Nonadiabatic Geometric Quantum Computation with Parametrically Tunable Coupling

Abstract

The nonadiabatic geometric quantum computation is promising as it is robust against certain types of local noises. However, its experimental implementation is challenging due to the need of complex control on multi-level and/or multiple quantum systems. Here, we propose to implement it on a two-dimensional square superconducting qubit lattice. In the construction of our geometric quantum gates, we only use the simplest and experimentally accessible control over the qubit states of the involved quantum systems, without introducing any auxiliary state. Specifically, our scheme is achieved by parametrically tunable all-resonant interaction, which leads to high-fidelity quantum gates. Meanwhile, this simple implementation can be conveniently generalized to a composite scenario, which can further suppress the systematic error during the gate operations. In addition, universal nonadiabatic geometric quantum gates in decoherence-free subspace can also be realized based on the tunable coupling between only two transmon qubits, without consulting to multiple qubits and only using two physical qubits to encode a logical qubit. Therefore, our proposal provides a promising way of high-fidelity geometric manipulation for robust solid-state quantum computation.

Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

“…Geometric quantum logic gates [22,23] based on adiabatic or nonadiabatic geometric phase [24][25][26][27], which depends only on the global properties of the evolution paths, provides us the possibility for robust quantum computation [28][29][30][31][32][33][34]. 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]…”

“…Comparing with the conventional Rydberg blockade [4][5][6], we consider RRI-induced blockade process seriously by second-order dynamics, which may be more accurate since we do not discard the stark shifts relevant to the "blockade". More importantly, our scheme can further reduce the geometric gate time of NGQC [42][43][44][45][46] without the limitation of cyclic condition. Specifically, we found that the certain gate time of NNGQC can be reduced by half compared with NGQC by choosing proper control parameter.…”

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

“…Usually, the existence of systematic errors tends to devastate the advantage of the robustness of holonomic gate in the NHQC [45,46]. To overcome this, we suggest implementing the holonomic gates with composite schemes [43,44]. To achieve this in DFS, we take U S (γ/N, θ, φ) as an elementary gate, where N > 1.…”

“…However, the robustness against systematic errors of the single-loop implementation is still the same as previous schemes. Then, we move another step further to incorporate the composite-loop technique [43,44] into our implementation, which is achieved by changing the way of accumulating the geometric phase. In addition, both the the single-loop and composite-loop implementations are experimentally tested, our experimental comparison between the two implementations shows that the composite-loop one can indeed further improve the noise resilience of the implemented holonomic quantum gates.…”

Geometric Quantum Computation with Shortcuts to Adiabaticity

“…On the other hand, efforts on putting forward the investigations of multiqubit holonomic gates are also made . In superconducting system, it is proposed that one can engineer robust manipulation on two qubit states through parameter tunable coupling with STA …”