We present an experimentally realizable stabilized charge pumping scheme in a linear array of Cooper-pair boxes. The system design intrinsically protects the pumping mechanism from severe errors, especially current reversal and spontaneous charge excitation. The quantum Zeno effect is implemented to further diminish pumping errors. The characteristics of this scheme are considered from the perspective of improving the current standard. Such an improvement bears relevance to the closure of the so-called measurement triangle (see [D. Averin, Nature (London) 434, 285 (2005)).
We examined properties of a Josephson-junction system composed of two coupled Cooper-pair boxes (charge qubits) as a candidate for observation of quantum holonomies. We construct a universal set of transformations in a twofold degenerate ground state, and discuss the effects of noise in the system.
We discuss adiabatic quantum phenomena at a level crossing. Given a path in the parameter space which passes through a degeneracy point, we find a criterion which determines whether the adiabaticity condition can be satisfied. For paths that can be traversed adiabatically we also derive a differential equation which specifies the time dependence of the system parameters, for which transitions between distinct energy levels can be neglected. We also generalize the well-known geometric connections to the case of adiabatic paths containing arbitrarily many level-crossing points and degenerate levels.Comment: 7 pages, 6 figures, RevTeX4, changes requested by Phys. Rev.
We construct non-Abelian geometric transformations in superconducting nanocircuits, which resemble in properties the Aharonov-Bohm phase for an electron transported around a magnetic flux line. The effective magnetic fields can be strongly localized, and the path is traversed in the region where the energy separation between the states involved is at maximum, so that the adiabaticity condition is weakened. In particular, we present a scheme of topological charge pumping.PACS numbers: 85.25. Cp, 03.65.Vf, 03.67.Pp When an electron is transported in magnetic field around a closed loop, it acquires a phase equal to the magnetic flux through the surface spanned by the electron path. This phenomenon has been known as the Aharonov-Bohm effect for nearly half of a century [1]. In the original paper the magnetic field forms a flux line, and electrons move in the region of zero field. Berry [2] considered this phenomenon to be an early example of the geometric phases, which he described in a more general context. For each quantum system undergoing adiabatic cyclic evolution of its parameters we can find phase shifts acquired by its energy eigenstates. Apart from the dynamical factor, there is a contribution which depends only on the geometry of the path traversed in the parameter space (the parameters are time dependent, as they are varied throughout the process, but the explicit time dependence does not enter the expression for the Berry phase, which makes it geometric in nature). Berry gives also a formula for this phase in the form of an integral of an effective magnetic field (we will refer to this field as the "Berry field") over a surface spanned by the path. This makes the similarity between geometric phases in arbitrary quantum system, and the AharonovBohm scenario even closer: one can think of the Berry field as analogous to the real magnetic field; the parameter space corresponds then to the real position space. The Aharonov-Bohm effect in the original setting is, however, easier to observe than the Berry phase in general. The first reason is that in the former case there is no adiabaticity condition constraining the electron velocity, while in the latter the rate of the parameters' variation should be much smaller than the inverse energy difference between the states involved. The second is that for strongly localized field any variation in the path of the electron does not affect the phase at all as long as the path encloses the flux line (this phase is thus topological). For the Berry phase, depending on the system, we encounter effective fields usually smoothly varying with the parameters, or even uniform, particularly for a spin-1/2 system, the phase is the flux of a monopole, or, in other words, the area spanned by the traversed loop on the unit sphere (see e.g. [2]). Fluctuations of externally controlled parameters first of all lead to dephasing of dynamical origin, but also smear the path, which affects the visibility of the effect even further.Here we show that geometric phases can appear in quantum...
We describe a qubit encoded in continuous quantum variables of an rf superconducting quantum interference device. Since the number of accessible states in the system is infinite, we may protect its two-dimensional subspace from small errors introduced by the interaction with the environment and during manipulations. We show how to prepare the fault-tolerant state and manipulate the system. The discussed operations suffice to perform quantum computation on the encoded state, syndrome extraction, and quantum error correction. We also comment on the physical sources of errors and possible imperfections while manipulating the system.
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