Accelerating Lattice Quantum Field Theory Calculations via Interpolator Optimization Using Noisy Intermediate-Scale Quantum Computing

The only known way to study quantum field theories in nonperturbative regimes is using numerical calculations regulated on discrete space-time lattices. Such computations, however, are often faced with exponential signal-to-noise challenges that render key physics studies untenable even with next generation classical computing. Here, a method is presented by which the output of small-scale quantum computations on noisy intermediate-scale quantum era hardware can be used to accelerate larger-scale classical field theory calculations through the construction of optimized interpolating operators. The method is implemented and studied in the context of the $1+1$-dimensional Schwinger model, a simple field theory which shares key features with the standard model of nuclear and particle physics.

Figure 1

Effective mass functions [Eq. (6)] constructed exactly via diagonalization (solid lines), and obtained from MC computations (open points), for the lightest vector meson. The green circles and red squares denote results obtained using the benchmark [Eq. (7)] and quantum-improved [Eq. (11)] operators, respectively. The black dashed line shows the result obtained solving an exact form of the classical GEVP using the same basis of interpolating operators, while the purple solid band shows the exact result for the optimized operator, given some uncertainty on the VQE input into its construction as described in the text. Note that the uncertainty is suppressed as the Euclidean separation between operators is increased. The large time behavior is a consequence of the backward propagating states around the boundary at finite Euclidean time.

Figure 2

Exact effective mass functions in an $L=6$ spatial-site Schwinger model computation, calculated using quantum-improved interpolating operators constructed on smaller Hilbert spaces. Green, orange, and purple curves (moving vertically down the figure) show results obtained via optimization of systems with flux truncations ${\tilde{\mathrm{\Lambda }}}^2=\{2,4,8\}$ on an $L=4$ system, respectively. The grey dashed and dotted curves indicate the exact classical GEVP solved on the full Hilbert space, and the exact result corresponding to the naive interpolating operator [Eq. (7)], respectively.