Improving Hamiltonian encodings with the Gray code
Abstract
Due to the limitations of presentday quantum hardware, it is especially critical to design algorithms that make the best possible use of available resources. When simulating quantum manybody systems on a quantum computer, straightforward encodings that transform manybody Hamiltonians into qubit Hamiltonians use N of the available basis states of an N qubit system, whereas 2^{N} are in theory available. We explore an efficient encoding that uses the entire set of basis states, where terms in the Hamiltonian are mapped to qubit operators with a Hamiltonian that acts on the basis states in Gray code order. This encoding is applied to the commonly studied problem of finding the groundstate energy of a deuteron with a simulated variational quantum eigensolver (VQE). It is compared to a standard "onehot" encoding, and various tradeoffs that arise are analyzed. The energy distribution of VQE solutions has smaller variance than the one obtained by the onehot encoding even in the presence of simulated hardware noise, despite an increase in the number of measurements. The reduced number of qubits and a shorterdepth variational Ansatz enables the encoding of larger problems on currentgeneration machines. This encoding also demonstrates improvements for simulating time evolution of the same system, producing circuits for the evolution operators with reduced depth and roughly half the number of gates compared to a onehot encoding.
 Publication:

Physical Review A
 Pub Date:
 April 2021
 DOI:
 10.1103/PhysRevA.103.042405
 arXiv:
 arXiv:2008.05012
 Bibcode:
 2021PhRvA.103d2405D
 Keywords:

 Quantum Physics;
 Nuclear Theory
 EPrint:
 22 pages, 15 figures