Effective interaction in unified perturbation theory

Takayanagi, Kazuo

doi:10.1016/j.aop.2015.11.006

Cited by 6 publications

(6 citation statements)

References 19 publications

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“…The effective Hamiltonian H eff defined on the subspace PΩ , i.e., H eff = PH eff P, is an operator satisfying [1,2] H…”

Section: Effective Hamiltonian In the Shrödinger Picturementioning

confidence: 99%

“…where ν = PνP is called the effective interaction. [2] In the above, the eigenstates of H in defining the effective Hamiltonian are required to approach the eigenstates of PH 0 P in the limit V → 0. The effective interaction ν can be expanded in powers of V , [2] i.e.,…”

Section: Effective Hamiltonian In the Shrödinger Picturementioning

confidence: 99%

“…Much progress has been made on this topic. [1,2] As the development of quantum information and quantum optics, it becomes common to use effective Hamiltonians in quantum entangled state preparation and quantum gate construction. [3][4][5][6][7][8][9] The method to calculate effective Hamiltonians presented by James and Jerke has been widely used in the fields of quantum information and quantum optics.…”

Section: Introductionmentioning

confidence: 99%

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A method to calculate effective Hamiltonians in quantum information*

Ren

Lin

2019

Chinese Phys. B

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Effective Hamiltonian method is widely used in quantum information. We introduce a method to calculate effective Hamiltonians and give two examples in quantum information to demonstrate the method. We also give a relation between the effective Hamiltonian in the Shrödinger picture and the corresponding effective Hamiltonian in the interaction picture. Finally, we present a relation between our effective Hamiltonian method and the James–Jerke method which is currently used by many authors to calculate effective Hamiltonians in quantum information science.

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“…The effective Hamiltonian H eff defined on the subspace PΩ , i.e., H eff = PH eff P, is an operator satisfying [1,2] H…”

Section: Effective Hamiltonian In the Shrödinger Picturementioning

confidence: 99%

Section: Effective Hamiltonian In the Shrödinger Picturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A method to calculate effective Hamiltonians in quantum information*

Ren

Lin

2019

Chinese Phys. B

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“…Here, H 0 includes the three transmons' energies, while V corresponds to their interaction. By detuning ω 2 away from ω 1 and ω 3 , the effective Hamiltonian of this system could be derived using the Bloch perturbation theory [20] (refer to Appendix A for details). Therefore, the connector Q 2 now behaves as a static quantum bridge to establish an edge between Q 1 and Q 3 with the effective coupling strength up to the fourth order as where…”

Section: A Detuned Qubits As Quantum Bridgementioning

confidence: 99%

Quantum walks of two identical particles in one-dimensional lattices

Zhang¹,

Wang²,

Wang³

2015

Journal of Shenzhen University Science and Engineering

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In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from simple qubit arrays, specifically grid lattices. The first approach utilizes a subset of qubits as tunable couplers, effectively yielding a range of non-trivial graph-based Hamiltonians. The second approach employs dynamic graph engineering by periodically activating and deactivating couplers, enabling the creation of effective quantum walks with longer-range couplings. Numerical simulations verify the effective dynamics of these approaches. In terms of these two approaches, we explore implementing various graphs, including cubes and fullerenes, etc, on twodimensional lattices. These techniques facilitate the realization of analog quantum simulation, particularly continuous-time quantum walks discussed in detail in this manuscript, for different computational tasks on superconducting quantum chips despite their inherent low dimensional simple architecture.

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“…The effective interaction is an extremely convenient concept to understand a quantum system in a large Hilbert space [1][2][3][4][5][6][7][8][9][10][11][12]. We first divide the Hilbert space into a model space (P-space) of a tractable size and its complement (Q-space).…”

Section: Introductionmentioning

confidence: 99%

Linked Diagram Theorem for Effective Interaction

Takayanagi

2018

Proceedings of the Ito International Research Center Symposium "Perspectives of the Physics of Nuclear Structure"

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We revisit the so-called linked diagram theorem for the effective interaction in open systems. First, we outline a novel proof of the linked diagram theorem, which is much simpler than the existing proof and leads naturally to a new form of the theorem. Second, we show that the linked diagram theorem in its known form gives many redundant diagrams which cancel among themselves in the exact perturbation expansion, while the new form is free of such redundant diagrams. At the end, we point out that all existing microscopic effective interactions suffer from such redundant contributions, and outline the way out of such difficulties.

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Effective interaction in unified perturbation theory

Cited by 6 publications

References 19 publications

A method to calculate effective Hamiltonians in quantum information*

A method to calculate effective Hamiltonians in quantum information*

Quantum walks of two identical particles in one-dimensional lattices

Linked Diagram Theorem for Effective Interaction

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