A verifiable quantum algorithm outperforms supercomputers and opens new perspectives for the study of complex systems and molecular structure. Developed by Google, Quantum Echoes demonstrates a reproducible quantum advantage, linking chaos, interference, and credible future applications in chemistry and physics.
A team at Google Quantum AI has announced a landmark result: for the first time, a quantum computer has executed a verifiable algorithm faster than a classical supercomputer. The algorithm, called Quantum Echoes, and reported in Nature, represents a significant step toward practical applications of quantum computing.
In the past, demonstrations of so-called “quantum supremacy” had already been achieved – most notably in 2019, with calculations that were infeasible for classical machines. However, those challenges were largely academic and difficult to verify directly. With Quantum Echoes, the discussion shifts to verifiable quantum advantage: the result can be reproduced and independently checked on another quantum machine of comparable capability, confirming its correctness. In other words, this is not a random output useful only for breaking a record, but a computation with concrete and reproducible scientific value.
The broader context is one of steady progress in quantum computing. After the initial 2019 demonstration, research efforts increasingly focused on reducing quantum error rates, long recognized as a major bottleneck. At the end of 2024, Google introduced Willow, a 105-qubit quantum chip with dramatically reduced errors. Thanks to these hardware improvements, in 2025 the team succeeded in running Quantum Echoes on Willow 13,000 times faster than the best equivalent classical algorithm executed on one of the world’s most powerful supercomputers.
This milestone suggests that quantum computers are beginning to outperform supercomputers not only on abstract benchmark problems, but also on targeted tasks with plausible real-world implications.
TAKEAWAYS
What are OTOCs and why they matter
At the core of Quantum Echoes lies an algorithm designed to estimate specific physical quantities known as OTOCs, short for Out-of-Time-Ordered Correlators. Put simply, an OTOC measures how much a quantum system “remembers” a small initial disturbance as time passes.
OTOCs originated in the study of quantum chaos. Much like the butterfly effect in classical chaotic systems, a quantum OTOC quantifies how a minimal perturbation – such as flipping the spin of a single particle – spreads and influences other parts of a quantum system as it evolves.
In a chaotic system, entanglement and complexity grow rapidly with the number of particles and the evolution time. Standard observables tend to lose memory of initial details: the effect of a disturbance becomes scrambled, blending into the overall system and becoming indistinguishable from the background. As a result, after some time, no measurable differences remain that can be traced back to the initial perturbation – the system effectively “forgets” its starting conditions.
This poses a limitation, because many of the most interesting quantum phenomena are hidden precisely in these subtle correlations that vanish quickly. Moreover, unlike classical systems, one cannot rely on exponential sensitivity to initial conditions to reveal chaos, since the Schrödinger equation is linear. The classical notion of chaos therefore needs to be rethought in the quantum domain.
This is where OTOCs come into play. They provide a powerful way to uncover hidden details using quantum echo protocols based on time reversal. In practice, one constructs an experiment in which the system is allowed to evolve, a small perturbation is introduced, and then the evolution is reversed through a controlled time inversion. The key question is how much of the initial disturbance reappears in the final echo.
If the system had not been perturbed, the time reversal would return it exactly to its initial state. Any residual difference observed in the final echo, instead, indicates how far and how deeply the disturbance has propagated through the system. Technically, the OTOC captures the correlation between the perturbing operator and the final measurement after the time-reversal protocol. A high OTOC value indicates that the initial information is still largely intact, while a low value signals that the disturbance has spread across many degrees of freedom.
OTOCs are important because they act as ultra-sensitive probes of internal quantum dynamics. They provide access to correlations that remain invisible to conventional measurements lacking time inversion. Over the past decade, OTOC-related concepts have been applied across frontier fields, from quantum metrology and many-body thermalization to speculative studies of how information disperses inside black holes.
Having an efficient algorithm to compute OTOCs experimentally amounts to gaining a tool for “seeing the invisible”: understanding phenomena such as entanglement growth or coherent trajectories hidden within apparent chaos.
