22 research outputs found
Multi-Photon Multi-Channel Interferometry for Quantum Information Processing
This thesis reports advances in the theory of design, characterization and
simulation of multi-photon multi-channel interferometers. I advance the design
of interferometers through an algorithm to realize an arbitrary discrete
unitary transformation on the combined spatial and internal degrees of freedom
of light. This procedure effects an arbitrary
unitary matrix on the state of light in spatial and internal
modes.
I devise an accurate and precise procedure for characterizing any multi-port
linear optical interferometer using one- and two-photon interference. Accuracy
is achieved by estimating and correcting systematic errors that arise due to
spatiotemporal and polarization mode mismatch. Enhanced accuracy and precision
are attained by fitting experimental coincidence data to a curve simulated
using measured source spectra. The efficacy of our characterization procedure
is verified by numerical simulations.
I develop group-theoretic methods for the analysis and simulation of linear
interferometers. I devise a graph-theoretic algorithm to construct the boson
realizations of the canonical SU basis states, which reduce the canonical
subgroup chain, for arbitrary . The boson realizations are employed to
construct -functions, which are the matrix elements of arbitrary
irreducible representations, of SU in the canonical basis. I show that
immanants of principal submatrices of a unitary matrix are a sum of the
diagonal -functions of group element over
determined by the choice of submatrix and over the irrep determined
by the immanant under consideration. The algorithm for
-function computation and the results connecting these functions
with immanants open the possibility of group-theoretic analysis and simulation
of linear optics.Comment: PhD thesis submitted and defended successfully at the University of
Calgary. This thesis is based on articles arXiv:1403.3469, arXiv:1507.06274,
arXiv:1508.00283, arXiv:1508.06259 and arXiv:1511.01851 with co-authors. 145
pages, 31 figures, 11 algorithms and 4 tables. Comments are welcom
Universal quantum computation with optical four-component cat qubits
We propose a teleportation-based scheme to implement a universal set of
quantum gates with a four-component cat code, assisted by appropriate entangled
resource states and photon number resolving detection. The four-component cat
code features the ability to recover from single photon loss. Here, we propose
a concrete procedure to correct the single photon loss, including detecting the
single photon loss event and recovering the initial states. By concatenating
with standard qubit error correcting codes, we estimate the loss threshold for
fault-tolerant quantum computation and obtain a significant improvement over
the two-component cat code.Comment: 5+22 pages, 5 figures, comments are welcom