Loading and extraction of information on near-term quantum computers

Abstract

To fulfill its promise of computational advantages, quantum computing requires efficient interfacing with classical computers. Thus, the existence of efficient algorithms for the loading and extraction of classical data on quantum computers is of fundamental importance. This necessity becomes even more relevant in the context of near-term intermediate-scale quantum (NISQ) computers and their limited resources. In this thesis, we present two articles addressing these issues. First, we present an amplitude encoding scheme that loads classical data onto any Hilbert subspace that is defined by computational basis states associated with bitstrings of fixed Hamming weight. We then use this encoding scheme as a subroutine of a novel sparse encoder as well as a new binary encoding protocol. The resulting quantum circuits outputted by the three encoders are deterministic, ancilla-free, and parameter-optimal, and the prepared quantum state is exact. We demonstrate our amplitude encoder on commercial quantum hardware and numerically investigate its capabilities as a variational quantum ansatz. Second, we present a protocol for randomized measurements in n-qubit quantum states that uses ultra short-depth circuits, i.e. O(1) in n, and is also robust to noise. This algorithm expands the classical shadows scheme to the more experimentally relevant scenario for NISQ devices. We show that the measurement channel resulting from our circuits admits a tensor network representation, alleviating the postprocessing costs that are typical of the classical shadows protocol. We numerically investigate the robustness of our protocol and demonstrate its capabilities with numerical experiments as well as deployment on commercially available NISQ hardware.