Time-Reversal Computation Offers Pathway to Practical Quantum Advantage
Researchers at Google Quantum AI have unveiled a quantum algorithm that they believe offers a viable path to demonstrating a quantum advantage over classical computers for a practically useful problem. The algorithm uses a time-reversal procedure, which—when run on Google’s recently developed Willow quantum chip—can calculate an important but elusive physical quantity that describes how quantum information spreads through a many-particle system [1]. The researchers estimate that the same computation performed with current classical methods on state-of-the-art supercomputers would take 13,000 times longer.
Unlike previous experiments claiming quantum advantage, the research team says that their protocol enables the results to be verified—either by running the same algorithm on different quantum hardware, or by making direct measurements of the many-particle system being simulated. The performance boost was also demonstrated for a computational task that could have practical use for predicting molecular structures rather than just being a theoretical benchmark. However, the small-scale “toy” problem tackled in this study means that quantum advantage has not yet been shown for a genuinely useful application.
The opportunity for others to validate the results stems from the algorithm’s ability to measure a real-world quantity, or observable, while other attempts to prove quantum advantage have relied on taking a random sample from a data distribution. The difficulty with this real-world approach is that quantum information related to the observable is typically spread among the qubits in a quantum computer. It is therefore difficult to recover this information with measurements that are localized in space and time.
However, researchers have developed experimental protocols that are less sensitive to this spreading, or scrambling, of quantum information. These schemes can be thought of as time-based interferometers, using the idea of time reversal to cause different states of the same system to interfere with each other as the system evolves forward and backward through time. The interference from these “quantum echoes” yields a measurable quantity, known as an out-of-time-order correlator (OTOC), that has already become a valuable tool in quantum sensing and metrology (see Synopsis: Quantum Scrambling Goes Anomalous).
The algorithm developed by the Google-led team measures these OTOCs in Willow—a quantum processor made from a lattice of 105 superconducting qubits (see Research News: Cracking the Challenge of Quantum Error Correction). Quantum information initially contained in a single qubit is dispersed through a sequence of gate operations that entangle qubits with their neighbors in an outgoing “wave” of quantum information. Once this forward sequence is complete, the protocol induces a local change in the quantum dynamics by perturbing a second qubit in the lattice. The final step involves performing the initial sequence of gate operations but in the reverse direction. At the end of this time reversal, the researchers measure the qubits and compute the OTOC. Alternatively, they can instruct the algorithm to repeat the whole procedure multiple times to determine so-called higher-order OTOCs.
The researchers found that the measured OTOCs reveal the effects of the perturbation with greater sensitivity than observables that only measure the forward evolution of the system. The team also showed that the second-order OTOC—taken after two time reversals and equivalent in concept to a double-path interferometer—generates constructive interference that makes it particularly sensitive to the underlying quantum dynamics. These second-order measurements uncover, for example, how the “front” of quantum information spreads through the qubit lattice.
The team reinforced these findings by comparing the OTOC measurements with two classical computation methods: numerical simulations that exactly replicate the qubit system and Monte Carlo algorithms that provide good approximations of complex quantum systems. For OTOC measurements taken after a single time reversal, there was good agreement between all three methods. But for the second-order OTOCs, the estimates from Monte Carlo simulations were unable to capture detailed quantum behavior seen in the qubit measurements. The team also estimated that a Monte Carlo algorithm running on the world’s fastest supercomputer would take around 3.2 years to compute second-order OTOCs for a 40-qubit system, while the experimental data can be collected in a little more than two hours—some 13,000 times faster.
As a demonstration of practical utility, the researchers showed that the quantum algorithm can learn from a dataset of second-order OTOCs to predict an unknown parameter of a quantum system. In this proof-of-principle experiment, 20 random quantum circuits were used to mimic a physical system, equivalent in size to a small organic molecule. “The observables we compute lend themselves to real-world applications because they allow us to compute, or to learn, the structure of molecules,” says Hartmut Neven, the lead researcher at Google Quantum AI in California.
Indeed, preliminary results indicate that the algorithm could be used to extend existing methods for mapping out molecular structures using nuclear magnetic resonance (NMR). These techniques work by measuring the coupling between atomic spins, and the Google team has worked with NMR experts to show that OTOC-based simulations could provide additional data that would help to determine longer distances in molecular structures [2]. The researchers report on proof-of-principle calculations related to two small molecules, but these computations could be done with classical computers. Still, Neven says that he remains optimistic that real-world applications that are only possible on quantum computers will emerge within the next five years.
More generally, the ability to simulate OTOCs could offer new insights into many different types of quantum systems. “The study of OTOC functions has implications for many areas of modern physics, from understanding the nature of novel materials to reconciling quantum mechanics with general relativity,” says Gerard Milburn of the National Quantum Computing Centre and the University of Sussex, both in the UK. “The ideas presented in this work might suggest how to build automated physics experiments that learn more about the world than we can using just classical computers and our simple experimental interventions.”
–Susan Curtis
Susan Curtis is a freelance science writer based in Bristol, UK.
References
- Google Quantum AI and Collaborators, “Observation of constructive interference at the edge of quantum ergodicity,” Nature 646, 825 (2025).
- C. Zhang et al., “Quantum computation of molecular geometry via many-body nuclear spin echoes,” arXiv:2510.19550v1.