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arXiv:1107.4394 · Physical Review A

Quasideterministic realization of a universal quantum gate in a single scattering process

Francesco Ciccarello, Dan E. Browne, L. C. Kwek, Henning Schomerus, Michelangelo Zarcone, Sougato Bose

Published May 17, 2012• 38 citations
arXivHTMLPDF

Abstract

We show that a flying particle, such as an electron or a photon, scattering along a one-dimensional waveguide from a pair of static spin-$\frac{1}{2}$ centers, such as quantum dots, can implement a controlled-z gate (universal for quantum computation) between them. This occurs quasideterministically in a single scattering event, with no need for any postselection or iteration and without demanding the flying particle to bear any internal spin. We show that an easily matched hard-wall boundary condition along with the elastic nature of the process are key to such performances.

DOI
10.1103/physreva.85.050305

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We show that a flying particle, such as an electron or a photon, scattering along a one-dimensional waveguide from a pair of static spin-12\frac{1}{2}21​ centers, such as quantum dots, can implement a controlled-z gate (universal for quantum computation) between them. This occurs quasideterministically in a single scattering event, with no need for any postselection or iteration and without demanding the flying particle to bear any internal spin. We show that an easily matched hard-wall boundary condition along with the elastic nature of the process are key to such performances.
We investigate whether a two-qubit quantum gate can be implemented in a scattering process involving a flying and a static qubit. To this end, we focus on a paradigmatic setup made out of a mobile particle and a quantum impurity, whose respective spin degrees of freedom couple to each other during a one-dimensional scattering process. Once a condition for the occurrence of quantum gates is derived in terms of spin-dependent transmission coefficients, we show that this can be actually fulfilled through the insertion of an additional narrow potential barrier. An interesting observation is that under resonance conditions this procedure enables a gate only for isotropic Heisenberg (exchange) interactions and fails for an XY\mathit{XY}XY interaction. We show the existence of parameter regimes for which gates able to establish a maximum amount of entanglement can be implemented. The gates are found to be robust to variations of the optimal parameters.
Abstract Universal quantum gates are the core elements in quantum information processing. We design two schemes to realize more general (SWAP)1/m and controlled-(swap)1/m gates (for integer m ≥ 1 ) by directing flying single photons to solid-state quantum dots. The parameter m is easily controlled by adjusting two quarter-wave plates and one half-wave plate. Additional computational qubits are not required to construct the two gates. Evaluations of the gates indicate that our proposals are feasible with current experimental technology.
We show how the spin independent scattering between two identical flying qubits can be used to implement an entangling quantum gate between them. We consider one dimensional models with a delta interaction in which the qubits undergoing the collision are distinctly labeled by their opposite momenta. The logical states of the qubit may either be two distinct spin (or other internal) states of a fermion or a boson or two distinct momenta magnitudes of a spinless boson. Our scheme could be added to linear optics-like quantum information processing to enhance its efficiency, and can also aid the scaling of quantum computers based on static qubits without resorting to photons. Three distinct ingredients -- the quantum indistinguishability of the qubits, their interaction, and their dimensional confinement, come together in a natural way to enable the quantum gate.
We consider a one-dimensional structure where noninteracting spin-sss scattering centers, such as quantum impurities or multilevel atoms, are embedded at given positions. We show that the injection into the structure of unpolarized flying qubits, such as electrons or photons, along with path detection suffice to accomplish spin-state teleportation between two centers via a third ancillary one. No action over the internal quantum state of both the spin-sss particles and the flying qubits is required. The protocol enables the transfer of quantum information between well-separated static entities in nanostructures by exploiting a very low control mechanism, namely scattering.
Universal quantum gates play a critical role in quantum information processing. Here, based on the scattering property of photons off single emitters in one-dimensional waveguides, we present some heralded protocols for realizing controlled-not, Toffoli, and Fredkin gates on hybrid systems. The control qubit of our gates is encoded on a flying photon, and the target qubits are encoded in the degenerate ground states of the emitter. In our schemes, the faulty scattering processes between emitters and photons caused by system imperfections can be transformed into the detection of photon polarization. That is, our three quantum gates are accomplished in a heralded way. Moreover, the quantum circuits for the three gates are versatile and compact, and no additional qubits are required. With current technique on manipulating the emitter-waveguide system, our protocols may be experimentally feasible. This work provides an effective avenue for implementing quantum logic gates.
The implementation of a high-fidelity two-qubit quantum logic gate remains an outstanding challenge for isolated solid-state qubits such as nitrogen-vacancy (NV) centers in diamond. In this work, we show that by driving pairs of NV centers to undergo photon scattering processes that flip their qubit states simultaneously, we can achieve a unitary two-qubit gate conditioned upon a single photon-detection event. Further, by exploiting quantum interference between the optical transitions of the NV centers' electronic states, we realize the existence of two special drive frequencies: a ``magic'' point where the spin-preserving elastic scattering rates are suppressed and a ``balanced'' point where the state-flipping scattering rates are equal. We analyzed four different gate operation schemes that utilize these two special drive frequencies, and various combinations of polarizations in the drive and collection paths. Our theoretical and numerical calculations show that the gate fidelity can be as high as 98%. The proposed unitary gate, combined with available single-qubit unitary operations, forms a universal gate set for quantum computing.