Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9912093 · Physical Review A

Optical holonomic quantum computer

Jiannis K. Pachos, Spiros Chountasis

Published Oct 19, 2000• 94 citations
arXivHTMLPDF

Abstract

In this paper the idea of holonomic quantum computation is realized within quantum optics. In a nonlinear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices, and interferometers provide the classical control parameter space where the adiabatic loops are performed. This results in logical gates acting on the states of the combined degenerate subspaces of the lasers, producing any one qubit rotations and interactions between any two qubits. Issues such as universality, complexity, scalability, and reversibility are addressed and several steps are taken towards the physical implementation of this model.

DOI
10.1103/physreva.62.052318

Related papers

Optical Holonomic Quantum Computation

Demosthenes Ellinas, Jiannis K. Pachos

Holonomic quantum computation (HQC) is materialized here with quantum optics components. Holonomies are the generalization of the Berry phases to unitary matrices. In a nonlinear Kerr medium the degenerate states of a laser beams are interpreted as qubits. Control manipulations with displacers, squeezers and two-mode interfering devices in a cyclic, adiabatic fashion produces holonomies. Hence, they are employed as logical gates for our HQC proposal. The effects of errors from imperfect control of classical parameters, the looping variation of which builds up holonomic gates, are also investigated. Additionally, the influence of quantum decoherence on holonomic tele-portation used as a computational primitive is studied, and particular features of control error resilience are discussed.

arXiv:quant-ph/0111075•Optical Fiber Communication Conference•Jan 1, 2001•0 citations

Single-loop multiple-pulse nonadiabatic holonomic quantum gates

Emmi Herterich, Erik Sjöqvist

Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [E. Sj\"oqvist et al., New J. Phys. 14, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a $\mathrm{\ensuremath{\Lambda}}$-type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level $\mathrm{\ensuremath{\Lambda}}$-coupling structure by utilizing carefully chosen laser pulses.

arXiv:1608.07418•Physical Review A•Nov 9, 2016•100 citations

Nonadiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces

Guofu Xu, Jiang Zhang, D. M. Tong +2 more

Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.

arXiv:1210.6782•Physical Review Letters•Oct 24, 2012•301 citations

QUANTUM HOLONOMIES FOR QUANTUM COMPUTING

Jiannis K. Pachos, Paolo Zanardi A

Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of Hamiltonians. The computational network of unitary quantum gates is realized by driving adiabatically the Hamiltonian parameters along loops in a control manifold. By properly designing such loops the nontrivial curvature of the underlying bundle geometry gives rise to unitary transformations i.e., holonomies that implement the desired unitary transformations. Conditions necessary for universal QC are stated in terms of the curvature associated to the non-abelian gauge potential (connection) over the control manifold. In view of their geometrical nature the holonomic gates are robust against several kind of perturbations and imperfections. This fact along with the adiabatic fashion in which gates are performed makes in principle HQC an appealing way towards universal fault-tolerant QC.

arXiv:quant-ph/0007110•International Journal of Modern Physics B•Apr 10, 2001•135 citations

Non-Abelian Berry connections for quantum computation

Jiannis K. Pachos, Paolo Zanardi A, Mario Rasetti

In the holonomic approach to quantum computation, information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-Abelian Berry connection and are obtained by driving the control parameters along adiabatic loops. We show how it is possible for a specific model to explicitly determine the loops generating any desired logical gate, thus producing a universal set of unitary transformations. In a multipartite system unitary transformations can be implemented efficiently by sequences of local holonomic gates. Moreover, a conceptual scheme for obtaining the required Hamiltonian family, based on frequently repeated pulses, is discussed, together with a possible process whereby the initial state can be prepared and the final one can be measured.

arXiv:quant-ph/9907103•Physical Review A•Dec 13, 1999•316 citations

Holonomic quantum gates: A semiconductor-based implementation

Paolo Solinas, Paolo Zanardi A, Nino Zanghı̀ +1 more

We propose an implementation of holonomic (geometrical) quantum gates by means of semiconductor nanostructures. Our quantum hardware consists of semiconductor macroatoms driven by sequences of ultrafast laser pulses (all optical control). Our logical bits are Coulomb-correlated electron-hole pairs (excitons) in a four-level scheme selectively addressed by laser pulses with different polarization. A universal set of single- and two-qubit gates is generated by adiabatic change of the Rabi frequencies of the lasers and by exploiting the dipole coupling between excitons

arXiv:quant-ph/0301090•Physical Review A•Jun 27, 2003•55 citations
In this paper the idea of holonomic quantum computation is realized within quantum optics. In a nonlinear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices, and interferometers provide the classical control parameter space where the adiabatic loops are performed. This results in logical gates acting on the states of the combined degenerate subspaces of the lasers, producing any one qubit rotations and interactions between any two qubits. Issues such as universality, complexity, scalability, and reversibility are addressed and several steps are taken towards the physical implementation of this model.
Holonomic quantum computation (HQC) is materialized here with quantum optics components. Holonomies are the generalization of the Berry phases to unitary matrices. In a nonlinear Kerr medium the degenerate states of a laser beams are interpreted as qubits. Control manipulations with displacers, squeezers and two-mode interfering devices in a cyclic, adiabatic fashion produces holonomies. Hence, they are employed as logical gates for our HQC proposal. The effects of errors from imperfect control of classical parameters, the looping variation of which builds up holonomic gates, are also investigated. Additionally, the influence of quantum decoherence on holonomic tele-portation used as a computational primitive is studied, and particular features of control error resilience are discussed.
Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [E. Sj\"oqvist et al., New J. Phys. 14, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a $\mathrm{\ensuremath{\Lambda}}$-type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level $\mathrm{\ensuremath{\Lambda}}$-coupling structure by utilizing carefully chosen laser pulses.
Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.
Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of Hamiltonians. The computational network of unitary quantum gates is realized by driving adiabatically the Hamiltonian parameters along loops in a control manifold. By properly designing such loops the nontrivial curvature of the underlying bundle geometry gives rise to unitary transformations i.e., holonomies that implement the desired unitary transformations. Conditions necessary for universal QC are stated in terms of the curvature associated to the non-abelian gauge potential (connection) over the control manifold. In view of their geometrical nature the holonomic gates are robust against several kind of perturbations and imperfections. This fact along with the adiabatic fashion in which gates are performed makes in principle HQC an appealing way towards universal fault-tolerant QC.
In the holonomic approach to quantum computation, information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-Abelian Berry connection and are obtained by driving the control parameters along adiabatic loops. We show how it is possible for a specific model to explicitly determine the loops generating any desired logical gate, thus producing a universal set of unitary transformations. In a multipartite system unitary transformations can be implemented efficiently by sequences of local holonomic gates. Moreover, a conceptual scheme for obtaining the required Hamiltonian family, based on frequently repeated pulses, is discussed, together with a possible process whereby the initial state can be prepared and the final one can be measured.
We propose an implementation of holonomic (geometrical) quantum gates by means of semiconductor nanostructures. Our quantum hardware consists of semiconductor macroatoms driven by sequences of ultrafast laser pulses (all optical control). Our logical bits are Coulomb-correlated electron-hole pairs (excitons) in a four-level scheme selectively addressed by laser pulses with different polarization. A universal set of single- and two-qubit gates is generated by adiabatic change of the Rabi frequencies of the lasers and by exploiting the dipole coupling between excitons