Universal, high-fidelity quantum gates based on superadiabatic, geometric phases on a solid-state spin-qubit at room temperature

Abstract

Geometric phases 1 and holonomies 2, 3 (their non-commuting generalizations) are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against noise and experimental imperfections. Despite their conceptual appeal and proven fault-tolerance 4-6 , for a long time their practical use in quantum computing was limited to proof of principle demonstrations. Only in 2012 Sjöqvist et al. 7 formulated a strategy to generate non-Abelian (i.e. holonomic) quantum gates through non-adiabatic transformation. Successful experimental demonstrations of this concept followed on various physical qubit systems [8][9][10][11] and proved the feasibility of this fast, holonomic quantum gate concept. Despite these successes, the experimental implementation of such non-Abelian quantum gates remains experimentally challenging since in general the emergence of a suitable holonomy requires encoding of the logical qubit within a three (or higher) level system being driven by two (or more) control fields. A very recent proposal by Liang et al. 12 offers an elegant solution generating a non-Abelian, geometric quantum gate on a simple, two-level system driven by one control field. Exploiting the concept of transitionless quantum driving 13 it allows the generation of universal geometric quantum gates through superadiabatic evolution. This concept thus generates fast and robust phase-based quantum gates on the basis of minimal experimental resources. Here, we report on the first such implementation of a set of non-commuting single-qubit superadiabatic geometric quantum gates on the electron spin of the negatively charged nitrogen vacancy center in diamond. The realized quantum gates combine high-fidelity and fast quantum gate performance. This provides a promising and powerful tool for large-scale quantum computing under realistic, noisy experimental conditions.

Robust and highly efficient discrimination of chiral molecules through three-mode parallel paths

“…The required respective phases of the three pulses can be determined by setting the phases of the corresponding fields. Recently, many microwave-regime experiments of the pulse shaping including the modulations of amplitudes, frequencies and phases (flip) by means of arbitrary waveform generators have been reported [54][55][56][57][58][59][60]. The electric dipole moments of the considered transitions are of 1 Debye order, and it is securable to control the Rabi frequencies within 0-10 MHz by using the maximum field strength around ∼ 2 V /cm.…”

Geometric Quantum Computation with Shortcuts to Adiabaticity

“…The single qubit gates proposed in ref. [] have been realized experimentally in NV center system . Comparing with non‐adiabatic holonomic control which requires three‐level system and two well‐controlled driving fields (see ref.…”

“…In ref. [], the authors also made a comparison of the operations between SGQC and the dynamical manner through randomized benchmarking analysis. Since the longest sequence duration (in total 99 gates) is much shorter than the longitudinal relaxation time ( T seq ≈ 32 µs ≪ T 1 ≈ 14 ms), the decoherence effects are expected to be negligible.…”

“…b) Comparison of robustness of Pauli‐Z gate realized by SGQC (blue solid line and the red dots) and flux‐based method (purple solid line and the blue dots) versus operation time. Adapted with permission . Copyright 2018, Springer Nature; Copyright 2018, Chinese Physical Society.…”

Berry-phase gates for fast and robust control of atomic clock states

“…Original proposals for holonomic quantum gates are based on this adiabatic evolution [4,[7][8][9]. However, in many physical systems of limited coherence time, it is difficult to satisfy the adiabatic condition and experimental implementation has been limited to longlived transitions [10] or the shortcut to adiabaticity [11,12]. Most other examples utilize nonadiabatic holonomic quantum gates [13][14][15][16][17], but their nonadiabatic characteristic makes them sensitive to parameter fluctuations [18].…”