Understanding Quantum Computation Part 1
Information Processing
A physical system is in a way corresponding to a computation machine. The computer (physical system) takes and input (initial state), put it through an algorithm (laws of physics) and produces and output (final state). Where that initial and final states are useful, we can call it information.
The Experiment
In classical physics, the simplest information bearing system in the computer is the “bit”, which has 2 “degrees of freedom”, with the label 1 and 0 each. If we do an experiment on the bit, and get an ouput, we measure that output and say whether the the label was just 1 or 0. We can say that the “value of the bit” is an “observable” that can take the possible values of either 1 or 0. In practice we know that the bit is an abstract system of some electrical sub system and often the observable of that sub system is the voltage
across some component, where it can take the values, e.g.
volts.
In this case, we have identified 2 observables, namely the voltage
and the value
(of the bit).
can take on many labels between 0V and +5V, we say the set of labels that
can possibly be is the “spectrum of the observable
“. Similarly, the spectrum of
is the set
.
Quantum Multiverse Interpretation
In order to understand why we do the things we do in the rest of this journey, we need to first explain the multi-universe interpretation of quantum physics. (Bear in mind that this is not the only interpretation of the physical phenomenons that we experience, this is only one that we will use for now)
In reality, every object in our universe has counterparts in other universes. Every event that affects an object also affects its counter parts in all other universes. This phenomenon is known as “quantum interference”. Hence if we were to do an experiment on a system and then consider one observable of the system, I would get one label for each of the counterpart systems in all universes. Although any of these labels will be in the spectrum of the observable, it may not be the same throughout all the universes. Furthermore, each isolated quantum system has many observables that may interact with each other.
Specification of Quantum Systems
In order for meaningful information to be carried in the system, change or transformation must occur. It is however arbitary as to where to draw the line between when the system merely changed its configuration or has ceased to exist. For example we could still theorectically measure the angle between a pair of scissors even if it has been disassembled into parts, but if the metal has been melted down into a pool of liquid, then eventhough the atoms still exists, it will no longer be aproperiate to speak of angles. Therefore despite the transformations, there should be some characteristic of the system where it stays invariant throughout the transformation so that it can be said to continue to exist.
Hence forth, in order to fully specify a quantum system that is of interest to us, we need to define its invariant chracteristics, or “constitution”, namely
– static constitution (observable, spectrum of observable)
– dynamic constitution (law of transfomation of the observable)
– state (as in the Heisenberg state)
Static Constitution
The static constitution of a system refers to all the algebraic equations relating the observables of the system that remains invariant. For example, if a system
has
observables
,
…
, then if there is a function
of some
, say
that remains true at any time, then it follows that
is an algebra of the observables of the system and it is part of the static constitution of the system. For example, a triangle has 3 observables angle
,
and
and
remains true regardless of time transformation of the observables. Thus
is part of the static constitution of the triangle.
The Measurement Technique
To discover the algebra of the quantum observables, we need a few steps more, particularly to get around the problem of measuring the observable.
In the case of the classical computer, the observable, voltage, can take on labels or real numbers in the range, e.g.
, which is a continum of infinite real numbers. A commercial voltmeter we have today only gives an approximate of its true value down to a limited number of decimal places. In many cases such as this one, there are no measurement intruments that can literally measure it precisely, and hence prepare it to a desired value. To simplify the problem, we define another observable, the value of the bit,
and then map
to either 0 or 1. The function f in this case is defined as

Things are slightly trickier in quantum systems because we no longer deal with a single real number value
, but a range of real number values
across all universes i.e.
is now a set of real number values all of which are between 0 and 5. Correspondingly, the pick and use other functions to map our spectrum of the observable to a new spectrum.
, always mapping to the value 1
, always map to 0, and so on. Then if a function
which relates
,
, etc. say
is true regarding of time transformation, then
forms the static consitution of the quantum system. Theorectically, there could be many of such
.
Dynamic Constitution
The dynamic consitution would then be the deriavative of the
with respect to time, meaning that they are the equations the govern how the observables will transform with respect to time while keeping true to the relation
.
