Quantum computers are anticipated to surpass contemporary classical computers in numerous scientific fields, such as chemistry, physics, and cryptography, yet demonstrating their superiority has proven difficult. The most recognized challenge where quantum computers are believed to hold an advantage, referred to by physicists as “quantum advantage,” centers around the process of factoring sizable integers, a complex mathematical problem central to the security of digital data.
In 1994, Caltech graduate Peter Shor (BS ’81), then affiliated with Bell Labs, created a quantum algorithm capable of rapidly factoring large integers within mere seconds, while this challenge could consume millions of years for a traditional computer. Ultimately, once quantum computers reach operational capacity—a target researchers estimate may be a decade or more away—these devices will proficiently factor large integers vital to cryptographic techniques.
However, aside from Shor’s algorithm, scientists have struggled to identify problems where quantum computers can demonstrate a clear advantage. Recently, a Caltech-led research team reported in a new Nature Physics study the discovery of a common physics challenge that these advanced machines could excel at addressing. The issue pertains to modeling how materials cool down to their minimum energy states.
“In nature, we can place a material in a refrigerator to cool it down to its lowest-energy state,” explains John Preskill, the Richard P. Feynman Professor of Theoretical Physics, the Allen V. C. Davis and Lenabelle Davis Leadership Chair of Caltech’s Institute for Quantum Information and Matter (IQIM), and an Amazon Scholar at the AWS Center for Quantum Computing at Caltech. “However, modeling this process is challenging for a quantum computer and even more so for a classical computer.”
In this recent investigation, the team designed a quantum algorithm (a series of computing commands) theoretically capable of identifying low-energy states—termed local minima by physicists—of any material. Their findings theoretically establish that this algorithm performs significantly better than its classical alternatives.
“This provides a novel approach to assess quantum advantage,” states co-author Hsin-Yuan (Robert) Huang (PhD ’24), a senior research scientist at Google Quantum AI who recently joined the Caltech faculty as an assistant professor of theoretical physics. “There are several additional methods to evaluate quantum advantage beyond Shor’s algorithm, but their practicality remains uncertain. This test, however, is designed for a wide range of physics domains, including materials science, condensed matter physics, high-energy physics, and chemistry.”
Scientists aspire to identify the lowest-energy, or most stable, states of materials to forecast their behavior. For instance, chemists might use computers to calculate a molecule’s local-minimum energy states when assessing it for drug applications. Computational models would assist in predicting how the molecule interacts with its biological target, thus expediting the drug discovery process.
The absolute lowest-energy state of a material is known as its ground state. As a material cools in a refrigerator, it will encounter low-energy plateaus along the way until it reaches the ground state. “It’s akin to hiking downhill in search of the lowest point. You might pause at a flat plateau en route, a local minimum,” explains Preskill. “For classical computers, locating these local minima can pose a significant challenge.”
Classic computers “become trapped in what they perceive as a local minimum, yet it isn’t,” Huang clarifies. “It’s as though the classical computer concludes it has reached the lowest point it can attain and cannot proceed further to uncover a genuine local minimum.”
Quantum computers—driven by the peculiar characteristics of the subatomic realm like entanglement and superposition—are more adept at tackling such problems. Similar to the scenario of factoring prime numbers, they possess the capability to explore options that classical computers cannot access. “Quantum computers won’t become ensnared by these illusory low-energy plateaus envisioned by traditional computers and can discover alternative paths,” Huang remarks. “They excel in navigating the energy terrain.”
Co-author Chi-Fang (Anthony) Chen, a former graduate student of Fernando Brandão, Bren Professor of Theoretical Physics at Caltech and director of applied science at the AWS Center for Quantum Computing, had previously been working on quantum algorithms to expedite local minima searches for materials. In this latest study, the team advanced the approach to construct an algorithm that definitively demonstrates superior performance compared to classical algorithms.
“This paper addresses the establishment of a well-justified category of physics problems where quantum advantage is evident,” states Preskill. “While quantum computers aren’t feasible for use at present, this is a domain in which they are likely to yield improved predictions.”
The research, titled “Local minima in quantum systems“, received funding from the National Science Foundation, the Department of Energy’s Office of Science, the Walter Burke Institute for Theoretical Physics, the AWS Center for Quantum Computing, and a Google PhD Fellowship. Other contributors to the study include Leo Zhou, a former Caltech postdoc currently an assistant professor of electrical and computer engineering at UCLA.
In related research, David Hsieh, Caltech’s Donald A. Glaser Professor of Physics, along with Gil Refael, the Taylor W. Lawrence Professor of Theoretical Physics, and their collaborators demonstrate how local minima can be accessed experimentally, beginning from the ground state. Using a crystal of Ca2RuO4 as a demonstration platform, which has a ground state characterized by electron spins aligned antiparallel from one lattice site to another, researchers stimulated the crystal with an ultra-quick burst of light lasting under one picosecond to elevate the material into a local-energy minimum where the spins are aligned in a parallel direction between sites. This parallel-aligned configuration remains stable for microseconds, revealing that the system is securely trapped in the local minimum.
According to Preskill, “the capability to compute and experimentally access local minima by driving systems far from thermal equilibrium could provide a method to adapt the properties of quantum materials on demand.”
The paper titled “Time-hidden magnetic order in a multi-orbital Mott insulator” has been published in Nature Physics and was supported by IQIM, a National Science Foundation Physics Frontiers Center; the Gordon and Betty Moore Foundation; the Simons Foundation; the Army Research Office; and a Caltech Postdoctoral Prize Fellowship. Additional authors comprise Xinwei Li and Iliya Esin, former Caltech postdoctoral researchers who are now assistant professors of physics at the National University of Singapore and Bar Ilan University, respectively; current graduate students Youngjoon Han and Yincheng Liu; previous graduate students Honglie Ning (PhD ’23), currently a postdoc at MIT, and Jun-Yi Shan (PhD ’22), presently a postdoc at UC Berkeley; former postdoc Kyle Seyler, now an assistant professor at the University of Arizona; and former Caltech WAVE student Cora Barrett, now a graduate student at MIT.