Quantum Programming - Part 1

INTRO
In modern digital computers, these instructions resolve down to the manipulation of information represented by distinct binary states. These bits may be abstractly represented by various physical phenomena, such as by mechanical, optical, magnetic, or electric methods and the process by which this binary information is manipulated is also similarly versatile, with semiconductors being the most prolific medium for these machines. Fundamentally, a binary computer moves individual bits of data through a handful of logic gate types.

LIMITATIONS OF ALGORITHMS
In digital computing, binary information moves through a processing machine in discrete steps of time. This is known as an algorithm’s complexity. An example of such an algorithm would be one that determines if a number is odd or even. These are known as linear time algorithms and they execute at a rate that is directly correlated to the size of the algorithm’s input.

This characteristic becomes obvious within a basic addition algorithm. Because the number of steps, and inherently the execution time is directly determined by the size of the number inputs, the algorithm scales linearly in time. Constant and linear time algorithms generally scale to practical execution times in common use cases, however, one category of algorithm in particular suffers from the characteristic of quickly becoming impractical as it grows. These are known as an exponential time algorithm and they pose a huge problem for traditional computers as the execution time can quickly grow to an impractical level as input size increases.

QUBIT
Much like how digital systems use bits to express their fundamental unit of information, quantum computers use an analog called a qubit. Quantum computing by contrast, is probabilistic. It is the manipulation of these probabilities as they move between qubits that form the basis quantum computing. Qubits are physically represented by quantum phenomena.

HOW QUANTUM PROCESSING WORKS
A qubit possesses an inherent phase component, and with this characteristic of a wave, a qubit’s phase can interfere either constructively or destructively to modify its probability magnitudes within an interaction.

BLOCH SPHERE
A Bloch sphere visualizes a qubit’s magnitude and phase using a vector within a sphere. In this representation, the two, classical bit states are located at the top and bottom poles where the probabilities become a certainty, while the remaining surface represent probabilistic quantum states, with the equator being a pure qubit state where either classical bit state is possible. When a measurement is made on a qubit, it decoheres to one of the polar definitive state levels based on its probability magnitude.

PAULI GATES
Pauli gates rotate the vector that represents qubit’s probability magnitude and phase, 180 degrees around the respective x, y and z axes of its Bloch sphere. For the X and Y gate, this effectively inverts the probability magnitude of the qubit while the Z gate only inverts its phase component.

HADAMARD GATES
Some quantum gates have no classic digital analogs. The Hadamard gate, or H gate is one of the most important unary quantum gates, and it exhibits this quantum uniqueness. Take a qubit at state level 1 for example. If a measurement is made in between two H gates, the collapsing of the first H gate’s superposition would destroy this information, making the second H gate’s effect only applicable to the collapsed state of the measurement.

OTHER UNARY GATES
In addition to the Pauli gates and the Hadamard Gate, two other fundamental gates known as the S gate and T gate are common to most quantum computing models.

CONTROL GATES
Control gates trigger a correlated change to a target qubit when a state condition of the control qubit is met. A CNOT gate causes a state flip of the target qubit, much like a digital NOT gate, when the control qubit is at state level of 1. Because the control qubit is placed in a superposition by the H gate, the correlation created by entanglement through the CNOT gate, also places the target qubit into a superposition.

When the control or target qubit state is collapsed by measurement the other qubits' state is always guaranteed to be correlated by the CNOT operation. CNOT gates are used to create other composite control gates such as the CCNOT gate or Toffoli gate which requires two control qubits at a 1 state to invert the target qubit, the SWAP gate which swaps two qubit states, and the CZ gates which performs a phase flip. When combined with the fact that a qubit is continuous by nature and has infinite states, this quickly scales up to a magnitude of information processing that rapidly surpasses traditional computing.

SUPPORT NEW MIND ON PATREON

[chengong]

We desperately need more quantum computing videos that aren't just repeating "a q-bit can be both 1 and 0 at the same time".

