Integrable quantum computation

Zhang, Yong

doi:10.1007/s11128-012-0409-4

Cited by 14 publications

(10 citation statements)

References 14 publications

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“…As a matter of fact, how to perform quantum computation in integrable systems has been a long-term research project investigated by few groups in mathematical physics. Integrable quantum computation [2] is defined as quantum computation associated with the integrable condition. For example, the integrability condition is the quantum Yang-Baxter equation, so that a multi-particle factorized scattering is identified with a quantum circuit model, where quantum computation without quantum control is considered rather seriously.…”

Section: Discussion: Quantum Computation In Integrable Systemsmentioning

confidence: 99%

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Quantum Computation Using Action Variables

Zhang¹,

Wu²

2021

Preprint

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Recently, Lloyd and Montangero have made a brief research proposal on universal quantum computation in integrable systems. The main idea is to encode qubits into quantum action variables and build up quantum gates by the method of resonant control. We study this proposal to argue quantum computation using action variables as fault-tolerant quantum computation, whose fault-tolerance is guaranteed by the quantum KAM theorem. Besides, we view the Birkhoff norm form as a mathematical framework of the extended harmonic oscillator quantum computation.

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Section: Discussion: Quantum Computation In Integrable Systemsmentioning

confidence: 99%

“…If a quantum computer is an integrable system with control terms, then it seems reasonable to devise appropriate methods to perform information processing tasks. Hence a realistic quantum computer has been naturally assumed to be associated with quantum integrable systems [2].…”

Section: Introductionmentioning

confidence: 99%

Quantum Computation Using Action Variables

Zhang¹,

Wu²

2021

Preprint

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“…At the root of our proposal there is the exploitation of Bethe-Ansatz techniques and quantum indistinguishability. Compared to other recent proposals for quantum logic in 1D [77,78,79], our method is more scalable, as it can use the machinery of integrable models, such as the Yang-Baxter relation, to realize composite operations between multiple par-ticles (see also [80,81]). Indeed, since in integrable models all complex n-body scattering effects can be factorized into two-body S matrices, one can straightforwardly apply our findings also in multi-particle scenarios.…”

Section: Discussionmentioning

confidence: 99%

Quantum gates between distant qubits via spin-independent scattering

Banchi

Compagno

Korepin

et al. 2017

Quantum

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We show how the spin independent scattering of two initially distant qubits, say, in distinct traps or in remote sites of a lattice, can be used to implement an entangling quantum gate between them. The scattering takes place under 1D confinement for which we consider two different scenarios: a 1D wave-guide and a tight-binding lattice. We consider models with contactlike interaction between two fermionic or two bosonic particles. A qubit is encoded in two distinct spins (or other internal) states of each particle. Our scheme enables the implementation of a gate between two qubits which are initially too far to interact directly, and provides an alternative to photonic mediators for the scaling of quantum computers. Fundamentally, an interesting feature is that "identical particles" (e.g., two atoms of the same species) and the 1D confinement, are both necessary for the action of the gate. Finally, we discuss the feasibility of our scheme, the degree of control required to initialize the wavepackets momenta, and show how the quality of the gate is affected by momentum distributions and initial distance. In a lattice, the control of quasi-momenta is naturally provided by few local edge impurities in the lattice potential.

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“…It has been found that the YBE is closely related to the generation of quantum entanglement 5 . Furthermore a new quantum computation model based on the notion of integrability was proposed, where the quantum gates are related to unitary solutions of the YBE 6 7 8 .…”

mentioning

confidence: 99%

“…The interest in this form comes from its relation to the braid group which has been recently linked to topological quantum computation 6 7 8 and a scheme for its verification through an optical setup has been proposed 17 and achieved 18 .…”

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confidence: 99%

Experimental realization of the Yang-Baxter Equation via NMR interferometry

Vind

Foerster

Oliveira

et al. 2016

Sci Rep

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The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.

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Integrable quantum computation

Cited by 14 publications

References 14 publications

Quantum Computation Using Action Variables

Quantum Computation Using Action Variables

Quantum gates between distant qubits via spin-independent scattering

Experimental realization of the Yang-Baxter Equation via NMR interferometry

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