Source-linked AI summary
Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition
Gavin E. Crooks
TL;DR
Quantum-circuit gradients are directly accessible with the parameter-shift rule only for gates whose generators have two unique eigenvalues. The paper extends the approach to broader parameterized gates through decompositions and the product rule, while discussing efficient classical simulation and scope limitations.
Problem
The parameter-shift approach applies directly only to gates with two unique eigenvalues, limiting its use for broader parameterized-gate families.
Method
The paper decomposes parameterized gates into products of parameter-shift-differentiable gates and combines their derivatives using the product rule.
Results
The method is demonstrated for 2-qubit gates, including canonical and cross-resonance gates, with the cross-resonance gradient obtainable from a binary decomposition rather than a full decomposition.
Takeaways & Limitations
The approach broadens parameter-shift gradient evaluation to a wider range of parameterized gates, supporting gradients used in variational quantum-algorithm optimization.
Takeaways & Limitations
For an arbitrary 2-qubit gate with 15 parameters, one gradient may require up to 30 expectation evaluations.
Abstract
from arXiv · showhide
The parameter-shift rule is an approach to measuring gradients of quantum circuits with respect to their parameters, which does not require ancilla qubits or controlled operations. Here, I discuss applying this approach to a wider range of parameterize quantum gates by decomposing gates into a product of standard gates, each of which is parameter-shift rule differentiable.