The Google experiment: how Quantum Echoes works
Google’s Quantum Echoes algorithm computes an OTOC by generating a quantum echo on a programmable superconducting processor with 105 qubits—the Willow chip. The term “echo” is intentional: the procedure resembles echo experiments long used in physics, such as spin echoes in NMR or the Loschmidt echo. Google describes it as sending a signal into the quantum computer, inverting it, and listening to the echo that returns.
In practice, the team implemented the following cycle of operations on the quantum processor:
- forward evolution: the qubit system is prepared in a known initial state and allowed to evolve under a sequence of quantum gates representing time evolution.
- perturbation: at a chosen point, an operation is applied to a single qubit – such as a spin flip – to introduce a controlled, localized disturbance.
- backward evolution: the dynamics are inverted by applying suitable quantum operations, ideally reversing the system’s evolution as if time were flowing backward.
- echo measurement: finally, the state of a reference qubit – often the one initially perturbed – is measured to determine whether it has returned to its original state.
If the backward evolution perfectly cancels all changes, the disturbance leaves no global trace. Any deviation observed, however, is precisely the echo of the perturbation: a signal revealing how the information has spread through the system.
This process exploits a crucial principle: constructive quantum interference. During the echo, the many possible evolution paths – conceptually akin to parallel trajectories taken by quantum information – are brought back into phase by the time inversion. As a result, the signal is amplified: quantum waves corresponding to the echo add up rather than cancel out.
This dramatically enhances sensitivity. Even very small effects become clearly measurable, emerging from background noise. In Google’s experiment, this constructive interference revealed signal contributions that would otherwise remain undetectable.
The experiment succeeded in measuring complex quantum correlations (second-order OTOCs) in a strongly entangled 105-qubit system, maintaining sensitivity even at long evolution times. What makes the result remarkable is twofold.
On one hand, it demonstrates high-level quantum correlations in a large-scale system, confirming that the quantum echo remains sensitive even when conventional measurements would vanish. On the other hand, the task is computationally prohibitive for classical computers, due to the immense complexity of simulating all interfering trajectories in such a large quantum system.
Indeed, the measured OTOC value receives contributions from a vast number of evolution paths – described in the paper as “Pauli strings forming large loops” within the system – producing a collective interference effect intractable for classical methods. This complexity is precisely what allows the quantum chip to outperform supercomputers on this problem, marking a clear example of quantum advantage.
Crucially, the result is verifiable. In principle, verification would require another quantum computer of comparable capability: running Quantum Echoes under the same initial conditions should yield the same outcome, confirming that the result is not an artifact or a random error. Within the current experiment, reproducibility was demonstrated internally by repeating the protocol many times on the same device.
This represents a substantial advance over earlier, non-verifiable quantum demonstrations and brings quantum computers closer to being reliable scientific instruments whose outputs can be meaningfully used by other researchers.
A “Quantum Ruler” for molecules: application in NMR
Another source of excitement surrounding Quantum Echoes lies in its first practical application in molecular chemistry. In a proof-of-principle experiment conducted in collaboration with the University of California, Berkeley, the team used the algorithm as a kind of molecular ruler to measure distances and angles within organic molecules.
The underlying idea is to combine traditional Nuclear Magnetic Resonance (NMR) spectroscopy with the computational power of quantum computing, overcoming some of the current limitations in molecular structure analysis.
NMR is a foundational tool in chemistry and biology. By exploiting magnetic interactions between atomic nuclei (spins), it provides information about distances and geometry within molecules – effectively acting as a molecular microscope. However, conventional NMR techniques have limitations. For example, they cannot directly measure distances between carbon nuclei beyond roughly 6 ångströms (0.6 nanometers). In large and complex molecules, this leaves significant gaps in structural information.
