Simulating topological systems on noisy quantum computers using Qiskit
By Bruna Shinohara de Mendonça, Qiskit Advocate
In 1938, the Italian physicist Ettore Majorana wrote a letter to his university’s dean saying he needed to sail away. He was never seen again. But even during his life, he produced mysteries — he postulated the existence of mysterious particles called “Majorana fermions,” for example. These particles would be their own antiparticle, serve as candidates for the elusive neutrino, and in materials science, they appear in systems with a special type of superconductivity. To top it all off, Majoranas are challenging to detect experimentally.
Majoranas have a place in quantum computation, too — in topological quantum computing. Topological quantum computing is a quantum hardware proposal that uses Majoranas as quantum bits (qubits). The main selling point of this hardware architecture is that it provides resistance to local perturbations, and is therefore efficient against one of quantum computing’s main villains, decoherence.
IBM Quantum systems have little to do with Majoranas at first glance, since their qubits are superconductor-based rather than Majorana-based. However, the theoretical modeling of Majoranas belongs to a class of problems in physics called “non-interacting fermionic Hamiltonians,” which are computationally easier to tackle than interacting systems while still presenting fascinating physical phenomena. Therefore, simulating these systems can be important as we build out our knowledge of quantum algorithms more generally.
Last year, Dr. Marko Rančić from TotalEnergies in France simulated a Majorana system with three noisy qubits in the paper “Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits.” In this work, Rančić managed to accurately recreate certain properties of Majoranas in one dimension, such as the spectral behavior, edge-correlation, and fermionic parity switches. The data was qualitatively okay, but IBM Physicists Kevin Sung, Olivia T. Lanes, and Nick Bronn thought they could improve the results by thinking more deeply about how to overcome errors. The joined with Rančić, which led to the new paper: “Preparing Majorana zero modes on a noisy quantum processor,” published this past summer.
This project fell into Sung’s lap. “Nick and Olivia handed me this project when I first joined IBM. I thought it would be fun to do and help me to get familiar with Qiskit and running problems in hardware,” he said.
When compared to Rančić’s previous work, this new work increases the number of qubits to seven and reproduces those Majorana features with better precision. In this work, the energy spectrum calculations allow clearer visualization of Majorana oscillation, another signature of the presence of Majoranas. The results of this work agree even better with theoretical predictions when using error mitigation techniques, such as dynamical decoupling and state purification. Such tools have been used for a different class of non-interacting fermionic Hamiltonians, Slater determinants, but had not been previously applied to Majorana simulations.
The paper also provided an opportunity for the researchers to explore error mitigation and suppression techniques. “In noisy computers, you try to squeeze out the best performance possible. There’s basically no reason not to do it!” said Sung. Bronn added, “a lot of error techniques come with a cost; we should try the ones with the lowest cost, as is the case for dynamical decoupling.” Dynamical decoupling is one of several error suppression techniques you can do via Qiskit Pulse, a Qiskit toolkit for sending precise instructions to the physical hardware, allowing for better performance in experiments.
Of course, not everything can go as planned. Sung pointed out that some error mitigation techniques, such as pulse scaling, did not improve the results. Meanwhile, Bronn felt the main roadblock was something else: Sung’s absence.
“We didn’t have Kevin until December.” he jokes. “I had a roadblock, and Kevin came at the right time. He had more experience with these kinds of fermionic systems.”
Some roadblocks, however, became building blocks. At some point running the code, Bronn noticed something amiss. Sung recalled: “Nick, after lots of staring, said ‘this looks weird!’” They found a bug in Qiskit Pulse — a floating point error in the compiler that would cascade into a larger problem during calculations. “We fixed and sent a pull request to Qiskit Terra. It was a nice side effect of running these experiments.”
Ultimately, this work demonstrates the importance of trying to simulate challenging new problems on today’s noisy hardware — even ones without a clear application to superconducting qubits, like Majoranas. Not only did it leads to improvements to Qiskit, but it made the modeling limitations clear. “Systems with one dimension can be simulated very nicely in our architecture, but not two dimensions,” Bronn said. Sung felt that it provided a practical application, too: benchmarking. “I’d like to see the possibilities for scalability of this type of problem,” he said.
And where do we go from here? The authors envision an easier-to-use landscape for error mitigation techniques. Their overarching goal is to democratize these error mitigation tools and methods for quantum computing for any application — even simulating Majoranas. Qiskit Pulse, although powerful, is instruction-based and can be daunting for the user that simply wants improved results and is not necessarily a hardware expert. The ambition is that researchers would be able to simply study what they want to study, lifting only the need-to-know pulse-level details. “I told this to a professor, and his group immediately tried the code out!” Bronn said.
So, whether you are charmed by Majorana physics, a fan of fermionic systems, or a person wanting to explore a zoo of error mitigation techniques, simply trying to study a mysterious new system with a quantum computer can help benefit the field of quantum more generally.
