Coherence Stabilization of a Two-Qubit Gate by ac Fields

Abstract

We consider a CNOT gate operation under the influence of quantum bit-flip noise and demonstrate that ac fields can change bit-flip noise into phase noise and thereby improve coherence up to several orders of magnitude while the gate operation time remains unchanged. Within a high-frequency approximation, both purity and fidelity of the gate operation are studied analytically. The numerical treatment with a Bloch-Redfield master equation confirms the analytical results.PACS numbers: 03.67. Pp, 42.50.Hz, 03.65.Yz Despite the remarkable experimental realization of qubits [1,2,3] and two-qubit gates [4] in condensed matter systems, the construction of a working quantum computer remains an elusive goal, not only due to deficiencies of the control circuitry, but also due to the unavoidable coupling to the environment. Several proposals to overcome the ensuing decoherence have been put forward, such as the use of decoherence free subspaces [5,6,7,8,9], quantum Zeno subspaces [10], dynamical decoupling [11,12,13,14], and coherent destruction of tunneling [15].A single qubit under the influence of bit-flip noise can be modeled by the spin-boson Hamiltonianwhere σ x,z denotes Pauli matrices and ξ is a shorthand notation for the quantum noise specified below. The influence of the bath is governed by the spectral density of the noise at the tunneling frequency ∆/ . A possible driving field may couple to any projection n of the (pseudo) spin operator σ, i.e., be proportional to n · σ. In Ref.[15], two particular choices have been studied and compared against each other: A driving of the form H(t) = Aσ z cos(Ωt) commutes with the static qubit Hamiltonian while it modifies the bath coupling σx ξ in such a way that the spectral density of the bath at multiples of the driving frequency becomes relevant. For a proper driving amplitude, this eliminates noise with frequencies below the driving frequency which, thus, should lie above the cutoff frequency of the bath. This scheme represents a continuous-wave version of dynamical decoupling [15]. By contrast, a driving of the type H(t) = Aσ x cos(Ωt) renders the qubit-bath coupling unchanged but renormalizes the tunnel splitting ∆ towards smaller values and thereby causes the so-called coherent destruction of tunneling (CDT) [16,17]. Then, decoherence is determined by the spectral density of the bath at a lower effective tunnel frequency. For an ohmic bath being linear in the frequency, the consequence is that both decoherence and the coherent oscillations in the rotating frame are slowed down by the same factor [15]. Therefore, the number of coherent oscillations is not enlarged and, thus, for single-qubit operations, CDT might be of limited use.In this work, we propose a coherence stabilization scheme for a CNOT gate based on isotropic Heisenberg interaction [18,19]. Our scheme does not suffer from the drawbacks mentioned above because (i) it involves only intermediately large driving frequencies that can lie well below the bath cutoff and (ii) it does not increase the operation ...

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