Fast and robust quantum computation with ionic Wigner crystals

Abstract

We present a detailed analysis of the modulated-carrier quantum phase gate implemented with Wigner crystals of ions confined in Penning traps. We elaborate on a recent scheme, proposed by two of the authors, to engineer two-body interactions between ions in such crystals. We analyze for the first time the situation in which the cyclotron (w_c) and the crystal rotation (w_r) frequencies do not fulfill the condition w_c=2w_r. It is shown that even in the presence of the magnetic field in the rotating frame the many-body (classical) Hamiltonian describing small oscillations from the ion equilibrium positions can be recast in canonical form. As a consequence, we are able to demonstrate that fast and robust two-qubit gates are achievable within the current experimental limitations. Moreover, we describe a realization of the state-dependent sign-changing dipole forces needed to realize the investigated quantum computing scheme.Comment: 14 pages, 11 figures, published versio

Phonon-mediated quantum spin simulator employing a planar ionic crystal in a Penning trap

“…16, but we use a different potential by including the rotating wall, while it is different from the approach used in Ref. 17). The minimization procedure employs both a locally calculated gradient and a locally calculated Hessian matrix, similar to the method described in Ref.…”

“…These eigenvectors do become the eigenvectors for the planar modes only in the case when B ef f = 0 (which occurs when the rotating frequency is equal to half the cyclotron frequency), where the eigenvalue problem simplifies to the traditional form for a phonon. This fact has been used for an analysis of the phonons in a Penning trap [17]. The basis vectors b αν k can be chosen to be real and they are also orthonormal iα b…”

“…We then quantize these phonons and show how they can be used with a spin-dependent optical dipole force to generate effective spin-spin interactions. Recently, others have shown how to find equilibrium positions for similar trapping potentials [16], and have evaluated the phonon spectra using different methods from the ones we employ [17].…”

Superposition states for quantum nanoelectronic circuits and their nonclassical properties

“…This is a stumbling-block for achieving robust quantum computations on the basis of nonclassical features of superposition states through encoding logical qubits with a treatment of the states [40,41]. A number of proposals to overcome this major hurdle in quantum computing has been suggested so far [42][43][44]. The development of techniques for protecting quantum information from decoherence is crucial for realizing universal quantum computation.…”

Effect of defects on phonons and the effective spin-spin interactions of an ultracold Penning-trap quantum simulator

“…We solve for the equilibrium structure of the crystal in a standard way [12,15,16], constructing initial "shell" configurations and minimizing the effective potential in the rotating frame. We express all distances in terms of a characteristic length, denoted 0 , which satisfies…”