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Cited by 39Quantum Information and CryptographyQuantum Computing Algorithms and ArchitectureQuantum and electron transport phenomena

An exact effective two-qubit gate in a chain of three spins

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Yung, M.-H., Leung, D.W., Bose, S.·2004·Quantum Information and Computation
DOI 10.26421/qic4.3-2
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Abstract

We show that an effective two-qubit gate can be obtained from the free evolution of three spins in a chain with nearest neighbor XY coupling, without local manipulations. This gate acts on the two remote spins and leaves the mediating spin unchanged. It can be used to perfectly transfer an arbitrary quantum state from the first spin to the last spin or to simultaneously communicate one classical bit in each direction. One ebit can be generated in half of the time for state transfer. For longer spin chains, we present methods to create or transfer entanglement between the two end spins in half of the time required for quantum state transfer, given tunable coupling strength and local magnetic field. We also examine imperfect state transfer through a homogeneous XY chain.

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  • The condition in Eq. (5) is not only sufficient but also necessary for perfect state transfer in mirror symmetric chains.

    “It has been shown [10] that the condition in Eq. (5) is not only sufficient but also necessary for perfect state transfer in mirror symmetric chains.”

    From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [10]

  • There are many possible solutions for constructing spin chains that allow perfect state transfer, and searching for them is in general an inverse eigenvalue problem.

    “Moreover, it has also been pointed out [10] that there are many possible solutions for constructing spin chains which allow perfect state transfer, and the searching for the solutions is in general an inverse eigenvalue problem.”

    From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [10]

  • For a mirror-symmetric Hamiltonian, < ̄x|e_k> = (-1)^k <x|e_k>, and hence |< ̄x|U(τ)|x>| = 1 if Eq. (5) holds.

    “Provided that the Hamiltonian in Eq. (1) or Eq. (3) is mirror symmetrical, i.e. λ j = λ ¯ j and ω j = ω N -j , one can show [10] that 〈 ¯ x | e k 〉 = ( -1) k 〈 x | e k 〉 , and hence |〈 ¯ x | U ( τ ) | x 〉| = 1 if”

    From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [10]

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Authors
Yung, M.-H., Leung, D. W., & Bose, S.
Affiliations
California Institute of Technology (US)
ORCID
Venue
Quantum Information and Computation
Publisher
Rinton Press
Published
2004-05
Volume
4
Issue
3
Pages
174-185
ISSN
1533-7146 (ISSN-L)
DOI
10.26421/qic4.3-2
OpenAlex
W1890558422
Cited by
39
References
13
Citations by year
2025: 1 · 2023: 1 · 2022: 3 · 2019: 1 · 2018: 1 · 2016: 1 · 2012: 3
FWCI
6.07
Type
journal article
Language
en
Open access
Locations
  • Quantum Information and Computation (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • UCL Discovery (University College London) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
Keywords
two-qubit gates, spin chains, quantum state transfer, entanglement generation, EBIT, quantum communication, free evolution, nearest-neighbor coupling, local magnetic field

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