Minimally-Entangled State Preparation of Localized Wavefunctions on Quantum Computers

Understand

Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires ${\cal O}(2^{n_Q})$ entangling gates on a quantum computer with $n_Q$ qubits per site.

• It is conceivable that, instead, initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates.
• In the case of a single site of a non-interacting scalar field theory, initializing to a symmetric exponential wavefunction requires $n_Q-1$ entangling gates, compared with the $2^{n_Q-1} + n_Q-3 + \delta_{n_Q,1}$ required for a symmetric Gaussian wavefunction.
• In this work, we explore the initialization of 1-site ($n_Q=4$), 2-site ($n_Q=3$) and 3-site ($n_Q=3$) non-interacting scalar field theories with symmetric exponential wavefunctions using IBM's quantum simulators and quantum devices (Poughkeepsie and Tokyo).