Quantum computers outperform classical ones, with results you can trust

These issues are typically handled by performing simplified calculations using fewer qubits and verifying the results on classical hardware. If that works, it’s assumed that the algorithm will continue to work when it is run with more qubits. But that’s not the only option. Some algorithms could produce results that are difficult to calculate but easy to verify—for example, factoring the product of multiplying two large primes. Unfortunately, if anyone has identified a calculation that could be run on today’s hardware, I’m not aware of it. S0 computer scientists have had to get creative. And really, that’s what today’s announcement is about: three creative ways of handling the fact that today’s processors are error-prone. One of the new efforts was a collaboration among IBM, RIKEN in Japan, and a small company called Qedma, which develops software that helps mitigate errors in current quantum processors. The work focuses on modeling a Floquet process, in which a system oscillates while subject to an external force that gradually alters its behavior. Think of a pendulum that gradually slows down due to friction. These sorts of processes can also occur in quantum systems, and the Qedma team modeled something called an Ising model, which you can think of as a hypothetical two-dimensional grid of magnets, where the orientation of each can affect its neighbors. After setup, the orientations will gradually undergo periodic flips as they try to find a low-energy configuration in which neighboring magnets have opposite orientations. The complexity of modeling the intervening states of the system during these flips increases as you add more magnets. So Qedma chose to model something that wasn’t too large to fit into existing quantum hardware, then worked with RIKEN to run two different classical algorithms on the Fugaku supercomputer, which was the world’s most powerful computer five years ago. The classical algorithms clearly showed that something was wrong, as they produced answers that diverged over time (one showing net magnetism decreasing smoothly, the other showing it increasing). In this case, the team made a couple of key variations. The first is that it mostly performed what are called Clifford gates, which are relatively easy to simulate on classical hardware. But it sprinkled in a few non-Clifford gates (specifically T gates) of a specific type chosen in part because they are less prone to error. “Z rotations (including T gates) are special in our hardware: they are implemented by virtual frame tracking and do not add extra noise,” the paper said. But the T gates also help ensure that this is especially hard to simulate on a classical computer. “It’s got a stronger complexity argument because of the [T gates], which you can prove on average is exponentially hard to sample for a classical computer,” Gambetta told Ars. That will make it very challenging for classical algorithms to catch up. The work also linked in a few additional qubits around the periphery of those used for the algorithm, arranged so that gentle measurements performed during the operations could detect whether errors had occurred; if they were detected, the results were discarded. (Note that this would also throw out valid results that were flagged by an erroneous read of these additional qubits.) The result was an algorithm that “combines the broad output statistics of hard sampling problems with circuit structure that can be exploited for error detection and fidelity certification,” the team said. The last of the new results comes from quantum software developer Algorithmiq, which used an algorithm similar to the one in Google’s “quantum echoes” work. A set of gates first alters a quantum system, after which the process is reversed. Additional operations performed during the reversal prevent the system from returning to its original state—instead, the noise creates an imperfect “echo” of the forward process. As with one of the earlier works, attempts to simulate this on classical hardware require some simplification, and different simplification methods yield different results. By its nature, then, the problem is beyond the reach of classical hardware. The less cynical take is that the hardware is out there, and why wouldn’t computer scientists be interested in discovering its limits and pushing the systems as far as they can? While the algorithms themselves aren’t useful, the techniques developed for them—minimizing noise, understanding its nature, and identifying actions that make it worse—could still be useful for improving performance on hardware capable of error correction. And if we’re not developing algorithms for noisy machines, we’re unlikely to find out if there are any useful ones out there. Still, it’s probably best to view the results as part of a natural progression. The first wave of claims of quantum advantage came when researchers were simply excited to have hardware with enough qubits to do something that was difficult to do classically. These new efforts are part of a separate wave, in which people are now making an effort to rigorously ensure that the results are also high quality. The next step will be to explore ways to build on these newer efforts to find algorithms with real-world implications. “So you’ve got two extremes,” Gambetta said. “You’ve got the previous couple of results where they were just comparing real material to quantum computers, but in a region where classical methods still work. Now, you’ve got toy models in a regime where classical methods don’t work, but I can guarantee that I can trust the quantum one.” Taking the next step is what the field is most excited about. “The holy grail is to compare a real material or a real experiment to a quantum computer,” Gambetta said. You can find links to the three arXiv papers at IBM’s blog post about the results. These and other attempts to outperform classical systems are hosted on its advantage tracker site.