Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

Abstract

Nonadiabatic geometric quantum computation (NGQC) has been developed to realize fast and robust geometric gate. However, the conventional NGQC is that all of the gates are performed with exactly the same amount of time, whether the geometric rotation angle is large or small, due to the limitation of cyclic condition. Here, we propose an unconventional scheme, called nonadiabatic noncyclic geometric quantum computation (NNGQC), that arbitrary single-and two-qubit geometric gate can be constructed via noncyclic non-Abelian geometric phase. Consequently, this scheme makes it possible to accelerate the implemented geometric gates against the effects from the environmental decoherence. Furthermore, this extensible scheme can be applied in various quantum platforms, such as superconducting qubit and Rydberg atoms. Specifically, for single-qubit gate, we make simulations with practical parameters in neutral atom system to show the robustness of NNGQC and also compare with NGQC using the recent experimental parameters to show that the NNGQC can significantly suppress the decoherence error. In addition, we also demonstrate that nontrivial two-qubit geometric gate can be realized via unconventional Rydberg blockade regime within current experimental technologies. Therefore, our scheme provides a promising way for fast and robust neutral-atom-based quantum computation.

Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

“…Therefore, the schemes of GQC based on single-loop evolution have been proposed [30][31][32][33][34][35][36][37][38], which further decreases the needed time for geometric gates. Notably, the elimination of dynamical phase has also been investigate in the case of quantum computation with non-cyclic geometric phases [39][40][41][42][43][44].…”

Optimized nonadiabatic holonomic quantum computation based on Förster resonance in Rydberg atoms

“…With the relaxation of the conditions, the NHQC+ approach can be compatible with various optimal control methods including counteradiabatic driving (CD) [17][18][19][20], dynamical decoupling (DD) [21][22][23], single-shot-shaped pulse (SSSP) [24,25], invariant based reverse engineering (IBRE) [26,27], etc., which further improves the robustness against systematic errors. To date, many NHQC+ schemes have been put forward in different physical systems, for example, superconducting circuit [28][29][30], spin qubits [31,32], and Rydberg atoms [33][34][35][36]. The Rydberg atom system is one promising candidate platform for physical implementation of quantum computing due to its long coherence time and strong interatomic interaction [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51].…”

Single-atom verification of the noise-resilient and fast characteristics of universal nonadiabatic noncyclic geometric quantum gates

“…In addition, the NGQC takes exactly the same amount of gating time regardless of the large or small geometric rotation angle involved, which is subject to the cyclic condition, but impossibly changed by optimizing other parameters. Actually, the cyclic requirement is not always necessary in accomplishment of the NGQC, as indicated in a recent proposal [55], in which the proposed nonadiabatic noncyclic geometric quantum computation (NNGQC) could reduce the gating time, while retaining the robust property of the geometric gates. In particular, compared to previously published noncyclic geometric models, e.g., [56][57][58], the proposal using simpler pulse sequences could be executed with a faster pace and more relevance to current laboratory technique.…”

“…Before specifying the experimental details, we first elucidate briefly the theory of constructing the singlequbit geometric gate using the basis states {|g , |e }. For our purpose, the light-matter interaction is given by the Hamiltonian in units of = 1 [55],…”

“…To understand the physics more clearly, we may map the system's states to two auxiliary states |Ψ 1,2 . In terms of (a) (b) the proposal [55], realizing a NNGQC requires the amplitude and phase of the laser in time evolution to satisfy a couple of differential equations as below,…”