Source-linked AI summary
Methodology for replacing indirect measurements with direct measurements
Kosuke Mitarai, Keisuke Fujii
TL;DR
Controlled-unitary implementations can be difficult on near-term devices, while direct measurements may require more time for a given precision. This paper develops conditions and protocols for replacing Hadamard tests with sequential direct measurements, then applies them to derivatives and out-of-time-order correlators.
Problem
Controlled-U gates can be difficult to implement, especially on NISQ devices, while direct measurements can require O(1/ϵ²) time for precision ϵ compared with O(1/ϵ) for indirect approaches.
Source: p. 1Method
The paper gives direct-measurement protocols for Hadamard tests with one or multiple controlled gates, using conditions on the unitary or projective measurements.
Source: pp. 1–3Results
The protocols can significantly reduce circuit depth and the accumulating effect of noise, and support direct evaluation of gradients, metric tensors, Hessians, higher derivatives, and OTOCs.
Source: pp. 2, 4Takeaways & Limitations
The protocols provide ways to evaluate quantities used in variational quantum algorithms and to measure OTOCs on quantum computers.
Source: pp. 2, 4
Abstract
from arXiv · showhide
In quantum computing, the indirect measurement of unitary operators such as the Hadamard test plays a significant role in many algorithms. However, in certain cases, the indirect measurement can be reduced to the direct measurement, where a quantum state is destructively measured. Here we investigate in what cases such a replacement is possible and develop a general methodology for trading an indirect measurement with sequential direct measurements. The results can be applied to construct quantum circuits to evaluate the analytical gradient, metric tensor, Hessian, and even higher order derivatives of a parametrized quantum state. Also, we propose a new method to measure the out-of-time-order correlator based on the presented protocol. Our protocols can reduce the depth of the quantum circuit significantly by making the controlled operation unnecessary and hence are suitable for quantum-classical hybrid algorithms on near-term quantum computers.