Geometric quantum computation

Ekert, Artur; Ericsson, Marie; Hayden, Patrick; Inamori, Hitoshi; Jones, Jonathan A.; Oi, Daniel K. L.; Vedral, Vlatko

doi:10.1080/09500340008232177

Cited by 243 publications

(182 citation statements)

References 22 publications

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“…This technique, as mentioned earlier, is readily implementable with current technology in quantum optics and has already been demonstrated by some of the authors using NMR [20]. It would be interesting to further analyse the robustness of geometric quantum computation to errors.…”

Section: (B) Design Of Geometric Phase Gatesmentioning

confidence: 99%

“…For the purposes of both experimentally detecting geometric phases and application in quantum computing, it is crucial to cancel the dynamic phases, as pioneered by Ekert et al [20]. Additionally, in order to perform conditional quantum gate operations using geometric phases only, it is necessary to find a way to eliminate the dynamic phase.…”

Section: (B) Design Of Geometric Phase Gatesmentioning

confidence: 99%

“…Recently, the study of geometric phases has generalized to the case of a pair of spins coupling with a magnetic field [14][15][16][17][18][19]. Notably, excellent pioneering discussions and a nuclear magnetic resonance (NMR) experimental demonstration have been made on twoqubit geometric phases, with one of the two qubits regarded as decoupled with the rotating field [20]. For example, Yi et al [14] studied the effect of inter-subsystem coupling on the adiabaticity of the composite system and that of its subsystems; Tong et al [15] calculated the geometric phases for states of two non-interacting spin-1 2 particles in a rotating magnetic field; Zhou & Zhang [18] examined the Berry phase of a bipartite system described by the antiferromagnetic Heisenberg XXZ model and driven by a one-site magnetic field; and Shi [21] examined the implementation of geometric quantum computation based on Zeeman coupling with a rotating magnetic field and isotropic Heisenberg interaction.…”

Section: Introductionmentioning

confidence: 99%

“…It is an approximation to the isotropic Heisenberg interaction in liquid NMR [28], and can also be realized in cold atoms in optical lattices [35], Josephson junction circuits [36] and so on. The Ising interaction was used in a pioneering construction of conditional phase gates based on geometric phases [20], which pointed out that a crucial issue is to cancel the dynamical phases. On the other hand, in the proposed schemes, the systems generally consist of two spins, one of which is coupled with a time-varying magnetic field [18].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Design of geometric phase gates and controlling the dynamic phase for a two-qubit Ising model in magnetic fields

Amniat-Talab

Jahromi

2013

Proc. R. Soc. A.

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ResearchCite this article: Amniat-Talab M, Rangani Jahromi H. We investigate how to obtain a non-trivial geometric phase gate for a two-qubit spin chain, with Ising interaction in different magnetic fields. Indeed, one of the spins is driven by a time-varying rotating magnetic field, and the other is coupled with a static magnetic field in the direction of the rotation axis. This is an interesting problem both for the purpose of measuring the geometric phases and in quantum computing applications. It is shown that the static magnetic field does not change the adiabatic states of the system, and it does not affect the geometric phases, whereas it may be used to control the dynamic phases. In addition, by considering the exact twospin adiabatic geometric phases, we find that a non-trivial two-spin unitary transformation, purely based on Berry phases, can be obtained by using two consecutive cycles with opposite directions of the magnetic fields, opposite signs of the interaction constant and the phase shift of the rotating magnetic field. In addition, in the non-adiabatic case, starting with a certain initial state, a cycle can be achieved and thus the Aharonov-Anandan phase is calculated.

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Section: (B) Design Of Geometric Phase Gatesmentioning

confidence: 99%

Section: (B) Design Of Geometric Phase Gatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design of geometric phase gates and controlling the dynamic phase for a two-qubit Ising model in magnetic fields

Amniat-Talab

Jahromi

2013

Proc. R. Soc. A.

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“…Therefore, the GP utilized Bloch vector manipulation was proposed as the low error rate manipulating method. However, no clear conclusion seems to have been obtained about the usefulness of the GP utilized operation [7][8][9][10]. Also, there seems to have been a few discussions which noise has an influence on the GP operation among the amplitude, the frequency, and the phase noises of the optical field.…”

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confidence: 98%

Simulation of laser manipulation of Bloch vector in adiabatic regime

Yano¹,

Satō²

2014

aap

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Simulations of the Bloch vector manipulation of two operations (one that utilizes the geometric phase (geometric operation) and the other that does not utilize the geometric phase (simple operation) in the adiabatic regime enabled us to study the tolerance of the geometric phase utilized operation against the laser noise. We simulated the Bloch vector manipulation by the laser field with the amplitude, the frequency, and the constant phase are proportionally, integrally, and derivatively controlled. The manipulation of the Bloch vector is a /2 rotation around 2-axis. There are few advantage by using the operation of the geometric phase over the simple operation. It has an advantage over only when the geometric phase operation is utilized such that the magnitude of the frequency of the noise is large, and that the noise correlation time is small. Keywords: Bloch Vector, geometric phase, PID control IntrtoductionThe realization of quantum computers will require long coherence time for materials and low error rate for control operations. [1-3] The low error rate for quantum computers requires a series of accurately controllable quantum operations. The field that manipulates a Bloch vector (a two-level atom) usually

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NMR Quantum Computation: A Critical Evaluation

Jones¹

2000

Fortschr. Phys.

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Liquid state nuclear magnetic resonance (NMR) techniques have produced some spectacular successes in the construction of small quantum computers, and NMR is currently by far the leading technology for quantum computation. There are, however, a number of significant problems with any attempt to scale up the technology to produce computers of any useful size. While it is probable that some of these will be successfully sidestepped during the next few years, it is unlikely that they will all be solved; thus current liquid state NMR techniques are unlikely to provide a viable technology for practical quantum computation.

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Geometric quantum computation

Cited by 243 publications

References 22 publications

Design of geometric phase gates and controlling the dynamic phase for a two-qubit Ising model in magnetic fields

Design of geometric phase gates and controlling the dynamic phase for a two-qubit Ising model in magnetic fields

Simulation of laser manipulation of Bloch vector in adiabatic regime

NMR Quantum Computation: A Critical Evaluation

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