State or Heisenberg State
A special function that maps an observable to a real number known as its “Expectation Value” is used to specify its state. The expectation value is the average outcome of the quantum observable over a region of the multi-universe. Therefore this special function predicts what the value of the observable will be in each universe that the observable is measured. But then how can we literally traverse the universes and collect all the outcomes? In other words, where can we get this special function that will help we achieve this feat? It turns out that the “Hermitian Matrix”, its properties and its algebra offers such a capability if you interpret its operations in the following manner that we will be discussing.
Matrix Mechanics
The formulation of Hermitian Matrices was first proposed by Heisenberg, Max Born and Pascual Jordan and it was called Matrix Mechanics. If we consider each observable as a Hermitian Matrix, then the eigenvalues of the matrix constitute the spectrum of the observable representated by the hermitian matrix. Subsequently, we can define the expectation function in the using Hermitian Matrix formulation.
Simplest Quantum System
The simplest physical system is one that has only 2 degress of freedom. An observable with only 2 possible values in its spectrum is called a “boolean observable”. The simplest quantum physical system is therefore a system with all its non-trivial observables being boolean observables and we call it a “qubit”. i.e. if all these observables are represented by Hermitian Matrices, then each of these matrix must have 2 eigenvalues each and must be 2 by 2 matrices according to properties of Hermitian Matrix. In fact, the qubit will have as many boolean observables as the number of possible 2 by 2 matrices.
Sharp Observables
Consider a quantum system in a state defined as
![{expectation}(delim{[}{matrix{2}{2}{a b b^{*} c}}{]}) = a {expectation}(delim{[}{matrix{2}{2}{a b b^{*} c}}{]}) = a](http://www.jakesee.com/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_956.5_6f0001019ae88a7e75901f9c255e7772.png)
And 2 observables represented by the matrix
, eigenvalues = {-1, 1}
, eigenvalues = {-1, 1}
That is to say, the observables Z and X each has the spectrum of possible values -1 or 1. But when we apply the expectation function,
, while
. This means across the multiverse, the outcome of
is always -1 while the outcome of
is -1 in half the universes and 1 in the other half. We say that
is sharp in this case, while
is not sharp. Remember that
and
are observables of the same quantum system. That is to say although
turns out to be the same in the multiverse, the quantum system as a whole is different across the same region. In fact the “uncertainty principle” tells us that even if we try to make
sharp, some other observable will inevitably become unsharp.
C# static initialization sequence
Object orientated code could break down dangerously when using static class members in an unorthodox manner. Static initialization sequence goes like this:
1. Program starts, mark all classes that has static members as statically uninitialized.
2. Enters a scope where static calls are made.
3. Check, in order of execution sequence, get the first class in scope that is statically uninitialized.
5. Enter class scope, mark current scope as visited and Goto (7) if one of these are true:
- No static calls in current scope
- All classes have been marked as initialised
- All classes have been marked as visited.
6. Goto (3)
7. Initialize all class static members with values in sequence
8. Resume (2)
IEumerable cannot be used as a single object datasource
In the case of binding a an object and its property to, say, a control using the feature
control.DataBindings.Add("Text", myObject, "PropertyName");
will always work except when myObject is of the IEnumerable type. Once that happens, the data binding architecture will attempt to use the list of objects returned by the Enumerator for updating of UI and data source, which is not desirable for our purposes. For example, with
public class MyObject : Hashtable
{
public string PropertyName { get; set; }
}
the DataBinding will fail logically because Hashtable is in fact an IEnumerable in disguise! Unfortunately there seems to be no way of telling .NET that we want it to treat MyObject as a single object, not unless we wrap it in another BindingSource or IEnumerable
ObjectGridView – An easier way to use DataGridView
With a project that I am currently working on, I frequently need to display object information in a DataGridView. However, the values that needs to be displayed does not always directly belong to the bounded objects, instead, it is often a value related to the objects. Furthermore the DataGridView only accepts an IList of objects and it translates the properties of each object in the IList to the displayed values in the DataGridView. There are times when the IList readily available is not the list of objects we need to display information for, but rather another related or parent object.
