Stoquastic simulations of non-stoquastic superconducting flux circuits

Abstract

There is a tremendous interest in fabricating superconducting flux circuits that are nonstoquastic -- i.e., have positive off-diagonal matrix elements -- in their qubit representation, as these circuits are thought to be unsimulable by classical approaches due to the presence of a sign problem and thus could play a key role in the demonstration of speedups in quantum annealing protocols. We show, however, that the elimination of the sign problem in these systems is possible by the direct simulation of the flux circuits. Our approach not only obviates the reduction of flux circuits to their qubit representation but also produces results that are more in the spirit of the experimental setup. We discuss the implications of our work, arguing that our findings cast doubt on the conception that superconducting flux circuits represent the correct avenue for universal adiabatic quantum computers.

Figures (5)

• Figure 1: Circuit schematic for the non-stoquastic two qubit rf-SQUID dwaveNonStoq. The two superconducting Josephson junctions are coupled both capacitively and inductively.
• Figure 2: Schematic overview of the change in the potential energy of the two qubit circuit Hamiltonian during the annealing process. (a) Single contour of the potential energy at $\phi_x=0$. The dot represents the majority of the probability density of the ground state wavefunction. (b) Single contour of the potential energy at $\phi_x=3\pi/4$. The solid ring represents the majority of the probability density of the ground state wavefunction, which is delocalized due to the presence of a phase transition. (c) Single contour of the potential energy at $\phi_x=\pi$. The dot represents the majority of the probability density of the ground state wavefunction, which is in the well associated with the $|00\rangle$ qubit state. (d)-(f) Same as (a), (b), and (c) but after the normal mode transformation.
• Figure 3: Magnitude of the relative error of the persistent current as a function of the convergence parameter $\Delta$. The current was computed using $\phi_1^z=0.1~m\phi_0$ and $\phi_2^z=0.9~m \phi_0$ at three different points in the anneal.
• Figure 4: Persistent current calculated for both exact diagonalization and ODE QMC at various $\phi_x$ points throughout the annealing process. (a) Anneal for the $|00\rangle$ qubit output. $\phi_1^z=0.1~\text{m}\phi_0$ and $\phi_2^z=0.9~\text{m} \phi_0$ were used as the problem Hamiltonian values. (b) $|01\rangle$, $\phi_1^z=0.5$ and $\phi_2^z=-0.5$ (c) $|10\rangle$, $\phi_1^z=-0.4$ and $\phi_2^z=0.25$ (d) $|11\rangle$, $\phi_1^z=-0.25$ and $\phi_2^z=-0.25$.
• Figure 5: Persistent current calculated for both exact diagonalization and QMC as a function of the transverse flux $\phi_x$ for four rf-SQUIDs system arranged on a square lattice.

Theorems & Definitions (1)

• Lemma A.1