| 1. |
- André, Tomas, et al.
(författare)
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Dark path holonomic qudit computation
- 2022
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - : American Physical Society. - 1050-2947 .- 1094-1622. ; 106:6
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Tidskriftsartikel (refereegranskat)abstract
- Nonadiabatic holonomic quantum computation is a method used to implement high-speed quantum gates with non-Abelian geometric phases associated with paths in state space. Due to their noise tolerance, these phases can be used to construct error resilient quantum gates. We extend the holonomic dark path qubit scheme in [M.-Z. Ai et al., Fundam. Res. 2, 661 (2022)] to qudits. Specifically, we demonstrate one- and two-qudit universality by using the dark path technique. Explicit qutrit (d = 3) gates are demonstrated and the scaling of the number of loops with the dimension d is addressed. This scaling is linear and we show how any diagonal qudit gate can be implemented efficiently in any dimension.
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| 2. |
- Azimi Mousolou, Vahid, et al.
(författare)
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Non-Abelian geometric phases in a system of coupled quantum bits
- 2014
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 89:2, s. 022117-
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Tidskriftsartikel (refereegranskat)abstract
- A common strategy to measure the Abelian geometric phase for a qubit is to let it evolve along an `orange slice' shaped path connecting two antipodal points on the Bloch sphere by two different semi-great circles. Since the dynamical phases vanish for such paths, this allows for direct interference measurement of the geometric phase. Here, we generalize the orange slice setting to the non-Abelian case. The proposed method to measure the non-Abelian geometric phase can be implemented in a cyclic chain of four qubits with controllable nearest-neighbor interactions.
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| 3. |
- Azimi Mousolou, Vahid, et al.
(författare)
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Non-Abelian quantum holonomy of hydrogen-like atoms
- 2011
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 84:3
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Tidskriftsartikel (refereegranskat)abstract
- We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogen-like atoms, where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian, while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge structure of the subsystems. We analyze the phase of the Wilson loop variable associated with the Uhlmann holonomy, and find a relation between the phase of the whole system with corresponding marginal phases. Based on the result for the model system we provide evidence that the phase of the Wilson loop variable and the mixed-state geometric phase [Phys. Rev. Lett. 85, 2845 (2000)] are in general inequivalent.
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| 4. |
- Azimi Mousolou, Vahid, et al.
(författare)
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Unifying Geometric Entanglement and Geometric Phase in a Quantum Phase Transition
- 2013
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 88:1, s. 012310-
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Tidskriftsartikel (refereegranskat)abstract
- Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are respectively the real and imaginary parts of a complex-valued geometric entanglement, which can be investigated in typical quantum interferometry experiments. We argue that the singular behavior of the complex-value geometric entanglement at a quantum critical point is a characteristic of any quantum phase transition, by showing that the underlying mechanism is the occurrence of level crossings associated with the underlying Hamiltonian.
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| 5. |
- Ericsson, Marie, et al.
(författare)
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Comment on `Detecting non-Abelian geometric phases with three-level Λ systems'
- 2013
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 87:3, s. 036101-
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Tidskriftsartikel (refereegranskat)abstract
- In their recent paper, Yan-Xiong Du {\it et al.} [Phys. Rev. A {\bf 84}, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned $\Lambda$ three-level system. They further propose a test to detect the non-commutative feature of this geometric phase. On the contrary, we show that the non-Abelian geometric phase picked up by the energy eigenstates of a $\Lambda$ system is trivial in the adiabatic approximation, while, in the exact treatment of the time evolution, this phase is very small and cannot be separated from the non-Abelian dynamical phase acquired along the path in parameter space.
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| 6. |
- Ericsson, Marie, et al.
(författare)
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Generalization of the geometric phase to completely positive maps
- 2003
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 67:2, s. 020101(R)-
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Tidskriftsartikel (refereegranskat)abstract
- We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference effect is embodied in a set of interference patterns defined by flipping the environment state in one of the two paths. We show for the qubit that this structure gives rise to interesting additional information about the geometry of the evolution defined by the CP map.
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| 7. |
- Ericsson, Marie, et al.
(författare)
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Towards a quantum Hall effect for atoms using electric fields
- 2002
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 65:1, s. 013607-
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Tidskriftsartikel (refereegranskat)abstract
- An atomic analogue of Landau quantization based on the Aharonov-Casher (AC) interaction is developed. The effect provides a first step towards an atomic quantum Hall system using electric fields, which may be realized in a Bose-Einstein condensate.
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| 8. |
- Eriksson, Anders, et al.
(författare)
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Monopole Field Textures in Interacting Spin Systems
- 2020
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - : American Physical Society (APS). - 1050-2947 .- 1094-1622. ; 101:5
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Tidskriftsartikel (refereegranskat)abstract
- Magnetic monopoles can appear as emergent structures in a wide range of physical settings, ranging from spin ice to Weyl points in semimetals. Here, a distribution of synthetic (Berry) monopoles in parameter space of a slowly changing external magnetic field is demonstrated in a system of interacting spin-1/2 particles with broken spherical symmetry. These monopoles can be found at points where the external field is nonzero. The spin-spin interaction provides a mechanism for splitting the synthetic local magnetic charges until their magnitude reach the smallest allowed value 1/2. For certain states, a nonzero net charge can be created in an arbitrarily large finite region of parameter space. The monopole field textures contain non-monopolar contributions in the presence of spin-spin interaction.
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| 9. |
- Filipp, Stefan, et al.
(författare)
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Off-diagonal generalization of the mixed-state geometric phase
- 2003
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 68:4, s. 042112-
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Tidskriftsartikel (refereegranskat)abstract
- The concept of off-diagonal geometric phases for mixed quantal states in unitary evolution is developed. We show that these phases arise from three basic ideas: (1) fulfillment of quantum parallel transport of a complete basis, (2) a concept of mixed state orthogonality adapted to unitary evolution, and (3) a normalization condition. We provide a method for computing the off-diagonal mixed state phases to any order for unitarities that divide the parallel transported basis of Hilbert space into two parts: one part where each basis vector undergoes cyclic evolution and one part where all basis vectors are permuted among each other. We also demonstrate a purification based experimental procedure for the two lowest order mixed state phases and consider a physical scenario for a full characterization of the qubit mixed state geometric phases in terms of polarization-entangled photon pairs. An alternative second order off-diagonal mixed state geometric phase, which can be tested in single-particle experiments, is proposed.
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| 10. |
- Friedenauer, Axel, et al.
(författare)
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Noncyclic geometric quantum computation
- 2003
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 67:2, s. 024303-
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Tidskriftsartikel (refereegranskat)abstract
- Geometric quantum computation is extended to the noncyclic case. Adiabatic NMR implementations of geometric phase shift gates at any precession angle and their concomitant fault tolerance with respect to the amplitude of the oscillating field are analysed. Nonadiabatic one-qubit geometric quantum computation is considered from the noncyclic perspective, with particular emphasis on errors in precession angles.
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