.. title: Quantum Class 2, Thurs 2022-09-01 .. slug: class02 .. date: 2022-09-01 .. tags: class .. category: .. link: .. description: .. type: text .. has_math: true .. sectnum:: .. contents:: Table of contents .. Class 1 ======= I edited the blog to show what we actually did. Homework 2 ========== is online, due Tues. Theory vs Experiment ==================== #. Sometimes the theoreticians posit something new, then the experimentalists try to build it. a. atom bomb #. classical computer #. quantum computer #. Other times the experimentalists (aka hackers) build something new. a. bridges #. airplanes #. medieval cathedrals #. steam engines #. calculus #. Then those may become so successful that bigger and bigger ones are built until those collapse / crash / fall down / blow up / have paradoxes. #. Then the theoreticians have to come in and clean up the mess to allow more progress. #. They may look for unifying themes in apparently separate problems. #. Group theory in abstract (modern) algebra happened that way. #. Anything discovered about groups was then valid in all the applied areas. #. All theories have limits that may or may not be relevant. #. Paradoxes expose limits. "All triangles are isosceles" error exposes something not covered by Euclid's axioms. #. Physics Nobels tend to go to theoretical explanations of surprising experiments. Although, there is nothing in common among all Nobel winners, not even intelligence (according to Enrico Fermi). #. Very rarely, experimentalists do something that the theoreticians had proven was impossible. a. Galileo seeing sunspots. #. Marconi radioing across Atlantic. #. Michaelson-Morley. (However several other contemporaneous inexplicable observations all proved to have classical explanations.) and something new is discovered / invented. Unfortunately the crackpots then seize on these rare examples... Video ===== #. Quantum Computing in Under 11 Minutes daytonellwanger https://www.youtube.com/watch?v=TAzZKAdX2Tw 10:56 more technical Intro to quantum computing ========================== #. This is from a. *Yanofsky and Mannucci, Quantum Computing for Computer Scientists*, #. *Hidary, 2nd edition*, and #. my opinions. #. Isomorphism between geometry and algebra. Work in whichever domain is easier. Results carry over. a. 2D: x+ij -> (x,y) #. 3D: quaternions. 3D rotations are not commutative, and so quaternions are not. There's a memorial on a bridge in Trinity College Dublin where William Rowan Hamilton thought of them. Quaternions are equivalent to 3D vector algebra. #. qbits - Bloch sphere. #. qbits vs qubits? Above my pay grade. #. Evidence for quanta: a. 1905 photo-electric effect explanation. Einstein Nobel. #. Ultraviolet catastrophe. #. 1922 Stern Gerlach experiment. Very influential. https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment #. Hidary 1.1 Quantum Computer Definition, p 3 A quantum computer is a device that leverages specific properties de- scribed by quantum mechanics to perform computation. #. State vector a. completely describes a system #. cannot be directly observed, only measured... #. which changes it. #. Hidary 1.1 Superposition and Entanglement, p 4 2 big properties. #. bra-ket notation. #. can rewrite a state vector in a different basis #. Hidary 1.3 The Superposition Principle, p 4 a. "The linear combination of two or more state vectors is another state vector in the same Hilbert space and describes another state of the system." #. Generally false in classical domain. Particle can go thru only 1 of 2 slits. However vibration states in a string add. #. Hidary entanglement p 7 description is confusing, defer till later. #. Yanovsky p 40, vector space review a. One qbit is a simple vector space. #. Can change basis, e.g., to Hadamard basis. p 51. #. Eigenvalues and eigenvectors, p 60 #. Hermetian matrices, p 63 #. Classical 2 slit experiment, p 86. Probabilities add. #. Quantum 2 slit experiment, p 93. Complex waves add. Probabilities might reduce. Quantum properties - Entanglement ================================= #. Crazy counterintuitive idea that's the basis for quantum speedup. #. Classical metaphor for entanglement: a. Start with a piece of paper. #. Tear it into two halves. #. Put each half into an envelope, seal them, and mix them up, so that you can't tell which half is in which envelope. #. Address and mail one envelope to a friend in Australia, and the other to a friend in Greenland. #. When the Australian opens his envelope, he knows what the Greenlander will find in his. #. However that doesn't let the Australian send any info to the Greenlander, or vv. #. This **has been demonstrated** with real qbits transported 1000 miles apart. #. Entanglement means that if you measure one qbit then what you observe restricts what would be observed when you measure the other qbit. #. However that **does not let you communicate**. #. The above metaphor is inaccurate in ways that don't affect us now. (It assumes a hidden variable, which is false.) #. Entanglement and superposition do funny things to operations. Consider the `Controlled NOT gate `_. It has 2 inputs, x and y. a. Classically, y is negated iff x=1. x doesn't change. #. If x and y are superposed with a Hadamard basis, then y can affect x. Video to watch on your own ========================== #. `Quantum Computing 2022 Update `_, 15:12, July 24 2022. #. You prepare discussion points and questions for next class. Misc intro to quantum computing stuff ===================================== This is misc stuff that you might find interesting, which I'm drawing from. Intro sites - 2 --------------- #. `"Spooky" physics | Leo Kouwenhoven | TEDxDelft (18:00) `_ #. A beginner's guide to quantum computing | Shohini Ghose https://www.youtube.com/watch?v=QuR969uMICM 10:04 #. https://towardsdatascience.com/introduction-to-quantum-programming-a19aa0b923a9?gi=69d861e26d80 #. https://medium.com/@jonathan_hui/qc-programming-with-quantum-gates-8996b667d256 #. https://medium.com/@jonathan_hui/qc-programming-with-quantum-gates-2-qubit-operator-871528d136db #. https://www.cl.cam.ac.uk/teaching/0910/QuantComp/notes.pdf a. They have a nice description of measurement starting at slide 10. #. Each measurement operator has a *basis* vector set. #. The operator represents the qbit as a linear combo of the basis vectors. #. Then it projects the qbit onto one of the basis vectors, with probability being the length of that component. #. It is possible for two different qbits to measure the same in some basis, but measure different in a different basis. #. `Can we make quantum technology work? | Leo Kouwenhoven | TEDxAmsterdam (18:19) `_ #. `Quantum Computing Concepts – Quantum Hardware (3:22) `_ #. `Experiment with Basic Quantum Algorithms (Ali Javadi-Abhari, ISCA 2018) `_ (19:05) #. `Quantum Computing for Babies `_ Current status sites -------------------- #. https://www.telegraph.co.uk/technology/2020/09/02/britain-must-act-fast-prevent-brain-drain-quantum-computing/ - good summary of programs around the world. #. `Quantum startup CEO suggests we are only five years away from a quantum desktop computer `_ No new homework =============== Finish 1 and enjoy Labor Day. Videos to watch for Tues ========================= #. Watch `A Beginner’s Guide to Quantum Computing `_, 18 min, by Dr. Talia Gershon, IBM Research.