About me

Additive quantum codes, often called stabilizer codes, are often studied in the qubit case. While this is the most common quantum computing setting, qudit devices which use more than 2-levels or systems where the continuous degree of freedom is leveraged have begun to pick up research steam for various reasons. My local-dimension-invariant form for stabilizer codes reduces the hurdle of constructing codes for these systems. For example, it permits the use of qubit codes, with simple deterministic modifications, on devices with any integral domain ring local-dimension (prime qudits, continuous spaces, infinite spaces, rotor systems, among other less physical options). The embedded information will utilize the full local-dimension of the original system's, and can be ensured to have the same level of protection. This provides a potentially useful tool and helps with unifying different stabilizer-like approaches.

Light-matter interactions (and systems isomorphic to them--hybrid devices) are incredibly crucial to the development of quantum technologies. A common introductory model is the Jaynes-Cummings model for certain superconducting devices. In this model a single spin-1/2 interacts with a harmonic oscillator and a split spectrum occurs due to the coupling between the systems. I have primarily studied the Tavis-Cummings model where N spin-1/2 particles interact collectively with a single harmonic oscillator. The results obtained can be of use also for cascading cavity arrays, multi-connected Tavis-Cummings models, and other collective system dynamics. While recursive solutions exist for the Tavis-Cummings model, for large N solving these equations becomes intractable. So the methods I led the development of permit for obtaining statistical measures of the energy spectra, and determining states of note for the model quickly, including optimally in the thermal case. In part the results suggest that above a very low temperature (specified in the works) the Holstein-Primakoff approximation breaks down rapidly for collective-spin systems, however, still only around sqrt(N) subspaces need to be accounted for.

Near-term quantum devices with addressable, high-quality qubits are slowly growing in size and capabilities. As more near-term uses, simulation methods are one of the more promising options, including the variational quantum eigensolver (VQE) and trotterization methods. These are more accessible as they center around Pauli operations and measurements. If we slightly increase the requirements on the devices to be able to perform Clifford group elements (which are classically easy), we ask how much more can we squeeze out of these devices? Through symplectic linear algebraic subspace considerations we find that we can: 1) promise that the problem is stated using as few qubits as possible, and 2) reduce the problem into as many independent parallelizable subproblems, as small as possible themselves, as possible. The latter is joint work with a pair of colleagues.

For many platforms the weight (or number of non-trivial operations) involved in performing an operation is negatively correlated with the quality of the operation. For quantum error-correcting codes (QECC) this is particularly true where the process of checking for errors really ought to be high quality. In a work with colleagues at Xanadu we provide a simple method for generating exceptionally low-weight stabilizer codes, with some perks not seen elsewhere. Whilst we achieve weights of at most 6 (compared to the surface code's 4), we are able to encode a constant fraction of information (compared to a single qubit for the surface code), while still retaining a similar level of protection. Additionally, compared to the prior leading method for weight reduction (via Hastings) our method avoids large blowup in the number of qubits needed, provides a simpler decoding scheme, and avoids costly short cycles within the Tanner graph. From numerical testing, it appears to perform quite well, albeit at a tradeoff of spatial locality in the checks.

• Quantum information theory

• Longer-term quantum algorithms

• Lower-bounds on query complexity (classical and quantum)

• Statistical mechanics (physics and chemistry settings)

• Quantum mechanics, particularly in the mesoscopic and continuous-variable (quantum optics) domains

• The Clifford group's structure and the further Clifford hierarchy