From qubits to qudits for improved NISQ computing performance

Trapped-ion experiments typically limit themselves to using two states per ion as a qubit, however well-chosen ions have a far larger accessible Hilbert space. In work being written up for publication, in collaboration between my team and Shivaji Sondhi's team (UOxf/Princeton), we have shown that using this larger Hilbert space can be efficiently and practically used to encode a larger number of qubits per ion - this enables significantly reduced effective error rates as entangling gates between qubits encoded in a single ion promise far lower error than entangling gates between ions, which can be exploited by well designed algorithms and compilers to significantly increase NISQ computing performance.

Aims and Objectives:

In this project the student will develop techniques to implement qudit operations including mid-circuit measurement on the Oxford-built ABaQuS series of quantum computer. These devices are designed to operate a high-fidelity gate-set on registers of 8 ions (currently in operation) to ~50 ions (designed). These techniques will be experimentally developed in the existing ABaQuS ion trap system.

The proposed work is made possible by the choice of qubit, Ba-137, allowing long-lived and coherent isolated metastable states, and allowing access to a well-connected space of >10 states for which we will develop techniques to efficiently encode qubit circuits onto qudits and to efficiently isolate logic subspaces from readout subspaces for mid-circuit qudit readout

The ABaQuS systems are hosted in the Oxford Physics Beecroft laboratory, and already have the required laser & control infrastructure required for this project. The micro-fabricated ion traps & beam delivery optical assemblies for this project are developed through a QCS partnership project with UOxf Engineering Science (Martin Booth) and an InnovateUK project (DISCOVERY; including M-Squared, Oxford Ionics, NPL, KNT).

Theory support is provide both by internal resources (my student Kaitlin Gili) and via a collaboration with Shivaji Sondhi and team (UOxf / Princeton).

The aims of this project are to (i) numerically investigate error-optimal circuit optimisation for qudit array systems, including connectivity and non-uniform gate error constraints, (ii) demonstrate enhanced computational performance on multi-qudit / multi-polyqubit systems over a similarly resourced constrained trapped-ion experimental systems, (iii) develop a langauge to efficiently describe poly-qubit connectivity constraints to allow efficient & generalized gate decompositions to be expressed, and (iv) develop robust benchmarking techniques that allow efficient characterisation of poly-qubit systems, validated by comparing application-level benchmarking against microbenchmark informed error models on real quantum hardware.

Novelty of the research methodology

These research methods are highly novel: theoretical understanding of compilation and modelling of poly-qubit systems is a new and rapidly evolving area, with little experimental validation. The experimental, compilation, & validation techniques we will create over this project will enable much greater insight into the feasibility of efficient poly-qubit / qudit operation for large scale quantum computation.

This project falls within the EPSRC Quantum Technologies research area