What about software? where do you start thinking about that?

Writing software for a quantum computer

In my opinion is actually not very very different from how we write software for just a normal computer

and we think about

software in terms of being able to write down instructions

for the computer and the computer executing these instructions changing some internal state when I write instructions for

any type of computer whether it be like a modern MacBook Pro or an old PDP-11

In both cases in the end, we have an assembly code that gets executed that's changing the memory the disk

The registers in your CPU and so on and it's not different with a quantum computer

It's just like the question is what are we changing?

And how do we change them? We can really describe these things

in quite simple terms, if we were to do this in with sort of full textbook honesty, we would discuss things like

finite dimensional vector spaces and in Hilbert spaces and

Linear operators and unitary maps and all that stuff and all that stuff is very very important

If if you're actually sitting down writing a program but to get an understanding of it

I think we can do away with it. And actually just think about things in terms of simple probabilities. So the idea of a Qubit

So Qubit is a Bit in a quantom computer

Yep it is. Yeah. It's sort of the fundamental building block. It's like a it's like a bit and a regular computer

The way I think of it is it's a resource in the computer. It's a resource that you can use to perform a computation

So a qubit to me is anything it's sort of abstract. But anything that has two states of being and

Some possibility or probability of those states. So for instance we can think about

Photons and their polarization a photon can be sort of polarized left and right or it can be polarized up and down

But if we're not looking then maybe it's it's possibly in one or the other. Maybe it's 50%

moving and traversing left and right and 50%

Moving up and down. This is just for photons

Turns out there are lots and lots of different ways to construct qubits the qubits that that we work on in the so called field

Of superconducting quantum computation. We use a device called a superconducting charge qubit

It doesn't matter all the details, but it suffice to say that the two states there

Are is their charge or is there no charge in this circuit?

And then of course, we have the same thing. It could we could have a probability like maybe there's a 10% chance

there's a charge or maybe there's a

90% chance there's a charge. These are called superconducting charge

Qubits again, it sounds complicated, but the essence is the same two states

but maybe it's in one or the other the interesting thing though is

When we have multiple qubits, and this is really where the power of quantum computation happens

We can actually think of it sort of simply

Diagrammatically that if qubits if I just represent them sort of as a circle here, maybe we have three the idea

Is that these qubits can interact this guy can interact with this guy?

this guy can interact with this guy and these can interact with one another and every time we add a qubit if we were to

Add a circle here. Let's say we added this fourth qubit right here

We noticed that every single one of them can now interact with it. We have to draw lots of these lines

It turns out that a quantum computer can deal with these additions of qubits in a very efficient fashion

But like I said a qubit is something where it has two states

So each of these guys can be in two states with a particular probability

let's say the two states and our just 0 and 1, our qubit can be 0 or 1 or

Possibly something in between. So if I write down these qubits with the probability, let's say we have three qubits here

I'll call it Q0

Q1 and Q2 what we have is

That qubit 0 let's say it's this one right here 1 and 2, well qubit 0 could be in 0 or 1

so it has some probability of being in 0

Qubit 1 also has some probability of being in 0 and qubit 0 also has some probability being in 0

maybe that's a 10% chance

But now we have to painstakingly go through a write every one qubit 0 has a probability of being in the 0 state

Qubit 1 also 0 and qubit 2 and we can write down all these possibilities

Etc, etc until we get to the possibility that all of them are one and each of them has a probability. Maybe this is 5%

Maybe this is 7%, maybe this is like 35%, maybe there's a very high percentage chance that all of them are one

8% and so on

so every time we add a qubit the size of this table doubles the number of probability percentages doubles and it turns out that

these probabilities right here are ultimately what a quantum computer is computing with when we do an

Instruction on a quantum computer when we instruct it to do something in the end

it's always about changing these probabilities to favor some computation that we're trying to do

When we start up a quantum computer, when we flick the switch on

it'll start as 100% in this state and everything else will be 0%

We start off here, and we know that we start off here. It might be that when we apply a certain operation

So for example an operation as is the so called

superposition

Initialization or we call it Hadamard initialization

This is if we have any number of qubits, so starting off in zero, and maybe we want every probability to be equal

So if we want to start off here

We do something called Hadamard initialization where we do

a particular instruction called the Hadamard gate and what happens is this 100% now turns into

Let's say we just have one qubit

It would be 50% chance in the zero State and 50% chance in the one state if we had two qubits Hadamard

initialization would cause us to be 25% chance with both qubits being 0

25% chance

0 1

25% chance being 1 0

25% chance being 1 1 the point is is that this particular instructions one instruction on a quantum computer?

Allows us to change these probabilities in a way that we'd like and it might be useful for us to do something like this Hadamard

Initialization with all the probabilities being equal because then from here we could do some operation that affects all these qubits and affects all these

Probabilities sort of in the same way. But like I said, this is just one possible instruction

So there can be an infinite number just like a normal computer it's not that they're an infinite number of instructions

It's that they're an infinite of possible things you could do with the instructions

So one of the greatest discoveries was that we can arrange these probabilities to be in whatever way that we would like

Using five instructions total

there are sort of five different ways that we can

Permute these things and change them and there are this, one is called a measure instruction

measure instruction is pretty important because while we're talking about probabilities

we can't actually see these probabilities in the quantum computer

They're just in there

At some point. We do want to see are they zeros or ones? Like we need to answer that question

So the measure instruction will take any list of probabilities and turn it into

One of them will change to 100% So each of these is 25% chance. It'll pick one

Let's say it's this one right here and measure is gonna make this a hundred percent with the other ones being zero percent

That's one way of changing and then incidentally we also get to read out from the clunkier that it was a 1 0

That's how we get our answers. That's the only way we get an answer. In fact from the quantum computer

The rest of them are just purely ways of changing these probabilities. There are lots of different ways

You can have instruction just like norm...

