Incoming links: Shor's algorithm
Course plan:
- Section "Programmer's model of quantum computers"
- look at a Qiskit hello world
- e.g. ours: qiskit/hello.py
- learn about quantum circuits.
- tensor product in quantum computing
- First we learn some quantum logic gates. This shows an alternative, and extremely important view of a quantum computer besides a matrix multiplication: as a circuit. Fundamental subsections:
- quantum algorithms
Quantum Computing with Trapped Ions by Christopher Monroe (2018)
Source. Co-founder of IonQ. Cool dude. Starts with basic background we already know now. Mentions that there is some relationship between atomic clocks and trapped ion quantum computers, which is interesting. Then he goes into turbo mode, and you get lost unless you're an expert! Video 1. "Quantum Simulation and Computation with Trapped Ions by Christopher Monroe (2021)" is perhaps a better watch.- youtu.be/9aOLwjUZLm0?t=1216 superconducting qubits are bad because it is harder to ensure that they are all the same
- youtu.be/9aOLwjUZLm0?t=1270 our wires are provided by lasers. Gives example of ytterbium, which has nice frequencies for practical laser choice. Ytterbium ends in 6s2 5d1, so they must remove the 5d1 electron? But then you are left with 2 electrons in 6s2, can you just change their spins at will without problem?
- youtu.be/9aOLwjUZLm0?t=1391 a single atom actually reflects 1% of the input laser, not bad!
- youtu.be/9aOLwjUZLm0?t=1475 a transition that they want to drive in Ytterbium has 355 nm, which is easy to generate TODO why.
- youtu.be/9aOLwjUZLm0?t=1520 mentions that 351 would be much harder, e.g. as used in inertially confied fusion, takes up a room
- youtu.be/9aOLwjUZLm0?t=1539 what they use: a pulsed laser. It is made primarily for photolithography, Coherent, Inc. makes 200 of them a year, so it is reliable stuff and easy to operate. At www.coherent.com/lasers/nanosecond/avia-nx we can see some of their 355 offers. archive.ph/wip/JKuHI shows a used system going for 4500 USD.
- youtu.be/9aOLwjUZLm0?t=1584 Cirac and Zoller proposed the idea of using entangled ions soon after they heard about Shor's algorithm in 1995
- youtu.be/9aOLwjUZLm0?t=1641 you use optical tweezers to move the pairs of ions you want to entangle. This means shining a laser on two ions at the same time. Their movement depends on their spin, which is already in a superposition. If both move up, their distance stats the same, so the Coulomb interaction is unchanged. But if they are different, then one goes up and the other down, distance increases due to the diagonal, and energy is lower.
- youtu.be/9aOLwjUZLm0?t=1939 S. Debnah 2016 Nature experiment with a pentagon. Well, it is not a pentagon, they are just in a linear chain, the pentagon is just to convey the full connectivity. Maybe also Satanism. Anyways. This point also mentions usage of an acousto-optic modulator to select which atoms we want to act on. On the other side, a simpler wide laser is used that hits all atoms (optical tweezers are literally like tweezers in the sense that you use two lasers). Later on mentions that the modulator is from Harris, later merged with L3, so: www.l3harris.com/all-capabilities/acousto-optic-solutions
- youtu.be/9aOLwjUZLm0?t=2119 Bernstein-Vazirani algorithm. This to illustrate better connectivity of their ion approach compared to an IBM quantum computer, which is a superconducting quantum computer
- youtu.be/9aOLwjUZLm0?t=2354 hidden shift algorithm
- youtu.be/9aOLwjUZLm0?t=2740 Zhang et al. Nature 2017 paper about a 53 ion system that calculates something that cannot be classically calculated. Not fully controllable though, so more of a continuous-variable quantum information operation.
- youtu.be/9aOLwjUZLm0?t=2923 usage of cooling to 4 K to get lower pressures on top of vacuum. Before this point all experiments were room temperature. Shows image of refrigerator labelled Janis cooler, presumably something like: qd-uki.co.uk/cryogenics/janis-recirculating-gas-coolers/
- youtu.be/9aOLwjUZLm0?t=2962 qubit vs gates plot by H. Neven
- youtu.be/9aOLwjUZLm0?t=3108 modular trapped ion quantum computer ideas. Mentions experiment with 2 separate systems with optical link. Miniaturization and their black box. Mentions again that their chip is from Sandia. Amazing how you pronounce that.
This is the true key question: what are the most important algorithms that would be accelerated by quantum computing?
Some candidates:
- Shor's algorithm: this one will actually make humanity worse off, as we will be forced into post-quantum cryptography that will likely be less efficient than existing classical cryptography to implement
- quantum algorithm for linear systems of equations, and related application of systems of linear equations
- Grover's algorithm: speedup not exponential. Still useful for anything?
- Quantum Fourier transform: TODO is the speedup exponential or not?
- Deutsch: solves an useless problem
- NISQ algorithms
Do you have proper optimization or quantum chemistry algorithms that will make trillions?
Maybe there is some room for doubt because some applications might be way better in some implementations, but we should at least have a good general idea.
However, clear information on this really hard to come by, not sure why.
Whenever asked e.g. at: physics.stackexchange.com/questions/3390/can-anybody-provide-a-simple-example-of-a-quantum-computer-algorithm/3407 on Physics Stack Exchange people say the infinite mantra:
Lists:
- Quantum Algorithm Zoo: the leading list as of 2020
- quantum computing computational chemistry algorithms is the area that Ciro and many people are te most excited about is
- cstheory.stackexchange.com/questions/3888/np-intermediate-problems-with-efficient-quantum-solutions
- mathoverflow.net/questions/33597/are-there-any-known-quantum-algorithms-that-clearly-fall-outside-a-few-narrow-cla
Shor's algorithm Explained by minutephysics (2019)
Source.