Journal
MATHEMATICS
Volume 10, Issue 15, Pages -Publisher
MDPI
DOI: 10.3390/math10152601
Keywords
variatonal algorithms; QAOA; quantum circuit optimization
Categories
Funding
- research project Leading Research Center on Quantum Computing [014/20]
Ask authors/readers for more resources
The quantum approximate optimisation algorithm combines quantum processing and classical outer-loop optimisation to approximately minimise the problem's generator. The optimal algorithm parameters reduce to one free variable in certain conditions, and a linear relation between circuit parameters is found due to the vanishing gradients of the overlap function.
The quantum approximate optimisation algorithm is a p layer, time variable split operator method executed on a quantum processor and driven to convergence by classical outer-loop optimisation. The classical co-processor varies individual application times of a problem/driver propagator sequence to prepare a state which approximately minimises the problem's generator. Analytical solutions to choose optimal application times (called parameters or angles) have proven difficult to find, whereas outer-loop optimisation is resource intensive. Here we prove that the optimal quantum approximate optimisation algorithm parameters for p = 1 layer reduce to one free variable and in the thermodynamic limit, we recover optimal angles. We moreover demonstrate that conditions for vanishing gradients of the overlap function share a similar form which leads to a linear relation between circuit parameters, independent of the number of qubits. Finally, we present a list of numerical effects, observed for particular system size and circuit depth, which are yet to be explained analytically.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available