Before we developed the first qubit, theorists did work that showed that a sufficiently powerful gate-based quantum computer would be able to perform calculations that could not realistically be performed 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 began building hardware that could perform quantum annealing without a strong theoretical understanding of how it would perform compared to standard computing hardware. And for practical computing, the hardware has sometimes been outperformed by more traditional algorithms.
But on Wednesday, a team of researchers, some from D-Wave, others from academic institutions, published a paper comparing its quantum annealer with various methods of simulating its behavior. The results show that real hardware has a clear advantage over simulations, although there are two caveats: errors begin to cause the hardware to deviate from ideal performance, and it is unclear how well this performance advantage translates into practical calculations.
On ice
D-Wave hardware consists of a set 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 like what is called "spin glass," a physical system with complex behavior. It is easiest to think of a rotating glass 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 advantageous for its neighbors to have the opposite orientation (spin down). If you start with a disordered system—a spinning glass—then the influence of each magnet on its neighbors causes the spins to flip as the system tries to find its way to the lowest energy state, called the ground state.
This process is called thermal annealing and has some limitations. In standard spin glass, it is possible to end up in situations where every path to the ground state passes through a high-energy barrier. This can trap the system in a local minimum instead of being able to evolve to the ground state.
However, the D-Wave system exhibits quantum behavior. This allows it to undergo tunneling, where it passes between two low-energy states without ever occupying the intermediate high-energy states. Thus, quantum annealing is expected to perform better overall than thermal annealing.
The behavior of the rotating glasses was studied separately from the D-Wave hardware, as they can be used to model various physical processes. But the company's business is based on the fact that it is possible to map various optimization problems onto the behavior of rotating glass. In these cases, the spinning glass finding its ground state is the mathematical equivalent of finding the optimal solution to the problem.
But again, we lack a theoretical understanding of whether it is possible to obtain these solutions in some other way that is faster or more efficient.
Modeling vs. the real thing
To get a better idea of how its hardware performed, the research team started by validating the D-Wave hardware using a small rotating glass consisting of only 16 turns. "At this scale, we can numerically develop the time-dependent Schrödinger equation," the researchers write, meaning that the system's behavior during quantum annealing can be directly calculated. This 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. (In fact, they ran 100 of these 16-turn systems in parallel on the CPU.)
These results confirmed that the D-Wave processor is undergoing the expected quantum annealing process. In fact, they found that the results generated by the D-Wave processor matched Schrödinger's calculations better than either of the two ways we can model annealing: either simulated thermal annealing or simulated quantum annealing.
With this verification in hand, the team turned to much larger spinning glasses, consisting of thousands of spins. At this point, it is no longer realistic to use Schrödinger's equations: "Simulating the Schrödinger 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 hardware with simulated annealing and simulated quantum annealing.
Both real hardware and simulators showed similar behavior in that the energy gap between the system and its ground state decreased exponentially as a function of annealing time. Put another way, the system starts in a relatively high-energy state, and the energy gap between this and the ground state shrinks as a function of time as the power is increased.
The key difference between the methods is the exponent - the larger the exponent, the faster the system approaches its ground state. The simulated quantum annealing had a higher exponent than the simulated thermal annealing, while the D-Wave machine had a higher exponent than either. And this suggests that performing quantum annealing in D-Wave hardware will get to the solution significantly faster than simulated annealing can.
The only problem identified in the study came when the researchers examined how the system scaled with the number of spins tracked. There was a consistent relationship between the annealing time and the amount of energy remaining in the system for both simulations. In contrast, the D-Wave hardware performance dropped slightly, bringing it somewhat closer to the simulated quantum annealing performance. It is a product of the loss of coherence in the system - essentially errors appear and prevent the hardware from behaving as a single quantum system.
The results are still closer to optimal than those produced by any of the annealing simulations at this time. But scaling is not as good as the system maintaining its coherence. And D-Wave has indicated that improving coherence is a goal for its next-generation processors.
What does it mean?
While the spin glasses are of interest to physicists, D-Wave markets the time on its systems as a way to solve optimization problems more generally—specifically, those with practical implications. However, it is difficult to translate the results in this paper into these practical problems, although the team suggests that this is the next step: "Extending this characterization of quantum dynamics to industrially relevant optimization problems, which generally do not allow for analysis via universal critical exponents or finite-size scaling, would mean an important next step in practical quantum computing."
More simply, Andrew King, director of performance research at D-Wave, told Ars that "industrial problems in general don't even have a well-defined idea of scaling in the same way that these rotating 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 more difficult for unexpected reasons," King said. Furthermore, there are cases where highly specialized algorithms can outperform a general optimization approach, at least if the problem size remains small enough.
Despite the practical uncertainty, the empirical demonstration of a scaling advantage in quantum annealing hardware appears to have resolved an open question about D-Wave's hardware.
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