Use of Quantum Sampling to Calculate Mean Values of Observables and Partition Function of a Quantum System

Understand

We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system.

• Our algorithm includes two sub-algorithms.
• The first sub-algorithm is for calculating, with polynomial efficiency, certain diagonal matrix elements of an observable.
• This sub-algorithm is performed on a quantum computer, using quantum phase estimation and tomography.