Digital Quantum Simulation of Nonadiabatic Geometric Gates via Shortcuts to Adiabaticity

Abstract

Geometric phases are used to construct quantum gates since it naturally resists local noises, acting as the modularized units of geometric quantum computing. Meanwhile, fast nonadiabatic geometric gates are required for reducing the information loss induced by decoherence. Here, we propose a digital simulation of nonadiabatic geometric quantum gates in terms of shortcuts to adiabaticity (STA). More specifically, we combine the invariant-based inverse engineering with optimal control theory for designing the fast and robust Abelian geometric gates against systematic error, in the context of two-level qubit systems. We exemplify X and T gates, in which the fidelities and robustness are evaluated by simulations in ideal quantum circuits. Our results can also be extended to constructing two-qubit gates, for example, a controlled-PHASE gate, which shares the equivalent effective Hamiltonian with rotation around the Z-axis of a single qubit. These STA-inspired nonadiabatic geometric gates can realize quantum error correction physically, leading to fault-tolerant quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era.

Nonadiabatic geometric quantum computation with shortened path on superconducting circuits

“…Besides, the adiabatic geometric phase has been generalized to the nonadiabatic case 11 , which is more suitable in the application for constructing quantum gates. Therefore, GQC using the nonadiabatic geometric phase has been received extensive theoretical explorations [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] and experimental demonstrations [30][31][32] .…”

“…But, for the cyclic case 27,28 , the shortened path still has mutation and/or the gate robustness is weak or untested. Besides, there are other methods for non-adiabatic GQC with optimal control 21 , dynamical decoupling 22 , shortcuts to adiabaticity 23 , and path optimization 29 to improve gate-robustness, but they need either longer gate-time and/or sudden mutative pulse control. In addition, there is no comprehensive study of the shortest allowed path under certain conventional conditions.…”