Google’s experiment addresses this limitation by using OTOCs as amplifiers of structural signal. In brief, the researchers suspended organic molecules – two model compounds, one with 15 atoms and another with 28 atoms – in a liquid-crystal medium. They then applied NMR pulse sequences that generate a many-body echo among interacting nuclear spins. During the echo, controlled perturbations were introduced on selected nuclei – known as butterfly spins – and the effect of these perturbations on the refocused signal was measured.
Effectively, the experiment measured an OTOC within a real molecular system. Polarization initially localized on one nucleus propagates through the network of molecular spins; the pulse sequence then reverses the evolution, refocusing the polarization back to the original nucleus. If a distant nucleus is perturbed during the process, the final echo amplitude decreases, indicating that the influence of the initial excitation had extended to that remote site.
This method makes it possible to determine how far the influence of an atom travels within a molecule – information directly related to interatomic distances.
Interpreting such enriched NMR signals quantitatively is not trivial. It would require simulating the quantum dynamics of many interacting spins with complex dipolar couplings, a task that becomes exponentially difficult for classical computers as the number of nuclei grows. This is where the quantum computer becomes essential.
The researchers used the quantum processor to simulate the relevant spin dynamics – via tailored quantum circuits – and extract the desired structural information from the NMR data. This hybrid approach allowed them, for example, to determine the average distance between two hydrogen atoms in specific positions within a toluene molecule, as well as the average torsion angle of a dimethyl-substituted biphenyl. The accuracy and precision were comparable to those obtained with independent traditional spectroscopic methods.
In other words, the quantum echo provided a measurement tool for structural features that would otherwise remain beyond the reach of conventional NMR alone.
The results are encouraging. Comparisons with established techniques confirmed that Quantum Echoes measurements align with known structural data, while also revealing additional details inaccessible to standard NMR. This suggests that integrating quantum computers into molecular analysis workflows could unlock previously hidden information – such as longer-range distances or higher-order correlations in macromolecules – deepening our understanding of complex chemical structures.
The authors describe this technique as a “quantum-scope”: a new quantum instrument that, much like telescopes and microscopes in earlier eras, could enable the measurement of natural phenomena that were previously unobservable. Potential applications include drug discovery, where understanding how candidate molecules bind to biological targets is crucial, and materials science, where detailed molecular structure determines the properties of polymers, battery components, or even materials used to build qubits themselves.
In this vision, quantum computing acts as both an amplifier and an interpreter of experimental signals, filling gaps left by existing techniques.
Current limits and open questions
Despite its success, it is important to remain realistic. Quantum Echoes, while promising, is an early step, and several limitations and open questions remain.
First, the experimental result applies to a specific class of problems – the computation of OTOCs and the extraction of structural parameters. It does not imply that quantum computers generically outperform classical ones across all computational tasks. Rather, it demonstrates that, when the algorithm and the physical system are carefully matched, a quantum computer can surpass even the best supercomputers on targeted problems.
The challenge ahead is to identify additional “useful” applications that exploit similar principles of constructive quantum interference to achieve verifiable quantum advantage. The field will need a broader repertoire of such algorithms, each tailored to real problems across scientific and industrial domains.
A second major limitation is the dependence on cutting-edge hardware. The Quantum Echoes experiment required an exceptionally high-quality device: 105 individually controllable qubits, fast quantum operations, and extremely low error rates. If the qubits were noisier or the gates less precise, the quantum echo would have been lost in noise before revealing anything meaningful.
As things stand, only a handful of laboratories worldwide possess the technology required to replicate such a result. Scalability therefore remains an open issue. Can error rates remain sufficiently low as the number of qubits and circuit complexity increase? Google’s engineers emphasize that achieving fully practical applications will require large-scale quantum error correction. Their next stated goal is the realization of a long-lived, near-perfect logical qubit, built by combining many physical qubits to cancel errors. Only with stable, error-corrected qubits will it be possible to run longer algorithms and tackle even more complex problems without losing computational fidelity.
