has traditionally been difficult on these machines. Correlation functions, measuring how closely different aspects of a system change together over time, are central to the method but derived from readily measurable data. Two qubits enable accurate imaginary-time evolution via real-time measurement analysis An algorithm achieving Imaginary-Time Evolution (ITE) using only two qubits was demonstrated on IBM hardware by Previous methods either required additional ‘ancilla’ qubits, spare quantum bits used to aid computation, or suffered from accuracy limitations when modelling complex systems. Linking ITE calculations, traditionally difficult for quantum computers, to easily implemented simulations based on measuring behaviours over time circumvents these issues. Demonstrations included one and two qubit systems exploring classical diffusion processes and quantum mechanical scattering, showcasing the method’s application across different physical models. The approach successfully applied to one dimensional Fokker-Planck equations, describing classical diffusion processes, verifying its ability to simulate particle movement governed by random forces; numerical tests utilising a cutoff time yielded agreement with established analytic solutions for Brownian motion and the Ornstein-Uhlenbeck process, while increasing this cutoff improves accuracy. Demonstrating versatility, the technique extended to imaginary-time evolution of integrated correlation functions in one dimension within quantum mechanical scattering. This showcases how identical computational steps can handle both classical and quantum physical models. It is important to note that ITE calculations have traditionally been challenging due to their complexity on current hardware. These results represent an advance towards more efficient simulations using fewer qubits than previously required for comparable outcomes. Analytic continuation streamlines access to ground state solutions in quantum many-body physics Although offering a pathway to Imaginary-Time Evolution (ITE) without extra qubits or complex calculations, the algorithm’s present form remains limited to one-dimensional systems; effective extension into higher dimensions presents a substantial challenge. Dr Field and Professor Green acknowledge scaling up to realistic simulations, those mirroring genuinely intricate physical scenarios, remains open for further investigation. Despite this limitation, it represents a step forward in making complex quantum simulations accessible because Imaginary-Time Evolution is notoriously difficult to implement on existing hardware. The connection between ITE, a computationally intensive technique used to understand stable states of quantum systems, and more easily achievable real-time simulations arises through analytic continuation. This mathematical process effectively extends functions beyond their initial boundaries, circumventing limitations inherent in directly implementing ITE on current quantum computers which typically require substantial resources or produce inaccurate results. The algorithm therefore provides a streamlined route towards understanding the ground state properties of many-body quantum systems.

This research demonstrated an algorithm for obtaining imaginary-time evolution by analysing measured real-time correlation functions. It offers a method for simulating complex physical models, including one-dimensional Fokker-Planck equations and quantum mechanical scattering, potentially using fewer qubits than previous approaches. By linking this technique to more readily achievable simulations, researchers addressed challenges associated with performing imaginary-time evolution calculations on existing hardware. The authors note that extending this work to higher dimensions requires further investigation. 👉 More information🗞 Imaginary time evolution of a quantum system through analytic continuation from real-time quantum simulation✍️ Peng Guo, Anto Shibu, Joshua Lin and Yong Zhao🧠 ArXiv: https://arxiv.org/abs/2608.19943 Stay currentSee today’s quantum computing news on Quantum Zeitgeist for the latest breakthroughs in qubits, hardware, algorithms, and industry deals. Tags: