BMW ships over two million cars every year. Each car has about 30,000 parts provided by over 100 global suppliers. It is easy to see why managing and coordinating the entire global supply chain is a complex and computationally intensive process. BMW, like other manufacturers, is currently limited to managing its supply chain and logics with classical computers and software. Although quantum computing is still in the prototype stage, BMW is interested in finding out if quantum computing had the potential to optimize and speed up supply chain management. Longer-term, the hybrid use of quantum computing and artificial intelligence will be a powerful tool for managing changing consumer demands, political shifts, tariff changes and other environmental effects.

For this project, BMW teamed up with Entropica Labs, a Singapore-based quantum computing startup, and Honeywell Quantum Solutions. Expectations were that developing and running appropriate benchmarks for near-term quantum computers could provide BMW valuable insights into quantum’s potential value.

Honeywell’s Model H1 quantum computer uses an advanced trapped-ion architecture robust enough to support the next several generations of Honeywell quantum processors. H1’s computational power comes from ten fully connected ytterbium ions and features high fidelity operations and low crosstalk. Honeywell currently holds the highest measured quantum volume record of 512 for quantum computing.

Honeywell was the first to develop a mid-circuit measurement feature and reset and conditional feed-back (MCMR).

**Entropica Labs**

Entropica was chosen to create the necessary quantum algorithms and run them on the Honeywell Model H1. Entropica was founded in 2018 by Tommaso Demarie and Ewan Munro, alumni of Singapore’s Centre for Quantum Technologies (CQT). In 2020 it raised USD 1.9 million in a seed funding round led by Elev8, a VC firm focused on deep-tech opportunities. In addition to prior experience with Honeywell’s Model 0 and Model H1, Entropica has also worked with other quantum cloud providers, including Rigetti Computing, IBM and Microsoft.

Cofounder Ewan Munro is the CTO of Entropica. He has a Master’s in Mathematical Physics from the University of Edinburgh and a Ph.D. in Physics from the Centre for Quantum Technologies at the National University of Singapore.

Tommaso Demarie, Entropica’s CEO, studied physics in Italy before moving to Australia to complete his Ph.D. in quantum information theory at Macquarie University in Sydney. After that he was a Postdoctoral Research Fellow at Singapore University of Technology and Design and the CQT.

Munro explained that Entropica had previously performed research using Honeywell’s first quantum computer, the model H0, as well as the initial release of the Model H1. Entropica’s previous Model H1 research focused on exploring capabilities of mid-circuit measurement and reset (MCMR). Because MCMR allows mid-computation reuse of qubits, Entropica created a machine learning application that cleverly used 6-qubits to run an application of “Bars and Stripes” that actually required 9-qubits. The three extra qubits were “phantom resources” recovered from the use of MCMR.

Munro said, “That was a very interesting problem, and the results were quite good.”

In another example of how powerful this feature is, I attended a recent quantum conference where Honeywell demonstrated similar use of mid-circuit measurement and reset using an algorithm called Bernstein-Vazirani.

In plain English, Bernstein-Vazirani can determine a secret bit string hidden in another function. Assume a 6-bit string is hidden in a file. The objective is to determine the value of the hidden number and find it in the least number of attempts possible. A classical computer would have to make six guesses to determine the secret number. The beauty of Bernstein-Vazirani is that it allows a quantum computer to find the correct answer on one attempt.

For the demonstration, the Honeywell researcher first ran the Berstein-Vazirani quantum algorithm using *6-qubits* to find the hidden value. The next demonstration showed that it ran equally as well with a *2-qubit* circuit that incorporated MCMR.

**Benchmarking**

For BMW’s proof-of-concept, Entropica used a mathematical protocol called number partitioning. It is a classical grouping problem that provides a common entry point for many logistics and supply chain problems of industrial interest.

For the most part, today’s quantum computers cannot do anything that can’t be done on a classical computer. In order to determine the accuracy of quantum experiments, researchers routinely run the same or similar algorithms on classical simulators or classical computers as a benchmark.

Entropica ran the Recursive Quantum Approximate Optimization Algorithm (R-QAOA)on the Honeywell Model H1. To provide a comparison to H1 results, the R-QAOA algorithm was also run on a classical simulator. For a classical computer benchmark, Entropica chose the Karmarkar-Karp algorithm. It is the go-to classical heuristic for number partitioning.

**Simplistically, this the way BMW’s proof of concept works:**

The algorithms separate a set of positive numbers into two groups called partitions, starting with the two largest numbers and ending with the smallest numbers. The “set difference” is the absolute difference between the sums of the two partitions. The smaller the set difference, the better the result.

**How does this proof of concept apply to logistics and supply chains?**

This exercise could be an example of loading material onto two different vehicles. In a case like that, the objective is to make sure neither vehicle carries more weight than the other. It could also represent load leveling between two servers.

**Results**

The chart reflects set differences for each methodology. The x-axis variable is the problem size, while the y-axis variable measures the performance. It is easy to see that R-QAOA running on the Honeywell Model H1 compares favorably to R-QAOA running on the classical shot-based simulator (labeled ‘sim’). This indicates that noise from the H1 device itself was minimal, compared to the fluctuations due simply to the finite number of measurements taken.

For the small problem instances studied on the algorithmic side, the depth-1 R-QAOA also has comparable performance compared to the classical Karmarkar-Karp (KK) heuristic.

Commenting on the Honeywell results, Demarie said, “At this stage of the industry, applied research is rapidly increasing our understanding of what quantum computers can and cannot do. It is encouraging – and exciting – to confirm experimentally that the performances of the Honeywell H1 device are very close to their expected behavior.”

**Analyst Notes:**

1.) Future work will explore whether higher-depth versions of R-QAOA can outperform the KK algorithm. With increased two-qubit gate fidelity and more qubits, my expectations would be that would easily be accomplished.

2.) Quantum computing is still in the experimental stage. There are no quantum systems currently operating in a production role. It will be at least 3 to 7 years before quantum computing can perform any reliable operational supply chain function.

3.) Entropica said that given the small number of qubits, the R-QAOA results using the model H1 were very good as well as informative.

4.) The training was performed on a classical computer rather than on the H1. That is, Entropica first obtained the optimal circuit parameters by simulation, and then ran those fixed circuits on H1. That was necessary because of limited access time to the H1. It would be beneficial to do the training on the QPU as well to verify end-to-end computation fidelity.

5.) Honeywell’s roadmap calls for the Model H1 to eventually scale to 40 qubits. Given that Ytterbium ions are natural qubits and even higher fidelities are expected, more qubits should result in even more impressive results.