Simulating Spin Chains Using a Superconducting Circuit: Gauge Invariance, Superadiabatic Transport, and Broken Time‐Reversal Symmetry

Abstract

Simulation of materials by using quantum processors is envisioned to be a major direction of development in quantum information science. Here, the mathematical analogies between a triangular spin lattice with Dzyaloshinskii-Moriya coupling on one edge and a three-level system driven by three fields in a loop configuration are exploited to emulate spin-transport effects. It is shown that the spin transport efficiency, seen in the three-level system as population transfer, is enhanced when the conditions for superadiabaticity are satisfied. It is demonstrated experimentally that phenomena characteristic to spin lattices due to gauge invariance, non-reciprocity, and broken time-reversal symmetry can be reproduced in the three-level system.

Quantum process tomography of adiabatic and superadiabatic stimulated Raman passage

“…which is experimentally realized by a two-photon process [39]. Here we obtain an effective Rabi coupling with absolute value Ω 02 (t) = 2 Θ(t) and complex phase φ 02 ; also it is convenient to use the notation φ 02 = −φ 20 .…”

“…The counteradiabatic condition also implies φ 01 + φ 12 + φ 20 = −π/2. Based on an analysis of gauge invariance [32,39], we can take for simplicity φ 01 = φ 12 = 0. Note that for φ 02 = π/2, the counterdiabatic Hamiltonian H cd yields the evolution exp ihΛ 5 t t i Θ(t)dt .…”

“…Note that for φ 02 = π/2, the counterdiabatic Hamiltonian H cd yields the evolution exp ihΛ 5 t t i Θ(t)dt . This is experimentally realized by a two-photon resonance pulse [39],…”

Experimental high-dimensional Greenberger-Horne-Zeilinger entanglement with superconducting transmon qutrits

“…Quantum control beyond the two-level system has been exploited in superconducting quantum processors since the very beginning of this technology. Starting from the use of the higher levels for qubit readout [15][16][17] and the explicit use of the third level for spin-1 quantum simulation [18], the first steps towards the realization of ternary quantum computation with superconducting transmon devices have been taken in the last 10 years [18][19][20][21][22][23][24][25][26]. More recently, these efforts have led to the implementation of high-fidelity single-qutrit gates [27,28].…”

Quantum map approach to entanglement transfer and generation in spin chains

“…On the other hand, new QIP protocols are being introduced, aimed at exploring the complexity of the geometry of high-dimensional Hilbert spaces [4], such as in particular quantum state transfer [5]. At the same time, remarkable progress has been made in order to experimentally verify these QIP protocols and communication processes on a variety of experimental platforms, with which the simulation of some quantum spin networks has been successfully achieved, using: cold atoms [6,7,8], Rydberg atoms [9,10,11], integrated photonic chips [12], trapped ions [13,14,15], atom-cavity systems [16,17], and superconducting circuits [18,19], among others.…”