Quasienergy Anholonomy and its Application to Adiabatic Quantum State Manipulation

Tanaka, Atushi; Miyamoto, Manabu

doi:10.1103/physrevlett.98.160407

Cited by 31 publications

(51 citation statements)

References 23 publications

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“…3, in terms of the averaged wavenumberk (see, (2)). The parametric evolution of the eigenenergy that connects |11 and |22 has a level crossing with two eigenenergies during C II .…”

Section: "Tunneling" and Direct Contributions Of The Interaction In Nmentioning

confidence: 99%

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Adiabatic cycles in quantum systems with contact interactions

Tanaka¹,

Cheon²

2017

Nanosystems: Phys. Chem. Math.

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An adiabatic cycle involving the δ-function potential is shown to excite Bose particles confined in a one-dimensional box. We consider a cycle, during which a wall described by a δ potential is applied and its strength and position are slowly varied. When the system is initially prepared in the equilibrium ground state, the adiabatic cycle brings all bosons into the first excited one-particle state, leaving the system in a nonequilibrium state. The absorbed energy during the cycle is proportional to the number of bosons.

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“…3, in terms of the averaged wavenumberk (see, (2)). The parametric evolution of the eigenenergy that connects |11 and |22 has a level crossing with two eigenenergies during C II .…”

Section: "Tunneling" and Direct Contributions Of The Interaction In Nmentioning

confidence: 99%

“…In general, an "exotic" quantum holonomy [2,3], in which one eigenstate turns into another eigenstate belonging to the same Hamiltonian, can be observed after the cyclic variation of the system parameters. In this paper, we examine an adiabatic cycle that excites a system consisting of Bose particles confined in a one-dimensional box.…”

Section: Introductionmentioning

confidence: 99%

Adiabatic cycles in quantum systems with contact interactions

Tanaka¹,

Cheon²

2017

Nanosystems: Phys. Chem. Math.

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“…Such phenomena are called eigenvalue and eigenspace anholonomies, or exotic quantum holonomy [2,3]. Its applications to adiabatic manipulation of quantum states, including adiabatic quantum computation [4], were also examined recently [5,6]. The eigenspace anholonomy was also examined through the adiabatic Floquet theory [7].…”

Section: Introductionmentioning

confidence: 99%

Quantum anholonomies in time-dependent Aharonov-Bohm rings

Tanaka

Cheon

2010

Phys. Rev. A

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Anholonomies in eigenstates are studied through time-dependent variations of a magnetic flux in an Aharonov-Bohm ring. The anholonomies in the eigenenergy and the expectation values of eigenstates are shown to persist beyond the adiabatic regime. The choice of the gauge of the magnetic flux is shown to be crucial to clarify the relationship of these anholonomies to the eigenspace anholonomy, which is described by a non-Abelian connection in the adiabatic limit.

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“…This adiabatic scheme, which will be called anholonomic adi-abatic quantum computation (AAQC), composes an interesting and nontrivial family of DAQC. In particular, AAQC does not approximate SAQC, and hence the question whether AAQC is equivalent to the standard quantum computation naturally arises [13].…”

Section: Introductionmentioning

confidence: 99%

“…A family of DAQC that essentially relies on the adiabatic passage along a quasienergy is recently proposed by one of the authors [13]. Here the adiabatic passage is composed with a help of Cheon's eigenvalue anholonomy [13,14,15,16], which enables us to design adiabatic passages that visit all eigenstates of a given unperturbed Hamiltonian. This adiabatic scheme, which will be called anholonomic adi-abatic quantum computation (AAQC), composes an interesting and nontrivial family of DAQC.…”

Section: Introductionmentioning

confidence: 99%

Adiabatic quantum computation along quasienergies

Tanaka

Nemoto

2010

Phys. Rev. A

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The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of parameter-dependent Hamiltonians. By contrast, discrete adiabatic computation utilizes adiabatic passage along the quasienergies of parameter-dependent unitary operators. For example, such computation can be realized by a concatenation of parameterized quantum circuits, with an adiabatic though inevitably discrete change of the parameter. A design principle of adiabatic passage along quasienergy is recently proposed: Cheon's quasienergy and eigenspace anholonomies on unitary operators is available to realize anholonomic adiabatic algorithms [Tanaka and Miyamoto, Phys. Rev. Lett. 98, 160407 (2007)], which compose a nontrivial family of discrete adiabatic algorithms. It is straightforward to port a standard adiabatic algorithm to an anholonomic adiabatic one, except an introduction of a parameter |v , which is available to adjust the gaps of the quasienergies to control the running time steps. In Grover's database search problem, the costs to prepare |v for the qualitatively different, i.e., power or exponential, running time steps are shown to be qualitatively different. Curiously, in establishing the equivalence between the standard quantum computation based on the circuit model and the anholonomic adiabatic quantum computation model, it is shown that the cost for |v to enlarge the gaps of the eigenvalue is qualitatively negligible.

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Quasienergy Anholonomy and its Application to Adiabatic Quantum State Manipulation

Cited by 31 publications

References 23 publications

Adiabatic cycles in quantum systems with contact interactions

Adiabatic cycles in quantum systems with contact interactions

Quantum anholonomies in time-dependent Aharonov-Bohm rings

Adiabatic quantum computation along quasienergies

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