About the project
What if a quantum algorithm could take a shortcut to the true answer? This project will test whether practical counterdiabatic controls can accelerate adiabatic quantum linear-system solvers within realistic noise and hardware limits. It will deliver theory, open software and rigorous benchmarks showing when these shortcuts offer genuine computational benefit.
Solving linear systems underpins simulation, optimisation, control and data analysis. Quantum linear-system algorithms prepare a state proportional to the solution and can benefit applications needing selected properties. Adiabatic solvers are attractive but can become slow when spectral gaps are small or matrices poorly conditioned. Counterdiabatic driving, a shortcut to adiabaticity, could suppress unwanted transitions. Exact controls may be nonlocal and costlier than the evolution they replace.
This project will investigate whether implementable counterdiabatic controls can reduce coherent circuit depth or improve robustness once their full construction, compilation and simulation costs are counted. You'll derive regularised local, variational, nested-commutator or Krylov approximations to the adiabatic gauge potential and establish error and resource bounds where feasible. Tests will determine how performance depends on condition number, sparsity, precision, matrix structure, noise and hardware connectivity.
The main focus is early fault-tolerant computation; small hardware demonstrations will provide validation, not advantage claims. Structured matrices from differential equations, networks and optimisation will be tested against unassisted and discrete-adiabatic quantum solvers and appropriate classical methods. Metrics will include solution-state fidelity, observable error, circuit depth, two-qubit gates, state preparation and readout.
Expected outputs are new control constructions, open software, reproducible benchmarks and a map of useful, break-even and unfavourable regimes.
