Joshua Kettlewell | Projects

Joshua Kettlewell

Ph.D Student,
Singapore University
of Technology and Design

Coming soon!

Coming soon!

This page is still under construction

Ill be finished soon!

So this page is mostly of use to myself. It contains links to resources I've found useful in the past, links to selected papers that I have read, and more. It may be useful to other PhD students in quantum information, so they don't get cuaght out when their professor mentions that "This is trivial! Just use *insert topic here*".

General topics important in quantum information processing

  • Church turing thesis
  • any physically realisable process can be simulated on a turing machine
  • extented Church turing thesis
  • can do this effieiently. this would kill a lot of quantum supremecy.
  • Dicke states
  • Fock states
  • Coherent states
  • Continous variable states
  • Squeezed states
  • Cat states
  • Cooper pairs
  • Completxity classes
  • NP,P,Parity L, P#
  • GHZ states
  • gate teleportation
  • Haar randomness
  • CHSH violation
  • church of the larger hilbert space
  • Mach Zehnder interferometer
  • Michelson interferometer
  • linear optics - photon preserving - rekt and zillinger paper using discrete bult optics, single equation... nsted mark zhender interferometers -- or wave guides, evanesient coupling. -- time bin encoding -- effiecient m mod interferometer with polynomail run time and m^2 optical elements hybrid schemes barret and kok - relaxation of states and wave plates. can make bell states. use atom ensemble qubits as they have long decoherence time. no go theory for single rail optical to make universal
  • Fizeau interferometer
  • Fabry-Perot interferometer
  • Hanbury Brown and Twiss effect
  • Evanescent field
  • Rieman hypothesis

Topics relating the homomorphic computing

  • homomorphic gentry - latice problems
  • carlso no go theorem
  • random walks on encrypted data
  • Boson sampling
  • Here is the article by Aarson and Arkhipov https://arxiv.org/abs/1011.3245 that made this area famous. Boson sampling has been experimentally run .. verification of boson sampling: I believe that all of these experiments fail to satisfy the conditions derived by rahimi keshari et al in model for boson sampling that accounts for experimental parameters, which when they are not satisfied the problem demonstration the results may be sampled by a classical process. This model accounts for detector efficiency (including darkcounts), source efficiency and waveguid efficiency. The complaint about Boson samplong is that a state which has a positive P function its sample problem is neccasarily easy to simulate - as it may be viewed as a mixture of coherent states. Some also contend that boson sampling is useless - its not even a unifrom random number generator. random numbers are weighted by the perminence. this is not to do with additive error on amplitured - is see if the errors cause this to just become mix of coherent. scattershort boson smapling: similar to multiplexing but no feed forward. feedforward is replace with classical post processing verification of boson sampling maybe not provably. there are lots of descion problems that arnt in hard non universal model of LOQC no feedforward no memory no entangling no qubits comletely passive all fock state inputs just sample the output. at output we get superpositions of all possible outputs. This belongs to #P (which is probably more complex than NP). implies sampling is hard. can't be used to calculate matrix perminence. Sampling would need an exponential amount to find this. U is Haar random. this is sampling problem, not a decision problem. easy to convert between encodings

Topics relating to statistical distances

  • noisy unitaries and dephasing
  • An analysis of compeletely trace preserving maps on m2, ruska, szarek
  • helmhotz
  • Bhattacharyya distance
  • Kolmogorov
  • Renyi
  • KullbackÔÇôLeibler divergence
  • shannon entropy
  • sterling numbers of the second kind
  • choi matrix and relation to bell states

Important Quantum Algorithms and protocols

  • Quantum fourier transfrom
  • Amplitude amplicfication
  • duestch jonza
  • simons algorithm
  • shors algorithm
  • grovers algorithm
  • seth lloyd sparse matrix
http://www.nature.com/news/first-quantum-computers-need-smart-software-1.22590

explanations of eigenvalues and eigen vectors

  • Eigens - 3 brown 1 blue
  • Matrix perminence
  • goshgerin circle theorem
  • trace distance and fidelity
  • strong convexity of the trace
  • geometrically unifrom states
  • unambiguos dicrimination of states
  • chernoff bound
  • tysons bound
  • quek paper on geometrically unifrom states
  • quek paper on semidefifinite programming
  • parity idea

Information theory

  • holevos bound
  • To bound mutual information between alice and bob
  • different norms - one norm, two norm, infinity norm.

Quantum crypto protocols

  • BQC
  • universal bqc
  • verificiation of BQC
  • one time programs
  • quantum random access codes
  • oblivious transfer
  • bit commitment
  • no go proofs on both
  • yaos millionaire problem
  • qunatum money wiesner
  • arronson
  • broadbent one time memories

classical crypto protocols

  • chinese remaineder theorem
  • RSA
  • Diffe Helman
  • Snow 3G
  • lattice based cryptography

classical optimization methods

  • runge kutta
  • newton raphson
  • evlution

Neural networks

This guide will walk you through the setup for neural-style on Ubuntu to edit images.

Links from DSA

classical optimization methods

  • languages
  • C++
  • Matlab
    • Quack!
    • A MATLAB package for quantum circuit simulation. Capabilities include state preparation, unitary evolution and non-unitary processes, measurement, partial traces, entropy and purity calculation, and state readout. Package includes MATLAB source code, examples and documentation. http://www.peterrohde.org/media/software/
    • Quant inf
    • various functions, routines, and other bits of Matlab, Octave and Mathematica code organized by topic, that might save someone, somewhere, from re-inventing the wheel. http://www.dr-qubit.org/Matlab_code.html
    http://www.dr-qubit.org/Matlab_code.html
  • R
  • Mathematica
  • https://www.youtube.com/watch?v=Zqkn8CoJp9k
  • Maple
  • python
    • qutip
    • tweepy
  • cuda
  • VHDL
  • verilog
  • labview
  • chinese
  • indonesian
  • german

Encodings

  • dual rail spatial encodng
  • beam splitters for single qubit unitaries
  • polarisation
  • h v encoding, uses waveplates
  • time bin
  • easy to convert between encodings