Background
The HQS Noise Mapper implements models to utilize the noise of the available devices to enable useful, near-term quantum computing. In particular, it implements noise mapping, the construction of a static noisy algorithm model based on a quantum circuit and physical noise on a quantum computer, as described in this section.
The noisy algorithm model is the static noise model that determines the effective time propagation when a quantum algorithm circuit of the coherent time propagation under a Hamiltonian is run on a quantum computer with physical noise. The scientific background of this method has been published in a recent paper: arXiv:2210.11371, where we consider the extent to which a noisy quantum computer is able to simulate the time evolution of a quantum spin system in a faithful manner. In this section we describe the specific set of assumptions about the noise of the device and the technical details of the implemented noise mapping.
Conditions
Noise mapping works when the quantum algorithm under consideration is fundamentally of the Trotterization type, meaning that the original Hamiltonian can be written as a sum of local Hamiltonians \[ H = \sum_k H_k \[ H = \sum_k H_k \] and the time propagation under each \(H_k\) is given by a well-defined sequence of native quantum gates. The noisy algorithm model can be extracted from a quantum circuit that represents one Trotter step in a Trotterized time-propagation algorithm.
To be as general as possible, the noisy-algorithm extraction does not construct this quantum circuit that propagates a state for a virtual time. The noise mapper accepts circuits that have already been fully compiled for the target architecture and annotated with the necessary meta-information.
Two forms of metadata annotation are required to apply noise mapping:
- Marking the decomposition blocks, which are the parts of the circuit that correspond to implementing a partial time propagation under a \(H_k\)
- Information about the physical noise
For further details on the usage of the associated functionalities, please refer to the functionalities section of this documentation.
Noise Mapping
The noise mapping in the Noise Mapper is based on the assumption that the Trotter time-step \(t\) is short enough with respect to the Lindblad terms \(\mathcal{L}_1\) and \(\mathcal{L}_2\), and that the following equation is respected. \[ \exp(\mathcal{L}_1 t) \exp(\mathcal{L}_2 t) \approx \exp(\mathcal{L}_2 t) \exp(\mathcal{L}_1 t) \approx \exp((\mathcal{L}_1 + \mathcal{L}_2) t) \]
where \(\exp(\mathcal{L} t)\) is shorthand for applying the full time propagation under the Lindblad terms for time \(t\).