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Enlarge / The D-Wave hardware is, quite literally, a black box.

D-Wave

Before we had developed the first qubit, theoreticians had done the work that showed that a sufficiently powerful gate-based quantum computer would be able to perform calculations that could not realistically be done on traditional computing hardware. All that is needed is to build hardware capable of implementing the theorists' work.

The situation was essentially reversed when it came to quantum annealing. D-Wave started building hardware that could perform quantum annealing without a strong theoretical understanding of how its performance would compare to standard computing hardware. And, for practical calculations, the hardware has sometimes been outperformed by more traditional algorithms.

On Wednesday, however, a team of researchers, some at D-Wave, others at academic institutions, is releasing a paper comparing its quantum annealer with different methods of simulating its behavior. The results show that actual hardware has a clear advantage over simulations, though there are two caveats: errors start to cause the hardware to deviate from ideal performance, and it's not clear how well this performance edge translates to practical calculations.

D-Wave's hardware consists of a collection of loops of superconducting wires. Current can circulate through the loops in either direction, with the direction providing a bit value. Each loop is also connected to several of its neighbors, allowing them to influence each other's behavior.

When properly configured, the system can behave as what's called a "spin glass," a physical system with complex behavior. A spin glass is easiest to think about as a grid of magnets, with each magnet influencing the behavior of its neighbors. When one magnet is in a given orientation (like spin up), it becomes more energetically favorable for its neighbors to have the opposite orientation (spin down). If you start with a disordered systema spin glassthen the influence of each magnet on its neighbors will cause spins to flip as the system tries to find a path to the lowest energy state, called the ground state.

This process is called thermal annealing, and it has some limits. In a standard spin glass, it's possible to end up in situations where every path to the ground state goes through a high-energy barrier. This can trap the system in a local minimum instead of allowing it to evolve into the ground state.

D-Wave's system, however, shows quantum behavior. This allows it to undergo tunneling, where it passes between two low-energy states without ever occupying intervening high-energy states. So, quantum annealing is expected to have better overall performance than thermal annealing.

The behavior of spin glasses has been studied separately from D-Wave's hardware because they can be used to model a variety of physical processes. But the company's business is based on the fact that it's possible to map a variety of optimization problems onto the behavior of a spin glass. In these cases, having the spin glass find its ground state is the mathematical equivalent of finding the optimal solution to a problem.

But again, we lack the theoretical understanding of whether it's possible to get these solutions in some other way that's faster or more efficient.

To get a better sense of how its hardware performed, the research team started by validating the D-Wave hardware using a small spin glass consisting of only 16 spins. "At this scale we can numerically evolve the time-dependent Schrdinger equation," the researchers write, meaning that the behavior of the system during quantum annealing could be directly calculated. That was compared to the same process running on a small corner of one of D-Wave's Advantage processors, which have roughly 5,000 individual qubits. (They actually ran 100 of these 16-spin systems in parallel on the processor.)

These results confirmed that the D-Wave processor undergoes the expected quantum annealing process. In fact, they found that the results generated by the D-Wave processor were a better match for the Schrdinger calculations than either of two ways we can model annealing: either simulated thermal annealing, or simulated quantum annealing.

With that validation in hand, the team turned to much larger spin glasses, consisting of thousands of spins. At this point, it's no longer realistic to use Schrdinger's equations: "Simulating the Schrdinger dynamics of QA with a classical computer is an unpromising optimization method, as memory requirements grow exponentially with system size." Instead, the researchers compared D-Wave's hardware to simulated annealing and simulated quantum annealing.

Both the actual hardware and the simulators all showed a similar behavior, in that the energy gap between the system and its ground state decayed exponentially as a function of annealing time. Put differently, the system starts in a relatively high-energy state, and the energy gap between that and the ground state gets smaller as a function of time raised to a power.

The key difference between the methods is the exponentthe bigger the exponent, the faster the system approaches its ground state. Simulated quantum annealing had a higher exponent than simulated thermal annealing, while the D-Wave machine had a higher exponent than either of them. And that indicates that doing quantum annealing in D-Wave's hardware will get to a solution considerably faster than simulated annealing can.

The one problem identified in the study came when the researchers explored how the system scaled with the number of spins being tracked. For both simulations, there was a consistent relationship between annealing time and the amount of energy left in the system. By contrast, the performance of the D-Wave hardware tailed off slightly, bringing it somewhat closer to the performance of the simulated quantum annealing. This is a product of a loss of coherence in the systemin essence, errors crop up and keep the hardware from behaving as a single quantum system.

The results are still closer to optimal than the ones that are produced in this time by either of the annealing simulations. But the scaling isn't as good as it is when the system retains its coherence. And D-Wave has indicated that improving coherence is a goal for its next generation of processors.

While spin glasses are interesting to physicists, D-Wave is selling time on its systems as a way to solve optimization problems more generallyspecifically those with practical implications. But it's difficult to translate the results in this paper to these practical problems, though the team suggests that's the next step: "Extending this characterization of quantum dynamics to industry-relevant optimization problems, which generally do not enable analysis via universal critical exponents or finite-size scaling, would mark an important next step in practical quantum computing."

Put more simply, Andrew King, director of performance research at D-Wave, told Ars that "industrial problems generally don't even have a well-defined notion of scaling in the same way that these spin glasses do."

"For industrial problems, I can say that problem A has more variables than problem B, but there may be other confounding factors that make problem B harder for unexpected reasons," King said. In addition, there are some cases where highly specialized algorithms can outperform a general optimization approach, at least as long as the size of the problem remains small enough.

Despite the practical uncertainty, the empirical demonstration of a scaling advantage in quantum annealing hardware would seem to settle what had been an open question about D-Wave's hardware.

Nature, 2023. DOI: 10.1038/s41586-023-05867-2 (About DOIs).

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Quantum effects of D-Waves hardware boost its performance - Ars Technica