Highly-Degenerate Photonic Waveguide Structures for Holonomic Computation
arXiv:2003.03090 · doi:10.1103/PhysRevA.101.062314
Abstract
We investigate an all-out optical setup allowing for generation of non-Abelian geometric phases on its large degenerate eigenspaces. The proposal has the form of an M -pod system and can be implemented in terms of integrated photonic waveguide structures. We show that by injecting a larger number of photons into the optical setup, the degeneracy of eigenspaces scales rapidly. After studying the spectral properties of our system for the general case, we show how arbitrary U(4) transformations can be generated on the dark subspace of an optical tripod filled with two photons. Moreover, a degeneracy in the bright subspaces of the system, absent in any atomic analogue, allows for the generation of universal single-qubit manipulations. Finally, we address the complexity issue of holonomic computation. Particularly, we show how two-qubit and three-qubit states can be implemented on a photonic tripod, where a natural multi-partite structure is inherited from the spatial mode structure of the waveguides.
11 pages, 3 figures
References in corpus (36)
- Fault-tolerant quantum computation by anyons
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Experimental realisation of the topological Haldane model
- Artificial gauge potentials for neutral atoms
- Optical Quantum Computing
- Universal Linear Optics
- Two-Bit Gates are Universal for Quantum Computation
- Holonomic Quantum Computation
- Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
- Geometric Manipulation of Trapped Ions for Quantum Computation
- Quantum-Information Processing with Semiconductor Macroatoms
- Non-adiabatic holonomic quantum computation
- Experimental Realization of Non-Abelian Geometric Gates
- Integrated photonic quantum gates for polarization qubits
- Chip-based photon quantum state sources using nonlinear optics
- Quantum tensor product structures are observable-induced
- Non-Abelian Berry connections for quantum computation
- Virtual Quantum Subsystems
- A Unified and Generalized Approach to Quantum Error Correction
- Quantum Error Correction
- Experimental observation of Aharonov-Bohm cages in photonic lattices
- A Short Introduction to Topological Quantum Computation
- PPLN Waveguide for Quantum Communication
- Holonomic quantum computation with neutral atoms
- Observation of Light Guiding by Artificial Gauge Fields
- Optical Holonomic Quantum Computer
- Measurement-induced Nonlinearity in Linear Optics
- Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace
- Non-Abelian braiding of light
- Fault-tolerant holonomic quantum computation
- Introduction to Quantum Computation
- Topological Protection and Quantum Noiseless Subsystems
- Artificial gauge fields with ultracold atoms
- Optimal design strategy for non-Abelian geometric phases using Abelian gauge fields based on quantum metric
- Holonomic quantum computation in subsystems
- Scheme for fault-tolerant holonomic computation on stabilizer codes
Cited by in corpus (7)
- Non-abelian Thouless pumping in a photonic lattice
- Nonadiabatic Holonomic Quantum Computation and Its Optimal Control
- Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing
- Symmetry-protected non-Abelian geometric phases in optical waveguides with nonorthogonal modes
- Deterministic photonic entanglement arising from non-Abelian quantum holonomy
- Particle-Number Threshold for Non-Abelian Geometric Phases
- Transmission and generation of arbitrary W states via an optomechanical interface