Efficient computation of quantum time-optimal control

Abstract

We present an approach to compute time-optimal control of a quantum system which combines quantum brachistochrone and Lax pair techniques and enables efficient investigation of large-scale quantum systems. We illustrate our method by finding the fastest way to transfer a single-particle excitation in a nearest-neighbor-coupled infinitely large qubit lattice with the fixed sum of squares of the couplings.

Figures (6)

• Figure 1: Schematic of a qubit array with imposed anti-periodic boundary conditions and different number $N$ of qubits comprising the ring. Quantum speed limit is achieved for the excitation propagating in the form of a localized wave packet maintaining its shape.
• Figure 2: Initial distribution of real $\ket{x(0)}$ (a) and imaginary $\ket{y(0)}$ (b) parts of the Lax eigenmode $\ket{a(0)}$ corresponding to the soliton-like solution in an array of 15 qubits with anti-periodic boundary conditions.
• Figure 3: Initial profile of the localized soliton-like solution $|\psi_n(0)|^2$ (a) and associated coupling amplitudes $|J_{n,n+1} (0)|$ (b) in an array of 15 qubits with anti-periodic boundary conditions. Time dependence of the probability $|\psi_{15}|^2$ (c) and the coupling amplitudes $|J_{14,15}|$ (dashed line) and $|J_{15,1}|$ (solid line) (d).
• Figure S4: The structure of the Lax eigenmode $\ket{a}$ for the $N=15$ qubit array closed into ring with anti-periodic boundary conditions. Real part $\ket{x}$ at time moments (a) $t=0$, (b) $t=\tau/2$, (c) $t=\tau$. Imaginary part $\ket{y}$ at times (a) $t=0$, (b) $t=\tau/2$, (c) $t=\tau$. The dark solid line shows the time evolution of the 15-th qubit over time $N\tau$, rescaled via $n = Nt/\tau$ and shifted to match the positions of the maxima.
• Figure S5: The structure of the site occupation $|\psi_m|^2$ for the 15-th qubit in the array with anti-periodic boundary conditions at times (a) $t=0$, (b) $t=\tau/2$, (c) $t=\tau$. Spatial distribution of the coupling amplitudes $J_{m,m+1}$ at times (a) $t=0$, (b) $t=\tau/2$, (c) $t=\tau$. Dark solid line shows the time evolution of the 15-th qubit population and 15-th coupling amplitude over time $N\tau$, rescaled via $n = Nt/\tau$ and shifted to match the positions of the maxima.