Background information

This chapter provides an overview of the fundamentals behind the HQS Qorrelator App. Reading the background chapters is not necessary for using the HQS Qorrelator App to calculate correlation functions, but provides a brief introduction into NMR in general and the quantum algorithms used by the HQS Qorrelator App.

In the first section, NMR, we describe the basics of nuclear magnetic resonance (NMR) from both experimental and theoretical perspectives. We discuss, for example, the different relevant parameters entering an NMR calculation, such as the chemical shifts and the couplings between nuclear spins, and introduce the relevant Hamiltonian of a molecule for NMR.

In maths, we describe in greater detail the mathematics behind the calculation of spectra in the HQS Qorrelator App.

In the next section, Quantum computing, we explain how quantum computers can be used to calculate NMR spectra. We analyze the relevant algorithms and discuss the influence of noise on spectrum calculations on quantum computers.

Furthermore, HQS Software provides special features for analyzing the effects of running quantum algorithms on NISQ era noisy hardware. The following two sections give the corresponding background documentation.

We consider physical noise, meaning noise on the hardware-level, that is caused by qubits coupling to some fluctuating environment, either during control operations, or at all times. This is assumed to cause damping, dephasing, and/or depolarization of their quantum states. Our model of a noisy quantum computer is based on adding corresponding non-unitary (noise) operations after or before (ideal) unitary gate operations. This model is described in detail on page modeling.

The HQS Qorrelator App allows the user to investigate how noise affects the calculation of correlation functions to obtain NMR spectra. Particularly, it derives the Lindblad open-system model that the noisy quantum simulator is effectively implementing in the time propagation that is part of the calculation of the correlation function. Foundations of this mapping (between physical and simulated noise) are discussed on page mapping or in more detail in this arxiv paper.