[razerpine]

I can't wait to watch this and not understand anything

[lemonsavery]

You did an amazing job. I'm a software developer who double majored in Computer Science and Physics. Representing the qubit states as positions on the surface of a sphere did wonders for my ability to actually grasp the transformations being done upon them. This paired with working through and explaining the fundamental gates was an absolute banger of an educational service. Thank you.

I can't imagine having to learn this in a classroom as opposed to a video. I probably spent twice the video's length rewinding and repeating pieces of dialog until I could parse them out fully.

[teslainvestah]

6:15 - this measurement is supposed to be in core years, not years per core.
Core years means that your productivity is the product of the number of cores you have and the number of years you work. So 20 core years could mean 1 core working for 20 years, 2 cores working together for 10 years, or 20 cores working together for 1 year.
if more difficult problems were said to take more "years per core", that would mean that adding more cores would make the problem take longer to solve, which doesn't make sense for this problem, unless large clusters of CPUs unionize and go on strike.

[KevinNijmeijer]

This has been by far the best explanation of quantum computing I've seen on youtube. Both very accessible language but also deep information. Thank you! Can't wait for part 2!

[smguy]

This is the first in depth quantum computer video I’ve found in years! I was so interested in the subject, but couldn’t find a video explaining what those « quantum gates » were in detail. Really looking forward to watching part 2, keep it up!

[newchannelization]

I always love the voice of the speaker and the word choices too. It is like a silken blanket for my ears and mind

[chaser]

In fact, New Mind's approach is what I hope to be the new wave of edu YT, embracing the technical details with clarity and focus (and amazing visual support). I watched a lot vids about quantum computing and all I got was a little more than knowing it exists. But with NM I am left both enlightened and fascinated. So I encourage you: don't shy away from fairly mundane but poorly understood science.

[mohammedsafiahmed]

the 'quantum mechanics' part of this video starts at around 6:34. Prior to that, the video talks about computer architecture and algorithmic complexity. That in itself is the best explanation I've ever come across.

[youTapdat]

Is part 2 going to include how these quantum gates are created? I liked the visual representations of them in the video, but I struggle to understand how one goes about actually making one of these gates. Is similar to conventional logic where transistors are combined to create gates so the quantum equivalent would be using qubits to create quantum gates?

[emanuellucaci]

As a Mechatronics engineer I understood pretty much nothing and loved it at the same time.
It would be interesting to see how a computer like this would work step by step in a simple program.

[greggapowell]

This was the best single explanation of Quantum computing that I have ever encountered. Thanks.

[The_Study_Bug]

During this summer I participated in a quantum computing camp where we learned all of these concepts, and even got to code them on really quantum computers. Thank u for the video, it's really good for reviewing those concepts!

[Cris_the_coder]

This has been the best video I've seen on quantum computing. Respect. I love to learn.

[Ara_-gumk]

I really like the way you maintain standards of your videos. "Made for science not specifically for views". Being an undergrad I like your vids a lot.

[sntk]

Thanks for your clear and concise intro. I'm struck by both your grasp of what's essential and by your ability to cover a lot of territory without feeling hurried.

[manofcultura]

Can’t wait for quantum computing to be used for its real purpose. Programming actual AI responses and keeping track of complex relationship matrices in Visual Novels.

[CarelessForce]

Incredible video, love the practical emphasis but I'd also love to understand how these gates actually work, highly doubt there's a better explanation than what you could provide out there. Either way, looking forward to part 2 :)

[C-M-E]

Quantum computing is like asking me to build something then make an electrical diagram instead of a blueprint. I can think of some genius solution, put it in a mechanical drawing and build it, but ask me how the electrics work, I'll just wave my angle grinder at you and use my Jedi mind tricks. "This is not the right engineer you're looking for. Go two doors down, make a left and ask for Jeff. Move along."

[Shaunmcdonogh-shaunsurfing]

Part 2, Part 2, Part 2…I can’t wait. Really struggling to understand how a problem is encoded and then the solution decoded with quantum computers.