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arXiv:quant-ph/0105006 · Physical Review A

Effect of noise on geometric logic gates for quantum computation

Alexandre Blais, A.–M. S. Tremblay

Published Jan 17, 2003• 62 citations
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Abstract

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.

DOI
10.1103/physreva.67.012308

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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.
We present an adiabatic geometric quantum computation strategy based on the non-degenerate energy eigenstates in (but not limited to) superconducting phase qubit systems. The fidelity of the designed quantum gate was evaluated in the presence of simulated thermal fluctuations in a superconducting phase qubits circuit and was found to be quite robust against random errors. In addition, it was elucidated that the Berry phase in the designed adiabatic evolution may be detected directly via the quantum state tomography developed for superconducting qubits. We also analyze the effects of control parameter fluctuations on the experimental detection of the Berry phase.
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.
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.
Recently, geometric phases, which is fault tolerate to certain errors intrinsically due to its geometric property, are getting considerable attention in quantum computing theoretically. So far, only one experiment about adiabatic geometric gate with NMR through Berry phase has been reported. However, there are two drawbacks in it. First, the adiabatic condition of Berry phase makes such gate very slowly. Second, the extra operation to eliminate the dynamic phase. As we know, geometric phase can exist both adiabatic(Berry phase) and nonadiabatic(Aharonov-Anandan phase). In this letter, we reports the first experimental realization of nonadiabatic geometric gate with NMR through conditional-AA phase. In our experiment the gates can be made faster and more easily, and the two drawbacks mentioned above are removed.
Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation (NHQC) and show that conventional NHQC schemes cannot guarantee the expected robustness due to a cross-coupling to the states outside the computational space. We implement a different set of constraints for gate construction in order to suppress such cross-coupling to achieve an enhanced robustness. Using a superconducting quantum circuit, we demonstrate high-fidelity holonomic gates whose infidelity against quasistatic transverse errors can be suppressed up to the fourth order, instead of the second order in conventional NHQC and dynamical gates. In addition, we explicitly measure the accumulated dynamical phase due to the abovementioned cross-coupling and verify that it is indeed much reduced in our NHQC scheme. We further demonstrate a protocol for constructing two-qubit NHQC gates also with an enhanced robustness.