Regular computers every single computer that's ever been built or every single CPU that's erver been built always has a different instruction set

One possible instruction set is the following we have this Hadamard

Is that named after someone?

Yes, it's named after I think he was a mathematician

He worked on a variety of mathematical subjects and there's a matrix that's actually one divided by square root of 2

1 1 1 negative 1 which is a so-called Hadamard matrix

Incidentally this is also used to represent how these probabilities change so Hadamard is one instruction

There's another instruction called Phase, again It just has the effect of changing probabilities around in a particular way

There's another instruction called the T gate not very

Creatively named there's another instruction called the CNOT gate and what's special

about the CNOT gate is that all of these right here act on one qubit

We say I want to do a measure on qubit 2 or i want to do a T gate on qubit 0

It sort of affects only one qubit. It'll affect a lot of probabilities because even though we're operating on one qubit here

it accounts for this entire column so it actually changes all the probabilities

CNOT is special because we get to choose two qubits

This is how we get this

interaction between them so CNOT you can say I want to do this on qubit 0 and qubit 2

For instance and this itself is an instruction in a sort of quantum assembly code

Are these instructions a bit like gates?

Yea, so they are like gates but there's an interesting reversal and for example a NAND gate is something like this where data is coming

Into the gate and data comes out of the gate

what's interesting about these gates and quantum computation is sort of the opposite you have data that's sitting there all these probabilities and

You like apply the gate to the Machine and all the probabilities change. So you're not sending data into the gate

You're not putting this gate on the chip like a NAND gate for instance

Is a gate that you would actually etch into a chip

Here it's an instruction that you apply to the computer and it changes these probabilities, but nonetheless

They're both different operations that you do on data

And how does what you do is code get changed into these operations of instructions

Yeah, so like with normal computers you can write these instructions out as assembly code. In fact one example is

Say I want the following probabilities

I have 0 0 0 1 1 0 1 1 I want this I want it to be 50% chance to be 0 0 or

50% chance to be 1 1 this is called a bell state with a bell state. It's interesting because

Theoretically let's suppose I have a qubit. Let's say close I could hold a qubit and

Let's say I gave you a qubit

it's 50% chance 0 0 or 50% chance 1 1

so even if we travelled halfway across the world and I decided to measure my qubit with the measure

Instruction and I determine that to 0

Then I know for certain that you must be a 0 because there's a zero percent chance that were different, but somehow we determine this

It's a 50% chance. It's not that it is already chosen literally is 50% chance. You don't know which one it is

So we can write a program to construct a bell state

I won't explain exactly why it works this way

But you do a Hadamard on my qubit, qubit 0 we do a CNOT on

My qubit and your qubit and we're done. This is a quantum program. You can write this out.

Now there are higher levels of quantum programming where we don't want to restrict ourselves these instructions

Maybe I want to more directly Express the probabilities and how I want them to change

They all have to add up to 1 of course. I mean, we have a certain percentage chance

It has to be 100% in the end, but maybe I want to shift the probabilities around in a particular way

But not in any of the ways that's in our gate set

I can write that down that can use something called a quantum

compiler a piece of software that that converts what I want into these native instructions that gives me the

next level of abstraction in the code

we can go all the way up to using a full-blown library for writing this stuff one library that

We've constructed is something called "PyQuil"

Which allows us to actually write Python code to express quantum computations in Quil is actually this instruction set here

Quil stands for quantum instruction language, which lets you write down this assembly code

But hey, who came up with this things?

is this a commercial thing or is this like...

Yeah, yeah so quil was originally this particular type of instruction set

Was a paper that I actually wrote a while ago

The idea of gates and everything was very well known for many decades previous to that

So this is a particular encoding of gates as instructions PyQuil is a library that's open source, it's free

There are no restrictions really on using it to construct these programs, but it does allow you to actually connect up to

Rigetti Computing's real quantum computers if you if you so pleased to actually run your programs

But if you don't want to connect up to the quantum computers and you just want to simulate on your own laptop this can connect

Up to a an open source

Simulation tool that we have if you just kind of want to see how these probabilities change and so on

Not quite you still have to express a quantum computation so a quantum computer doesn't print things out it's

it's manipulating these probabilities so at some point you start to express things as

Quantum instructions, so definitely if you wanted to make a bell state writing the bell state program you could do that

But could you write "Hello world?" No, and this goes back to the fact that the quantum computer is a coprocessor

Just like saying you don't write 'Hello World' on your GPU generally

You don't express any particular computation and you also don't compile Python Into code on your GPU

You write special code within Python that gets run on your GPU and it's the same thing with quantum computing

and i know you said there are certain stabilty issues do you get hard answers outta this?

So, yeah, so when an answer comes out when you measure you do get definite answer out, however

since there's noise what we have to do is write our program get an answer out and store that and actually

Rerun it multiple times

We have to gather statistics about the answer and it turns out that the more you do this the more