Improving Hamiltonian encodings with the Gray code

Understand

Due to the limitations of present-day quantum hardware, it is especially critical to design algorithms that make the best possible use of available resources.

• When simulating quantum many-body systems on a quantum computer, straightforward encodings that transform many-body 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 ground state energy of a deuteron with a simulated variational quantum eigensolver (VQE).