# Experiment results of the Next-generation D-Wave QPU (demo version)

## Next-generation D-Wave QPU

On June 10, 2022, D-Wave published a press release about next-generation QPU. Advantage2 will have more than 7000 qubits; the new topology is called the Zephyr topology, and the degree is 20. In other words, the new QPU is a specification that surpasses the current "Advantage," which has about 5000 qubits and 15 orders (Pegasus topology).

Already the demo version which has 500 qubits is released in D-Wave Leap. And that features are below.

### 1. More compact embeddings

A note on embedding: When performing quantum annealing on a real machine, an operation called minor-embedding is required. If the graph structure of the Hamiltonian you want to solve differs from that of the physical qubit graph, you cannot naively encode the problem into the device. For this reason, multiple qubits on the hardware are mapped to the same logical bits, as shown in the figure below. This mapping is called embedding, and the set of qubits corresponding to the same logical bit in hardware is called a chain.

- While embedding creates chains, too long chains degrade the quality of the solution, and the increased order of Advantage2 allows embedding with shorter chains, even for dense problem graphs.

- The documentation of D-Wave also mentions that the maximum chain length that can be expected to provide a stable solution is 5-7 qubits [3].

- D-Wave's visualization tool, also alerts the user to the presence of chains longer than seven qubits.

### 2. Increased energy scale

Dr. Emile Hoskinson, Advantage2 development leader, says,

Increasing the energy scale increases the depth of the valleys; this makes them easier to find and makes it harder for noise to knock the system out of them. What we get is both an improved solution quality and an increased probability of finding good solutions, because we can cut through the system noise more easily [1].

For those unfamiliar with physics, the relationship between noise and energy scale, such as temperature, will be the subject of a future article.

### 3. Reduction of error rates

New devices have lower error rates than conventional devices due to the above two and other factors.

The demo version of Advantage2, which has about 500 qubits, is already available on Leap and can be touched by users.

## Tried the demo version of Advantage2

I have run the demo version of Advantage2 albeit briefly, and share the results.

Just pass "Advantage2_prototype1.1" as the solver argument as follows, and then you can use it as usual.

### Experiment

- Random 2D Travelling salesman problem.

- The coefficient of penalty is fixed at 0.8.

- num_reads is 1000.

- chain strength prefactor was moved in the range [0.6, 3.0].

**Modeling code**

For mathematical modeling, we used , a modeling tool that can automatically construct QUBO from constrained optimization problems. Installation can be done with the pip command.

In our cloud service , we provide more powerful QUBO engine and parameter tuning with JijModeling. If you are interested in our services, please contact us using the inquiry form.

## Results

I benchmark the following indicators.

- The smallest objective value among the feasible solutions obtained

- The mean objective value among the feasible solution

- The rate of feasible solution

### Results with conventional “Advantage” in 6 cities (n=6) and 7 cities (n=7)

In 6 cities (left figure), even with the conventional “Advantage”, we were able to obtain a feasible solution with a maximum probability of about 20% by adjusting the chain strength. For 7 cities (n=7), we are still able to obtain a relatively stable feasible solution, although the probability drops to about 2%. It should also be noted that the coefficients of the constraint terms are fixed for now, so there is room to improve the results by tuning them.

### Results with conventional “Advantage” and “Advantage2” in 8 cities (n=8).

On the left is the result of the solution with the current Advantage and on the right is the result with the Advantage2 demo version. When no feasible solution is found, both the objective function and the ratio of feasible solutions are plotted as 0.

At n=9, the Advantage2 demo version did not have enough qubits. In fact, even at n=8, embedding results in 359 physical qubits on the device. After all, the problem size of n=9 is probably too large for the demo version, which has only about 500 qubits.

## Discussion

The reason for the difference between the current Advantage and Advantage2 in the 8 cities seems to be due to the “more compact embedding” mentioned at the beginning of this article.

As explained above, longer chains degrade solution quality. The recommended chain length is said to be within seven qubits. Here we compare the chain length distribution for the eight-city problem when embedded in the current Advantage with that of Advantage2.

The left figure shows the current version and the right figure shows the Advantage 2 version. From this, we can see that Advantage 2 has more compact embeddings, i.e., the chain length has been reduced, and we believe this may have contributed to the improvement in solution quality.

## Summary

n=8 | Advantage | Advantage2 |

Feasible rate | 0.4% | 2% |

Chain length distribution | 4-11 | 3-8 |

We confirmed that Advantage2 outperforms the current Advantage without special settings.

There are well-known methods for determining the weight of the penalty for the traveling salesman problem QUBO. However, in this case, we did a simple experiment where we did not use those methods but set values. Therefore, note that proper determination of the parameters may improve the feasible solution for both devices.

## References

[1]：https://medium.com/d-wave/a-sneak-peek-into-our-next-generation-advantage-quantum-computer-3cbe8def208e