In this paper, we introduce the multi-observable dynamic mode decomposition (MODMD) approach combining ODMD with classical shadows for efficient low-lying energy computations on near-term and early fault-tolerant quantum computers.
In this paper, we introduce k-NoCliD, a method to reduce the number of measurements for estimating expectation values that relaxes the constraint of commutativity.
We propose two methods for implementing operator resolvents on a quantum computer based on Hamiltonian simulation: a first method based on discretization of integral representations of the resolvent through Gauss quadrature rule and a second method that leverages a continuous variable ancilla qubit. We use these results to study the implementation of rational functions on a quantum computer and illustrate their potential for estimating low-lying energies.
This paper provides a review on quantum computing for computational problems in materials science and a perspective on the challenges to face in order to solve representative use cases, and new suggested directions.
We develop a performance model to project the classical hardware requirements required for real-time decoding of large-scale quantum computations. Based on this model, we estimate that the equivalent of a petaflop-scale system will be required for real-time decoding of applications relavent to condensed matter physics and quantum chemistry.