**PLAYING WITH QUBITS**

**A Challenge to Quantum Physicists**

**Tom Leonard**

*Retired Professor of Statistics*

**Universities of Wisconsin-Madison and Edinburgh****CHAPTER 1: GETTING STARTED**

**1.1. My Grand Scheme (13**^{th}September 2019)
This
morning I gave a brief ministry to South Edinburgh Quakers on
Morningside Road
on
the other side of Edinburgh, to
a meeting in
the plush
basement of the more
basic
Open Door CafÃ©
which I
have attended for almost three years (though
I am not a Quaker myself and
struggle with the concept of a
Creator
God as
well as the
apparent irrationality of consensus
decision making).
I
was
responding
to three previous ministries during our hour of, otherwise
silent, contemplation. As I remember, I suddenly
leapt
to my feet with the help of my bright
blue walking
frame
Freddie, and, sounding
holier than thou,
blethered
something like:

*Before 2017, I spent a couple of years driving around the Scottish countryside with Thomas, enjoying all the sorts of views of coastlines and sunsets which you have described. Now I no longer have a car, and I plan to spend the remainder of my old age studying the mathematics of Quantum theory, so that I can escape from reality. My flatmate has just given me a beginner's book, and I intend to research and generalise its contents, in the hope of also discovering more about nature, genetics, evolution, and so on and so forth.*

Everybody
had a good, silent, chuckle at that!
As
with all such ministries, my
utterances were
interpreted by
the members present
as the spontaneous' Word of the Living God'. What I said, out of my
sub-conscious,
might sound over-ambitious, but I am proudly
Attention
Deficit and neurodiverse, a
highly
eccentric
septuagenarian, and
eclectic enough to firmly believe that I will be able to use my
old-fashioned
skills in probability and
frequentist
and Bayesian
statistics
to discover mathematical methodologies
which
turn out to be earth shattering generalisations of quantum mechanics.

The
book I am referring to
is
entitled

*Quantum Mechanics: The Theoretical Minimum*, and it was written in quite amiable style by Leonard Sussman and Art Friedman (2014). I will mainly focus on this book for a while, and check any extensions for originality later
Along
the way I will doubtlessly derive lots
of
things which are already well-known e.g. to the
courageous
quantum
Bayesians who
follow
in the foot steps of my sadly deceased friend Ed Jaynes [It
was Ed who
encouraged me to use the idea of

*maximum entropy*when representing incomplete information. These is one of the various themes discussed in my book*Bayesian Methods*(with John Hsu, 1999)]. At the very least I will learn a bit about the diverse approaches to quantum mechanics and provide my readership with a easy way of surveying them. Concepts like quantum cognition particularly appeal to me. Maybe this will produce ways of describing how we people on the spectrum of neurodiversity actually think.
What
are my skills in Mathematical Physics? Pretty slim! While I obtained
a grade one in Physics at G.C.E.
ordinary
level, and a grade B at advanced level, I scarcely remember any of
the Physics I studied at High School, and wouldn't even be able to
operate
a Bunsen burner or
describe a Wheatstone Bridge. However, my A grades at advanced level
in Pure and Applied Mathematics helped me obtain lowly

*Gamma*grades in my first and (repeated) second year Applied Maths courses at Imperial College London in 1967 and 1969. Fortunately I did better in Statistics, after a monumental disaster in 1968, and quickly progressed, after graduating with a very lucky first class honours degree, to obtain my M.Sc. and Ph.D. from University College London (supervised by Dennis V. Lindley) during 1971 and 1973.
The
title of my Ph.D. thesis was

*Bayesian Methods for the Simultaneous Estimation of Several Parameters*. I, for example, derived alternatives to the shrinkage estimators for multinomial probabilities which had been used by I.J. Good and Alan Turing, when developing cryptanalysis techniques to solve the Nazi Codes during the Second World War. My entertaining correspondences with Jack Good (who also published 25 papers entitled*Partly Baked Ideas*) helped to stimulate this and further research.
Maybe
I'll be able to use some of my ideas from my Ph.D, thesis and my
follow up articles to extend the
quantum mechanics literature, for example by developing further
probabilistic representations for a collection of entangled Qubits.
This might be used to
imply
spatial correlations between electrons in different states of spin.

I
must say that I'm extremely impressed by the
superb
theoretical level of
mathematical physics,
which epitomizes
the amazing heights of human accomplishment. I
have only come close to this level in three of my published papers,
by Leonard (1978), Leonard and Hsu (1992), and Chiu, Leonard and
Tsui(1996), and all of these utilised theory developed by the great
applied mathematician Richard E. Bellman.

*Richard E. Bellman (1920-84)*

I
have more recently been impressed to learn that Roger Penrose thinks
that an older Universe could have existed before the 'Big Bang', and
that it might be possible to use Quantum Theory to explain human
consciousness.

My
flat
is packed with books which my much more diversely
intellectual
flatmate orders on the Internet, and they come crashing through the
door several times a week. We've
recently discussed the amazing complexity of biochemistry, epigenetics,
the human
genome,
and
our biological, neurological and reproductive systems, and we'
ve
wondered how all of this has
been produced so
speedily by
our
evolutionary
process,
and
how
the geological systems, which affect the weather on the surface of
our planets and
thereby
create
a propensity for Life, could
have
existed
before intelligent
life forms came into being.

I
also live in hope that a joint 'afterlife' can be predicted in some
convincing scientific way.
So immense mysteries remain, and these certainly shouldn't
be blamed on some mythical
divinity
or other. How
far Science will progress before our planet is destroyed by the
return of the dinosaurs, or
whatever, is
another question.

In
the morning, I will return to first principles and examine the
properties of Qubits
in greater detail. Maybe they will ultimately explain everything!