Quantum logic operations and creation of entanglement in a scalable superconducting quantum computer with long-range constant interaction between qubits

Berman, G. P.; Bishop, A. R.; Kamenev, D. I.; Trombettoni, Andrea

doi:10.1103/physrevb.71.014523

Cited by 6 publications

(2 citation statements)

References 23 publications

(38 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We are principally interested in using the chain to encode 5,6,7 and protect or correct 8,9,10,11 quantum information. "Logical gate" operations on a chain of SQUIDs can create 12 useful non-classical correlations quantified by their "entanglement of formation" 13 . Chains can propagate excitations, qubits 14,15,16,17 , and even entangled singlets, (|↑↓ − |↓↑ )/ √ 2 18,19,20 .…”

Section: Introduction a Squids And Squid Chainsmentioning

confidence: 99%

Chain-boson model for the decoherence and relaxation of a few coupled SQUIDs in a phonon bath

Skinner¹,

Hu²

2008

Phys. Rev. B

View full text Add to dashboard Cite

We develop a "chain-boson model" master equation, within the Born-Markov approximation, for a few superconducting quantum interference devices ͑SQUIDs͒ coupled into a chain and exchanging their angular momenta with a low-temperature phonon bath. Our master equation has four generators; we concentrate on the damping and diffusion and use them to study the relaxation and decoherence of a Heisenberg SQUID chain whose spectrum exhibits critical-point energy-level crossings, entangled states, and pairs of resonant transitions. We note that at an energy-level crossing, the relevant bath wavelengths are so long that even well-spaced large SQUIDs can partially exhibit collective coupling to the bath, dramatically reducing certain relaxation and decoherence rates. Also, transitions into entangled states can occur even in the case of an independent coupling of each SQUID to the bath. Finally, the pairs of resonant transitions can cause decaying oscillations to emerge in a lower-energy subspace.

show abstract

Section: Introduction a Squids And Squid Chainsmentioning

confidence: 99%

Chain-boson model for the decoherence and relaxation of a few coupled SQUIDs in a phonon bath

Skinner¹,

Hu²

2008

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…2, can be obtained in a similar way. In this extended multipartite coupling case, the long-range interaction between the devices would appear, which decays exponentially as β |i−j| with i and j being the site labels of the two involved devices [18]. Therefore, the long-range interaction is negligible if β ≪ 1, and in typical experiments β ≃ 0.05 [19].…”

mentioning

confidence: 99%

Implementing topological quantum manipulation with superconducting circuits

et al. 2009

View full text Add to dashboard Cite

A two-component fermion model with conventional two-body interactions was recently shown to have anyonic excitations. We here propose a scheme to physically implement this model by transforming each chain of two two-component fermions to the two capacitively coupled chains of superconducting devices. In particular, we elaborate how to achieve the wanted operations to create and manipulate the topological quantum states, providing an experimentally feasible scenario to access the topological memory and to build the anyonic interferometry.Topological ordered states emerge as a new kind of states of quantum matter beyond the description of conventional Landau's theory ͓1͔, whose excitations are anyons satisfying fractional statistics. A paradigmatic system for the existence of anyons is a kind of so-called fractional quantum Hall states ͓2͔. Alternatively, artificial spin lattice models are also promising for observing these exotic excitations ͓1,3,4͔. Kitaev models ͓3,4͔ are most famous for demonstrating anyonic interferometry and braiding operations for topological quantum computation.Since anyons have not been directly observed experimentally, a focus at present is to experimentally demonstrate the topological nature of these states. Abelian anyons maybe relatively easy to achieve and to manipulate in comparison with the nonabelian ones, thus it is of current interest to explore them both theoretically and experimentally. Kitaev constructed an artificial spin model ͓3͔, i.e., the toric code model, which supports the abelian anyon. But the wanted four-body interactions are notoriously hard to generate experimentally in a controllable fashion. Alternatively, it was proposed ͓5͔ to generate dynamically the ground state and the excitations of the model Hamiltonian, instead of direct ground-state cooling, to simulate the anyonic interferometry. On the other hand, implementation of another Kitaev's honeycomb model ͓4͔ was also suggested in the context of ultracold atoms ͓6͔, polar molecules ͓7͔, and superconducting circuits ͓8͔. The honeycomb model ͓4͔ is an anisotropic spin model with three types of nearest-neighbor two-body interactions, which support both abelian and nonabelian anyons. It was shown ͓4͔ that the toric code model can be obtained from the limiting case of the honeycomb model. Using this map, preliminary operations for topological quantum memory and computation were also addressed ͓9-12͔. Nevertheless, in this case, anyons are created by the fourth-order perturbation treatment, which would blur the extracted anyonic information ͓12͔. In addition, this map is good but not exact, so that one may get both anyonic and fermionic excitations. Therefore, new methods for implementing the model and manipulating the relevant topological states are still desirably awaited.Recently, a two-component fermion model ͓13͔ with conventional two-body interactions was shown to have anyonic excitations, which obey the same fusion rules as those of the toric code model and are mutual semions. This model is promising because ...

show abstract

Always on non-nearest-neighbour coupling in scalable quantum computing

Zhou

Guo

2007

New J. Phys.

View full text Add to dashboard Cite

We study the non-nearest-neighbor interaction effect in 1-D spin-1/2 chain model. In many previous schemes this long-range coupling is omitted because of its relative weak strength compared with the nearest-neighbor coupling. We show that the quantum gate deviation induced by the omitted long-range interaction depends on not only its strength but also the scale of the system. This implies that omitting the long-range interaction may challenge the scalability of previous schemes. We further propose a quantum computation scheme. In this scheme, by using appropriate encoding method, we effectively negate influence of the next-nearest-neighbor interaction in order to improve the precision of quantum gates. We also discuss the feasibility of this scheme in 1-D Josephson charge qubit array system. This work may offer improvement in scalable quantum computing.

show abstract

Quantum logic operations and creation of entanglement in a scalable superconducting quantum computer with long-range constant interaction between qubits

Cited by 6 publications

References 23 publications

Chain-boson model for the decoherence and relaxation of a few coupled SQUIDs in a phonon bath

Chain-boson model for the decoherence and relaxation of a few coupled SQUIDs in a phonon bath

Implementing topological quantum manipulation with superconducting circuits

Always on non-nearest-neighbour coupling in scalable quantum computing

Contact Info

Product

Resources

About