Minimally-Entangled State Preparation of Localized Wavefunctions on
  Quantum Computers
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). With the digitizations attainable with $n_Q = 3,4$, these
tensor-product wavefunctions are found to have large overlap with a Gaussian
wavefunction, and provide a suitable low-noise initialization for improvement
and \emph{Somma Inflation}. In performing these simulations, we have employed a
workflow that interleaves calibrations to mitigate systematic errors in
production. The calibrations allow tolerance cuts on gate performance including
the fidelity of the symmetrizing Hadamard gate, both in vacuum ($|{\bf
0}\rangle^{\otimes n_Q}$) and in medium ($n_Q-1$ qubits initialized to an
exponential function). The results obtained in this work are relevant to
systems beyond scalar field theories, such as the deuteron radial wavefunction,
2- and 3-dimensional cartesian-space wavefunctions, and non-relativistic
multi-nucleon systems built on a localized eigenbasis.
Natalie Klco Martin J. Savage