Geometric Quantum Computation with Shortcuts to Adiabaticity

Abstract

Realization of a large-scale quantum computation relies on fast and high-fidelity quantum control. Geometric quantum control is thought to be a promising candidate for quantum computation which consolidates the robustness against both random noise (through the global geometrical feature) and systematic errors (through adiabatic characteristic). The adiabatic process of geometric control can be accelerated through an auxiliary Hamiltonian in different scenarios by means of shortcuts to adiabaticity (STA). Especially, the auxiliary Hamiltonian can be absorbed into the original interacting configuration in most of the cases, which allows STA to coalesce with the Abelian or the non-Abelian geometric control. As a consequence, geometric quantum control can have an enhanced robustness against decoherence after speeding up by STA. Here, the recent theoretical and experimental advances in geometric quantum computation based on STA are reviewed.

Effective non-adiabatic holonomic quantum computation of cavity modes via invariant-based reverse engineering

“…Therefore, NHQC can reduce the influence of decoherence to the unitary operations by shortening the operation time. In addition, recent works [33][34][35][36][37] have indicated that NHQC is compatible with a lot of control and optimal methods, such as reverse engineering [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] and the systematic-error-sensitivity nullified optimal control method [55][56][57][58][59][60]. By using proper control methods in NHQC, robustness against systematic errors can be significantly enhanced.…”

Robust stimulated Raman shortcut-to-adiabatic passage by invariant-based optimal control

“…They offer alternative fast and accurate processes which can reproduce the same final populations, or even the same final state in a shorter time, compared to the adiabatic evolution [8,9]. Recently, STA have been widely used to implement rapid and robust quantum information processing in theory, such as quantum state transfer [10][11][12][13][14][15][16], quantum gates [17][18][19][20][21][22][23][24], and generation of quantum cat state [25][26][27], etc. For instance, in 2012, Chen et al [11] used the invariantbased shortcut to accelerate the STIRAP to realize population transfers in a short time.…”

Implementing conventional and unconventional nonadiabatic geometric quantum gates via SU(2) transformations

“…Quantum computation has been shown to be more efficient than classical one in solving some problems, such as factoring large integers, searching big database and finding optimal solutions by quantum annealing [1]. However, it still faces great challenges both in theory and applications, especially, due to the inevitable decoherence or noise introduced by the interaction with environment, which destroys the coherence of the state which should be maintained in the parallel computation.…”