What does it mean for the 5000Q annealer to achieve quantum advantage
Introduction: Before we developed the first qubit, theorists had done some work showing that a sufficiently powerful gate-based quantum computer would be able to perform computations that cannot be practically done on conventional computing hardware. All that was needed was to build the hardware that would enable the theorists to work.
When it comes to quantum annealing, the situation is basically the opposite. D-Wave set out to build hardware capable of performing quantum annealing without much theoretical understanding of how its performance would compare to standard computing hardware; and, in actual computing, the hardware was sometimes outperformed by conventional algorithms.
Yesterday, a paper published in the journal Nature really dispelled this doubt.
(NYSE: QBTS) published a peer-reviewed milestone paper on April 19: its 5000-qubit Advantage™ quantum computer performs significantly faster than classical computing on the "3D spin-glass optimization problem (a class of intractable optimization problems). " is significantly faster than classical computing. However, it is not yet clear how this performance advantage translates into real-world computation.
The experimental paper, titled "Quantum critical dynamics in a 5,000-qubit programmable spin glass," was published in the journal Nature.
Dr. Alan Baratz, CEO of D-Wave, said, "This research marks a major achievement in quantum technology because it demonstrates the computational advantages over classical methods for a class of intractable optimization problems. For those seeking evidence of the unparalleled performance of quantum annealing methods, this work provides clear proof."
For this research, D-Wave and Boston University scientists collaborated to use the QA processor to study the critical dynamics of spin-glass QPT. The ultra-slow dynamics of spin-glass states makes this phase transition extremely important in quantum optimization studies; the results show that the D-Wave quantum processor can compute coherent quantum dynamics in large-scale optimization problems.
The D-Wave hardware consists of a set of superconducting wires in the shape of a loop. Current can be circulated through these loops in any direction, and the direction provides a bit value. Each loop is also connected to several neighboring loops, allowing them to influence each other's behavior.
Programmable quantum spin glass experiments.
When properly configured, the system can behave as a "spin glass" - a physical system with complex behavior. A spin glass is most easily thought of as a lattice of magnets, each of which influences the behavior of its "neighbors". When a magnet is in a given direction (e.g. spin up), it is energetically more favorable for its "neighbors" to have the opposite direction (spin down).
If one starts with a disordered system, then the effect of each magnet on its "neighbors" will result in a spin flip as the system tries to find a path to the lowest energy state (ground state).
This process is called thermal annealing, and it has some limitations. In a standard spin glass, it is possible for each path to the ground state to pass through a high-energy "barrier". This could trap the system in a local minimum rather than allowing it to evolve to the ground state.
However, the D-Wave system shows quantum behavior. This allows it to undergo quantum attempts to pass between two low energy states without occupying the intermediate high energy state. Thus, quantum annealing is expected to have better overall performance than thermal annealing.
The behavior of spin glasses can be used to model a variety of physical processes, and D-Wave's business is based on the fact that it is possible to map various optimization problems onto spin glass behavior. In these cases, having the spin glass find its ground state is mathematically equivalent to finding the optimal solution to the problem.
To better understand the performance of its hardware, the team first verified the D-Wave hardware using a small spin glass consisting of only 16 spins.
At this scale, we can numerically evolve the time-dependent Schrödinger equation, which means that the behavior of the system during quantum annealing can be directly calculated," the paper reads. This compares with the same process run in a small corner of one of D-Wave's Advantage processors, which has about 5,000 individual quantum bits. (They actually ran 100 of these systems in parallel on that processor.)"
These results confirm that the D-Wave processor underwent the expected quantum annealing process. In fact, they found that the D-Wave processor produced better results with Schrödinger's calculations than either of the two ways we can model annealing.
Experimental results for Schrödinger's dynamics
With this validation, the team moved on to larger spin glasses: composed of thousands of spins. At this point, it was no longer practical to use the Schrödinger equation: "Simulating the Schrödinger dynamics of QA with a classical computer is an unpromising optimization method because the memory requirements grow exponentially with the size of the system." Therefore, the researchers compared D-Wave's hardware with simulated annealing and simulated quantum annealing.
The results showed that all hardware and simulators showed similar behavior: the energy gap between the system and its ground state decayed exponentially as a function of annealing time. In other words, the system starts from a relatively high energy state and the energy gap between it and its ground state becomes smaller as time increases.
The key difference between these two methods is the exponent. The larger the exponent, the faster the system approaches its ground state. The exponent of simulated quantum annealing is higher than that of simulated thermal annealing, while the exponent of the D-Wave machine is higher than both of them. This suggests that performing quantum annealing in D-Wave's hardware will lead to a faster solution than simulated annealing.
Experimental results after dynamic finite size expansion of 3D spin glass
These findings have a direct impact on optimization, showing that coherent quantum annealing can improve the quality of the solution much faster than classical algorithms. The observed speedup coincides with the theory of coherent quantum annealing and shows a direct link between coherence and the core computational power of quantum annealing.
Critical scaling of the final residual energy
One of the issues identified in the study was the consistent relationship between annealing time and the amount of energy remaining in the system as the researchers explored how the system scaled as the number of spins increased. In contrast, the performance of the D-Wave hardware was slightly degraded.
Still, these results are closer to optimal than any of the annealing simulations produced during this time. And D-Wave has said that improved consistency is a goal for its next generation of processors.
While spin glasses are interesting to physicists, it is difficult to translate the results of this paper into practical problems, although the team suggests that this is the next step: "Extending this feature of quantum dynamics to industry-relevant optimization problems that are typically not analyzable by universal critical exponents or finite-size expansions would mark the next an important step forward in practical quantum computing."
More simply put, Andrew King, D-Wave's director of performance research, said, "Industrial problems often don't even have a well-defined notion of scaling, as with these spin glasses."
"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. Moreover, in some cases, highly specialized algorithms can outperform general optimization methods, at least as long as the size of the problem remains small enough.
Despite the practical uncertainties, the empirical demonstration of the scaling benefits of quantum annealing hardware still resolves open questions about the advantages of D-Wave hardware.
This work supports D-Wave's ongoing commitment to relentless scientific innovation and product delivery as the company continues to develop its future annealing and gate model quantum computers. To date, D-Wave has brought five generations of quantum computers to market and is launching an experimental prototype of its sixth generation machine, the Advantage2™ system, in June 2022.
"Not only is this the largest quantum simulation demonstration to date, but it also provides the first theoretically supported experimental evidence that coherent quantum dynamics can accelerate the implementation of better solutions for quantum annealing." Mohammad Amin, a researcher in quantum algorithms and systems at D-Wave, concluded, "The observed acceleration can be attributed to the complex critical dynamics of the quantum phase transition process, and we believe these findings have significant implications for quantum optimization and will have practical applications in solving real-world problems."
Link to paper:
https://www.nature.com/articles/s41586-023-05867-2
Reference links:
[1] https://finance.yahoo.com/news/d-wave-demonstrates-first-ever-150000390.html
[2]https://arstechnica.com/science/2023/04/quantum-effects-of-d-waves-hardware-boosts-its-performance/
[3] https://www.dwavesys.com/solutions-and-products/systems/
