Scholes Group quantum “mimics” invoke the quantum world while working out of the classical
Last year, the Scholes Group published a paper in the Proceedings of the Royal Society A detailing how certain quantum-like states can be expressed in classical systems using networks to encode information. The paper was based on using just one or two qubits, a simple approach that had limited application to the size of the state space.
Mulling over a broader solution last summer, Gregory Scholes came up with the idea at the heart of his group’s latest paper: using mathematical expander graphs to produce tangible, complex classical networks that mimic the signature states and correlations of quantum systems of any size and complexity.
PAPER: Quantum-like product states constructed from classical networks
JOURNAL: Physical Review Letters
AUTHORS: Gregory Scholes and Graziano Amati
WHAT IT IS: The Scholes Group has developed a means to access a physical representation of the exponential complexity of quantum computing on a classical platform by using expander graphs, a concept that Scholes plucked from discrete mathematics. Graphs are broadly defined as mathematical structures representing function. They permit the manifestation of massive space states using a pairwise relationship between objects comprised of vertices and edges.
ON SYNCHRONIZATION: This new framework serves as a kind of translator between the classical and the quantum, providing a map that both generates the state space of a quantum information system and templates a corresponding classical many-body system. One example of such a classical system is a network of synchronizing oscillators.
Synchronization is generally dismissed as a resource for quantum technology because it is nonlinear. But Scholes has discovered how to translate such systems into a state space that replicates the quantum mechanical laws. The basis of the idea is that synchronization of specially constructed large nonlinear systems, for example coupled oscillators, can produce robust emergent states that mimic the properties of quantum states. The underlying networks are guaranteed to produce a single distinguished state counterbalanced by a separate “lump” of random states.
COMMENT FROM P.I. GREGORY SCHOLES, WILLIAM S. TOD PROFESSOR OF CHEMISTRY: “I use this as an almost philosophical tool to understand some of the deeper questions in quantum mechanics. The thought experiments become concrete, so you can address questions in a whole new light. If I take my little quantum bit network and multiple it by itself or by the other qubit networks more generally using a special kind of product operation, the graph becomes massive very quickly. That is a physical representation of the exponential complexity exploited by quantum computers.”
P.I. Gregory Scholes, the William S. Tod Professor of Chemistry and first author on the paper.
“And what Graziano has been working on is, can we run a quantum algorithm on this network even though it’s classical? The answer is yes. It’s complex, but you can do it—at least for modest numbers of qubits. So instead of having a huge, expensive genuine quantum computer, perhaps one day you will be able buy a chip that would do exactly the same thing classically and the output would be indistinguishable from the quantum computer.
“Essentially what the paper tells you is that we can construct quantum mimics that enable us to generate and exploit a quantum world without being in the quantum world.”
COMMENT FROM SECOND AUTHOR GRAZIANO AMATI: “Compared to Greg’s previous manuscript (PRSa), our work extends the analysis to systems of arbitrary dimensions, explicitly addressing scalability—an aspect not formally explored in the earlier work. While we recognize that an exponential number of classical resources is required to fully capture quantum correlations, we emphasize that classical systems offer significant advantages in terms of implementation and processing feasibility.”
Postdoctoral fellow Graziano Amati.
“Our findings suggest that classical many-body systems can encode the correlations necessary to construct robust global (emergent) states, which can be in turn mapped onto quantum states. By scaling these classical systems, we explore the feasibility of storing and processing information in a quantum-like way using classical resources. Current limitations in system size due to available experimental resources do not hinder testing the viability of this formalism for important classes of quantum-inspired algorithms, e.g. for processes related to entanglement.”
Amati is a postdoctoral fellow in the Scholes Group.
NEXT STEPS: The group is currently conducting a formal analysis of quantum-like information processing within this framework. Additionally, an upcoming paper, now in preprint, provides experimental perspectives on implementing this approach in small- to medium-scale setups, such as LC circuits and spin-torque oscillators. Researchers are also further strengthening the connections between classical network dynamics and quantum information theory.
FUNDING: This research was funded by the National Science Foundation under Grant No. 2211326, and the Gordon and Betty Moore Foundation through Grant GBMF7114.