Quantum Computing through Comics

Is there a specific website that lets you use this data - other than Hackaday? I was thinking that scratch would, but it does not. also, I love how easy she makes it to understand.

Hi Kitty, I was reviewing class #5/ comic #23 (teleportation) and I can’t figure out why, when Alice entangles her new qubit |A'> to the previously entangled pair |A> |B>, she firstly applied the CNOT gate then secondly the Hadamard gate: that is the reverse order of gates to obtain entanglement, isn’t it? May you please elaborate on this step a bit more?

Great question, Davide. The best way to see it would be to go through the math at each step. What happens if you reverse CNOT and H? Would it work for some states?  |A'> in general is a superposition state of |0> and |1>. What happens if you apply a H gate? Another place to look is jumping to Session 13: Teleportation + codingRecording: https://youtu.be/nPJeI-J5934 and try coding the circuit with Q#.

My question is about the Basic Gates kata, Task 2.3. Two-qubit gate - 3. I can do it by thinking intuitively about what gates do, but I don't want to rely on intuitions. I'm looking for a way to do it using only matrices (maybe by writing down the matrix for the multi-qubit transformation that I want to achieve, and factoring that matrix into the matrices for basic gates). Is there a way to do something like this?

Hi Barry, for sure, you can express all quantum gates as matrices and qubits as vectors. For this question, you can write down the CNOT matrices and control and target qubits. 

I have no doubt that I can express a sequence of basic gate operations with matrices. My question is, are there mathematical tools to find a sequence of operations to go from an arbitrary start state to a desired target state. The basic gates H, CNOT, and Phase45 are universal -- so is there a method to determine which of them to apply?

Interesting thought. We can use the arbitrary general matrices that are described by each qubit's angles and then calculate what the angles are. Then we will find out which universal gates they are. We can calculate manually or express in a generic tool like Mathematica or MatLab. 2x2 matrix would be easy but as the matrices grow bigger, it can get messy.   

Hi, I'm currently in class 3 where you explain quantum entanglement. Say, there are 3 quantum particles in entanglement. Is this ( 1 ∕√2 | 000> + 1 /√2 | 111> ) the only possible configuration. I guess they can be entangled in any possible ways.

If yes, consider the state ( 1 ∕√2 | 010> + 1 ∕√2 | 011> ). Here if we observe the first two particles, the third particle's state cannot be determined. On the other hand, it is enough to observe only third particle. Is this valid entanglement?

Hi, thanks for asking. We can entangle them in many different ways. ( 1 ∕√2 | 000> + 1 /√2 | 111> ) is a maximally entangled state. The amplitude in front of each term can also be different. The example you gave does not have the three qubits entangled though. When we measure the third qubit (or any qubit), we still won't know what the other two qubits are. It is not different from writing 1 ∕√2 | 01>(|0>+|1>) then we can see the first two qubits are not correlated with the last qubit. Whereas in the case of ( 1 ∕√2 | 000> + 1 /√2 | 111> ) we cannot write them as separate qubits.

there is superposition like 1/2(|00⟩+𝑖|01⟩−|10⟩−𝑖|11⟩), how to understand when there is imaginary part? for |01⟩, i^2 = -1, does it have a negative probability to appear? or we only consider the real part, so the probability of |01⟩ and |11⟩ is 0?

Great that you are asking about this! Thank you. I have not mentioned this part in order to reduce the math for beginners. We cannot have negative probability. In fact, it should be the modulus | i |^2 that we calculate for probability, so the amplitude can be any number. If you express an imaginary number with magnitude and phase, you will see that it is the magnitude (always positive) squared that gives the probability. I can show this detail in one of the next classes. Glad we are ready. 

Can anyone help me with setting up the katas on my local computer? I'm working on Windows but I can also try using a Mac. I was able to open a notebook but I kept getting messages that the server couldn't obtain a lock (apparently from dotnet). Then I saw a note about uninstalling microsoft.quantum iqsharp and installing a particular version. When I try to reinstall iqsharp, I get an error message Failure to install and it gives four possible reasons.

