Chinese Journal of Quantum Electronics

Influence of the noise on geometric quantum gates

Lian Hu

Published Jan 1, 2007• 0 citations

Abstract

The ability of geometric quantum gate against the fluctuations of control external field was researched.We replace the random fluctuations by the periodic perturbation.In this approximation,the result shows that no matter the Berry geometry phase or the Aharonov- Anandan(A-A)geometry phase has the same ability against the stochastic fluctuations as their corresponding dynamics phases.And numerical results also justify that the Berry phase is more powerful to resist the external field fluctuation than that of the A-A phase.We believe that this distinction is caused by adiabatic approximation purely.Lastly,it is validated that the geometry quantum gates constructed by an orthogonal state scheme are more powerful against the fluctuations.

Related papers

Effect of noise on geometric logic gates for quantum computation

Alexandre Blais, A.–M. S. Tremblay

We introduce the nonadiabatic, or Aharonov-Anandan, geometric phase as a tool for quantum computation and show how this phase on one qubit can be monitored by a second qubit without any dynamical contribution. We also discuss how this geometric phase could be implemented with superconducting charge qubits. While the nonadiabatic geometric phase may circumvent many of the drawbacks related to the adiabatic (Berry) version of geometric gates, we show that the effect of fluctuations of the control parameters on nonadiabatic phase gates is more severe than for the standard dynamic gates. Similarly, fluctuations also affect to a greater extent quantum gates that use the Berry phase instead of the dynamic phase.

arXiv:quant-ph/0105006Physical Review AJan 17, 200362 citations

Experimental limits on the fidelity of adiabatic geometric phase gates in a single solid-state spin qubit

Kai Zhang, Naufer Nusran, Bradley R. Slezak +1 more

While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically by careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (∼10) operations. This occurs inspite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. We have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.

New Journal of PhysicsMay 17, 20168 citations

Exploring the effect of noise on the Berry phase

S. Berger, Marek Pechal, A. A. Abdumalikov +5 more

We experimentally investigate the effects of noise on the adiabatic and cyclic geometric phase, also termed the Berry phase. By introducing artificial fluctuations in the path of the control field, we measure the geometric contribution to dephasing of an effective two-level system for a variety of noise powers and different paths. Our results, measured using a microwave-driven superconducting qubit, clearly show that only fluctuations which distort the path lead to geometric dephasing. In a direct comparison with the dynamic phase, which is path independent, we observe that the Berry phase is less affected by noise-induced dephasing. This observation directly points towards the potential of geometric phases for quantum gates or metrological applications.

arXiv:1302.3305Physical Review AJun 26, 2013101 citations

Geometric phase subject to stochastic noise

Xin Li, Zhongfang Li

We strictly study geometric phase gates driven by a classical fluctuating magnetic field. In the derivation of the stochastic Liouville equation of this system, we turn to the cumulant expansion method of Kubo and white noise assumption. The directional dependence of Berry and Aharonov–Anandan (AA) phase gates on noise is assuredly captured. For nonadiabatic evolution, enhancing angular frequency of the rotating magnetic field can be beneficial to realize fault-tolerant AA phase gates.

Journal of Physics A Mathematical and TheoreticalFeb 9, 20114 citations

Suppressing the geometric dephasing of Berry phase by using modified dynamical decoupling sequences

Xiao-Ke Qin, Guang‐Can Guo, Zheng-Wei Zhou

Even though traditional dynamical decoupling methods have the ability to resist dynamic dephasing caused by low frequency noise, they are not appropriate for suppressing the residual geometric dephasing, which arises from the disturbance of the geometric loop in the parameter space. This prevents the precision of quantum manipulation-based geometric quantum gates from being promoted further. In this paper, we design two kinds of modified dynamical decoupling schemes to suppress the residual geometric dephasing. The further numerical simulation demonstrates the validity of our schemes.

arXiv:1703.05654New Journal of PhysicsDec 19, 20164 citations

Geometry of Grover Search : A Comparison between Geometric and Holonomic Quantum Computation

Rasmus Wallentin

Geometric quantum phases enable the construction geometric quantum gates, whose action only depend on the evolution path in state space. Geometric gates may offer increased robustness to control parameter noise. In this report, the conditions under which non-adiabatic geometric and holonomic quantum gates preserve their geometric character under sequential composition are analysed. Grover’s search algorithm requiring non-commuting operations is used as a representative example. The basic concepts of qubits, quantum gates and quantum circuits are explained. The concept of geometric phases is introduced and derivations of Abelian and non-Abelian non-adiabatic geometric phases are provided (Aharonov-Anandan and Anandan phase respectively). Construction of geometric and holonomic universal quantum gate sets with the aforementioned geometric phases are briefly described.Explicit calculation of two non-commuting Abelian and non-adiabatic geometric time evolutions show that the successively combined operation is not geometric. A proof of successive combinations of non-Abelian and non-adiabatic geometric time evolutions preserving their non-adiabatic Abelian and geometric properties is given. The report concludes that it is in general not possible to perform quantum circuits completely geometrically with a geometric universal quantum gate set. However, performing quantum computations with gates from a holonomic universal gate set is geometric and holonomic throughout the computation.

Jan 1, 20260 citations