Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace

Abstract

High-fidelity quantum gates are essential for large scale quantum computation, which can naturally be realized in a noise resilient way. It is well-known that geometric manipulation and decoherence-free subspace encoding are promising ways towards robust quantum computation. Here, by combining the advantages of both strategies, we propose and experimentally realize universal holonomic quantum gates in both a single-loop and composite scheme, based on nonadiabatic and non-Abelian geometric phases, in a decoherence-free subspace with nuclear magnetic resonance. Our experiment only employs two-body resonant spin-spin interactions and thus is experimental friendly. In particularly, we also experimentally verify that the composite scheme is more robust against the pulse errors over the single-loop scheme. Therefore, our experiment provides a promising way towards faithful and robust geometric quantum manipulation.

Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

“…In contrast to the earlier adiabatic-process-based geometric quantum computation [35][36][37][38], nonadiabatic geometric quantum computation (NGQC) and nonadiabatic holonomic quantum computation (NHQC) based on Abelian [39][40][41][42][43][44][45][46] and non-Abelian geometirc phases [47][48][49][50][51][52][53][54][55][56] in two-and threelevel system, respectively, can intrinsically protect against environment-induced decoherence, since the the construction times of geometric quantum gates is reduced. The nonadiabatic geometric gates of NGQC and NHQC have been experimentally demonstrated in many systems including superconducting qubit [57][58][59][60][61], NMR [62][63][64][65], NV center in diamond [66][67][68][69]. However, there are many theoretical proposals to apply geometric quantum computation [70][71][72][73] and NGQC [42,[74][75][76][77] in Rydberg atom platform.…”

Error-Tolerant Geometric Quantum Control for Logical Qubits with Minimal Resource

“…Recently, GQC [11][12][13][14][15][16][17] based on the nonadiabatic geometric phases [4,5] have been proposed to implement robust and high-fidelity quantum gates, which eliminate the restriction of slow evolution. Remarkably, experimental demonstrations for elementary geometric quantum gates have also been achieved on various systems, such as trapped ions [18,19], NMR [20][21][22][23], superconducting quantum circuits [24][25][26][27][28][29][30], and nitrogen vacancy centers [31][32][33][34][35][36], etc. Meanwhile, to further consolidate the geometric robustness, many efforts have been made to make GQC being compatible with various optimal-control techniques, including the composite pulse [37,38], dynamical decoupling [39,40], time-optimal control [41], path optimization [42], etc.…”

Composite Short-path Nonadiabatic Holonomic Quantum Gates

“…But for the realization of an arbitrary single-qubit gate, it needs to concatenate two separate cycles, which will increase the decoherence induced error. To remove this obstacle, researchers have come up with an improved approach enables to realize arbitrary single-qubit gate through a single-loop evolution [19][20][21], which has also been experimentally verified [22][23][24][25][26][27].…”