In order to fill my needs, I ended up writing an extended version of the DataGridView, which is in some ways inspired by the amazing ObjectListView. The following code shows what is possible with ObjectGridView.
public class House
{
public string GetAddress();
}
public class Person
{
public string FirstName { get; set; }
public string Street { set; }
public Car Car { get; set; }
}
public class Car
{
public string Model { get; set; }
}
public static main()
{
var persons = new BindingList<Person>();
var houses = new Dictionary<Person, House>();
ObjectGridView ogv = new ObjectGridView();
ObjectGridViewTextBoxColumn colName, colModel, colAddress;
// ...
// regular DataGridView data association
colName.DataPropertyName = "FirstName";
// display a sub object of the bounded object
colModel.ValueGetter = delegate(object model)
{
Person p = (Person)model;
return p.Car.Model;
}
// display related information via a method call
colAddress.ValueGetter = delegate(object model)
{
return houses[(Person)model].GetAddress();
}
// customised value setting when cell is being edited
colAddress.ValueSetter = delegate(object model, object value)
{
Person p = (Person)model;
p.Street = Convert.ToString(value);
}
// regular DataGridView databinding for 2 way updating of UI and datasource
ogv.DataSource = new BindingSource(persons, null);
}
Justify Human Existence
I cannot justify the existence of the human race.
People say it is “immoral” to kill or take life away but we have been doing so for all ages since the dawn of time. Even the life of a plant, is still life.
If we should not kill, then what justifies its survival?
Is not killing with one’s own hands, only a way to avert the emotional distress generated in our mental state? Then how can not killing be moral if it is based on a selfish motive?
Some say we do not kill, because the victim deserves to live. Then justify it!
Less accidents and natural disasters, living things are most killed by other living things mainly as a resource. But the human species, being at the top of the food chain, are resources to no other.
As a matter of fact, the people are mostly killed because someone else finds us a thorn in the eye.
All humans do is consuming resources, consume and destroy other living things.
All other living things deserve to live because they serve as resources to other species in the ecology e.g. food chain, except the human species.
“Human resource” should really be a misnomer.
Big corporations like to speak of “human resource” and how to make use of it to create more financial success. “Human resource” is one of the greatest delusion and excuse for human survival and existence. As much as we like to believe that living humans (rather than dead ones – like other dead things we consume) are resources, we are merely consumers and we deplete resources at an increasingly higher rate than before.
Let us rationalize this “financial success”.
In a profiting trade or transaction, a resource is exchanged for money. The resource is ultimately consumed, but the money is not. The resource in its manufactured form can be food, a car, furniture or a house; but in their raw form, they all stem from the basic ingredients found on earth, metals, plants, animals, fuels etc. These resources are depleted with every exchange.
Big corporations use “human resource” in more and more “efficient” ways to generate money, but at the same time, deplete resources at alarming rates. The outcome is that now we have lots of money to share and distribute, but no resources.
Now, for goodness sake, how deluded humankind is to think that “human resource” is what we think it is? The only reasonable explanation I can think of is that humankind enjoys feeding their ego.
What good is financial success and loads of paper money when there are not enough resources to exchange for?
Environmentalists like to speak of a sustainable environment. If you study about sustainable farming, you will most definitely learn that sustainability is about control and balance of the farm ecology.
Superimpose the same story on the earth ecology, it is not difficult to see that the cause of imbalance is the human species, and the mode of control is to kill and/or stop procreating. But I know, it is counter intuitive to any animal instinct and almost impossible to implement.
But know this, we are supposed to be the beings with the highest order of sentience, capable of discerning the greater purpose for the benefit of all of livingkind.
The reason why we are designated to be at the top of the food chain is because; we will and must also know sacrifice and self destruction.
Suicide, contraceptive, abortion, cigarettes, drugs, disease, weapons, hate, war are all that we have learnt to do.
I think it was back in primary school I learnt in a science class that human cells are suicidal (ref. apoptosis and paraptosis). This counter-intuitive nature of a basic living unit etched in my head forever.
Indeed, even nature teaches as that in order to sustain live, we must also learn to suicide at the same time.
It can be seen that the principles of life sustainability is not much different between cells, organisms and animals.
Highlight Selected Row in DataGridView
To make the entire DataGridViewRow highlighted when the row selected is set to true,
set the DataGridView.SelectionMode to FullRowSelect.