Circuit compilers for near-term quantum computers

The number of elementary gate operations in a quantum computation determines the runtime of the quantum computer. It is clearly advantageous to have faster computations that use fewer gates and "circuit compilation" is the art of optimizing and automating this process. For near-term quantum computers (without error correction) effective compilation is especially important because these devices will be noisy and this imposes a practical limit on the number of gates before an error becomes inevitable. Therefore, compilation protocols and software are crucial to whether we will be able to demonstrate a quantum advantage before full blown error-corrected devices are available. This project will develop compilation methods exploring this theme, and thus the project therefore falls within the EPSRC quantum technologies research area.

Specifically, the following two directions will be explored:

1. Random compilers. It has been shown that randomness in circuit optimization can be a useful tool by allowing use to "average" out coherence noise sources. Currently, there are only a few explicit uses of randomization (e.g. by randomization of Trotter decompositions, see e.g. arXiv:1811.08017). We will make use of convex optimization tools (such as CVX) to develop better probability distributions for random circuits.

2. Weakly interacting systems: many systems of interest are either bosonic or fermionic with weak interactions, such as vibrational molecular dynamics problems. The non-interacting part of the Hamiltonian is easier to classical simulate and manipulate using the covariance matrix formalism and the project will investigate ways this information can be exploited to further refine circuits.

This is a joint Oxford-Sheffield project. Primary support will come from Dr Earl Campbell (Sheffield) and Prof. Simon Benjamin (Oxford). There are also (at least) two PDRAs with deep, relevant expertise who will be available for additional support postdoc Balint Koczor at Oxford, and Joshka Roffe at Sheffield.

Training will be provided by the Campbell and Benjamin groups, both of whom have key relevant expertise and a number of researchers working in the field. Depending on how the project progresses, the student may require access to HPC facilities. An available facility is the NQIT-funded computing system based in the ARC centre in Oxford. The ARC centre offers full training and support, and moreover NQIT has developed the leading quantum simulation package QuEST (see arXiv:1802.08032) which the student would use.

This project is closely aligned with the NQIT-Sheffield-IBM partnership project that is now active. We hope and expect that the student's work will continue this industry link, and will represent a thread of continuity whereby IBM's support can continue from NQIT into the era of the National Hub in Quantum Computing and Simulation.