Abstract
This study investigates the frame potential and expressiveness of commutative quantum circuits. Based on the Fourier series representation of these circuits, we express quantum expectation and pairwise fidelity as characteristic functions of random variables, and expressiveness as the recurrence probability of a random walk on a lattice. A central outcome of our work includes formulas to approximate the frame potential and expressiveness for any commutative quantum circuit, underpinned by convergence theorems in probability theory. We identify the lattice volume of the random walk as means to approximate expressiveness based on circuit architecture. In the specific case of commutative circuits involving Pauli-Z rotations, we provide theoretical results relating expressiveness and circuit structure. Our probabilistic representation also provide means for bounding and approximately calculating the frame potential of a circuit through sampling methods.
| Original language | English |
|---|---|
| Journal | IEEE Transactions on Quantum Engineering |
| DOIs | |
| State | Accepted/In press - 2024 |
Funding
This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
| Funders | Funder number |
|---|---|
| U.S. Department of Energy |
Keywords
- Commutative quantum circuit
- expressiveness
- frame potential