There is also the issue of independent verification and trust. By definition, quantum advantage implies that classical verification is either impossible or impractically slow. In the case of Quantum Echoes, verifiability relies on the ability to run the same algorithm on another comparable quantum computer. At present, however, few such machines exist, so verification has been largely internal, through repeated runs on the same device.
In the future, as more groups gain access to powerful quantum hardware, broader replication and cross-validation should become possible. For now, the scientific community must rely on indirect checks: simplified classical simulations on reduced systems, consistency with known physical laws, and agreement with independent experimental measurements – such as the NMR comparisons already performed.
Another open question concerns the scope of applicability of the method. Quantum Echoes has demonstrated its ability to extract structural information in systems exhibiting chaotic many-body dynamics and a measurable echo. But how general is this approach? Will it work for any complex quantum system, or only for those amenable to echo-type formulations involving controlled time reversal?
In the molecular experiments, for example, a highly specific setup was required – molecules isolated in a liquid-crystal environment to suppress unwanted interactions. Applying the same scheme to noisier or more open systems may prove more challenging. Moreover, the time-reversal protocol demands precise knowledge and control of interactions among qubits or spins. If the physical model is not known accurately enough, the echo may fail to refocus correctly.
In their work, the researchers also used OTOC experiments as a form of Hamiltonian learning, inferring details of the quantum chip’s own Hamiltonian by comparing measurements with theoretical expectations. This adds further value, but also highlights the need for deep system understanding and accurate modeling to fully exploit the algorithm.
In short, significant scientific and technological challenges remain: increasing the number of usable qubits, further reducing or correcting errors, developing new quantum algorithms for other problems, and integrating these methods into established experimental practices. Progress will likely require years of continued research and development.
Looking ahead: implications and next steps
Despite these uncertainties, the progress demonstrated by Quantum Echoes is tangible and opens multiple avenues. For the scientific community, having a tool such as quantum-computed OTOCs means being able to investigate complex quantum systems – from materials with emergent properties to fundamental physics simulators – through a new analytical lens.
It may, for instance, enable deeper studies of how quantum information spreads through different systems, a topic relevant not only to fundamental physics but also to understanding decoherence and improving quantum computers themselves. As suggested, similar algorithms could also help extract information from highly intricate experimental signals – not only in NMR, but potentially in optical spectroscopy or other measurement techniques involving complex dynamics.
From an application perspective, the demonstration that a quantum computer can meaningfully contribute to determining molecular structure is particularly significant. Drug design, materials discovery, and protein chemistry could all benefit from approaches in which the quantum computer becomes an integral part of the laboratory toolkit. Importantly, this does not mean replacing classical instruments. A quantum computer does not “measure” a molecule on its own; it still relies on experimental data such as NMR signals. Rather, it complements classical tools by analyzing complexity they cannot handle effectively.
Looking forward, hybrid quantum-classical workflows may become increasingly common, with quantum resources used specifically where they excel: managing strongly correlated, high-complexity systems.
From the perspective of decision-makers and funders, results such as Quantum Echoes provide a clear signal that investments in quantum technology are beginning to pay off. The idea of achieving a useful quantum advantage is no longer just theory: there is a concrete example, published in a prestigious journal and obtained by a multidisciplinary team (quantum computing engineers together with chemists and NMR physicists). This could stimulate further support for quantum research, but it also requires careful management of expectations. We are not yet at the stage of a fully operational “quantum internet” or universal quantum computer, but we are beginning to see the first pieces of the puzzle in which qubits do things that classical computers cannot do in specific areas.
Ultimately, Quantum Echoes marks a change of pace: it demonstrates that quantum computers can not only compute faster, but also reveal new information about complex systems, thanks to algorithms inspired by profound concepts in quantum physics (such as echo and interference). The road to large-scale applications is still long and uncertain – more reliable qubits, new algorithmic ideas, and further confirmation will be needed – but this result offers exciting proof of principle. Like any major scientific advance, it raises many questions in addition to answering the initial ones. The community now has a concrete example of a verifiable quantum advantage to build on: it will be up to researchers to explore how far it can go.