Frankly, I'm lost because I'm not an experienced dotnet or jupyter user. If anyone has time for a brief online help session, that would be great.

Kitty,

your presentation at the Makers' Faire was excellent. And actually your second about fashion was interesting. 

I have a question, what is your recommendation for a beginning quantum mechanics text and a good math review text. I feel comfortable with restarting my undergrad calculus.

Thank you

Hi John, thank you for attending both sessions. 

For quantum mechanics, a widely used one is Introduction to Quantum Mechanics by David Griffith. 

A book on quantum computing that everyone uses is: Nelson and Chaung, Quantum Computation and Quantum Information – 10 th Anniversary Edition (you can find free PDFs to download). It's not the most easy to read though. I heard this one is pretty good: Quantum Computing: An Applied Approach, and Quantum Computing for Software Engineers.  

If you are interested in hardware (not specifically for quantum computers), I loved Introduction to Solid State Physics by Charles Kittel.

For math...maybe the standard high-school and undergrad textbooks from China? See if they have translations into English. I haven't used textbooks for math for a while. My undergrad was in England and can't remember what we used there. The lecture notes were pretty good. Are you in the UK? 

Thanks for the book recommendations.

I live in Delaware, recently retired from pharma industry, PhD in analytical chemistry. Now I can pursue my intellectual hobbies. I needed a refresher in linear algebra and matrices.

I looked at the chem quantum stuff. It is above my knowledge but it is the same old boring stuff with H atoms. As an analyst I am more interested in finding signals in the noise.

Thank you for your help

I was looking for a good book as a handbook for my Quantum Theory studies to review and discuss Lie groups, Clifford Algebras, SU(2), tensors, spintors, and just a bunch of fundamentals that are spotty in my past. I found this book where the author shares it freely on the Internet (I'm buying it from Amazon because I'm a nice guy).

If you're interested, the book is called "Quantum Theory, Groups and Representations: An Introduction" by Peter Woit.

He makes it publicly available a la his professor's site at Columbia:

http://www.math.columbia.edu/~woit/QM/fall-course.pdf

Maybe more technical than most would want, but for those looking to read deeper with a companion handbook for the formalism behind the physical application, this seems to cover a lot that I have been looking for in a bunch of other books.

Enjoy!

Aaron

Hey Kitty, I was reviewing past slides and I have a question about number 11 (about the weather).  I dont understand why there is a nagative amplituded in the quatum calculation. Is it a real example in that for these number this must be the correct calculation or is the negative case one of several possibilities. I wonder if the point of this slide is that there are solutions represented by both negative and positive terms and this just illustrates one example of what the solution could be.

Yes, the negative sign was put there on purpose to show what happens if the amplitude can be negative, since in the quantum case the amplitude can be positive or negative.

Thanks Barry and Robert. 

There is a set of gates that can be combined to produce any arbitrary amplitude of a qubit. With three qubits, you will apply those gates to them individually so you get the a,b,c,d,e,f,g,h, you want.  A way to visualize a qubit is the Bloch sphere - a 3D representation of a qubit vector. You can write any arbitrary gates into a gate (matrix) to move the vector along the Bloch sphere.  This will exactly be the topic for the coming week. Watch out for my comics on Wednesday and Sunday. 

(this is in response to the question Barry asked at the end of class and in the chat application)

Barry, I wonder if your question can be broken down into two parts. 1) given a 3qbit system with state amplitudes (a,b,c,d,e,f,g,h), what at the 3 qbit states that produce it and 2) how do you manipulate a qbit to have a particular state other that 0,1 and root(2)? 

Hi Marcelo, in the Files section above you will find  the first two video classes and their accompaning slides. Note that the video  URLs do not come in as links for me so I had copy and paste them.  The third meeting will be next Sunday.