Introduction to Quantum Computing

BACKUP

28.11.2024 09:00-12:00 (CET)

Join Zoom Meeting:
https://cscfi.zoom.us/j/67364596298?pwd=eSb4MOGt2wD6TNyBaHOa0sGubNoLZ9.1

Meeting ID: 673 6459 6298
Passcode: 794521

tags: quantum

This is the collaborative document for the "Introduction to Quantum Computing" course organised in November 2024.
Course page
Lesson material
Instructor: Stefan Seegerer, IQM Quantum Computers (Connect on LinkedIn)

✏️ Links to activities

During the workshop, we will use some interactives on IQM Academy.

• Activity 1a: https://bit.ly/iqm-1
• Activity 1b: https://www.iqmacademy.com/play/bloch/
• Activity 2: https://bit.ly/iqm-2
• Activity 3: https://bit.ly/iqm-3
• Acitivty 4: https://academy.meetiqm.com/curriculum/workshop-en-2.html
• Activity 5: https://bit.ly/iqm-express
• Optional: Gradient descent https://www.iqmacademy.com/learn/variational_qa/variational04/

✏️ Q & A -Add your questions here

Your questions are answered here. We will answer them, and this document will store the answers for you for later use!

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• Q1: Qubits can be entangled. But must be?

  • A: Probably not yet.. ↖️ The answer is no, they don't have to, but if you want to take use of quantum computing, you should.

• Q2: 150 qubits are physical qubits or logical qubits?

  • I don't quite understand where the question is coming from, but of course depending on context it can mean both. Currently, IQM is working on its 150 physical qubit device.

• Q3: How does Measurement Based QC relate to Gate Based / Annealing?

  • A: Measurement can be seen as an operation in both gate based and annealing. However, measurement based qc is a different paradigm in which computation is performed by sequentially measuring qubits in specific bases, with the outcomes determining the evolution of the computation. (In Measurement based qc the qubits need to be entangled before ofc)

• Q4: Starting 1|0> + 0|1>, applying X gate and applying Y gate leads to same state visually but if we look at kets then one is imaginary?

  • You can answer this with the bloch sphere vizualization if you apply the "Show ket" option. It indeed is two different states, just that the imaginary part (we call it the phase) you cannot measure https://www.iqmacademy.com/play/bloch/

• Q5: What does "ket" numbers mean? Probabilities? Weights?

  • A: Let’s consider it just a name for now :) It comes from its visual representation that is the bra-ket notation (because it has those brackets around <a|b> and we just use the latter part) It represents a vector

• Q6: How can 2D approximations, such as circles, effectively represent qubit states, and what are their limitations compared to the full Bloch sphere?

  • A: This is an excellent question. 2d vizualization such as circles depend on what approximation is used. Sometimes it is just capturing part of the state space of a qubit. But other such as the one used here: https://github.com/iqm-finland/iqm-academy-cheat-sheets/blob/master/circuit-magicians/en/cheat-sheet-for-circuit-magicians.pdf are used to represent multi-qubit systems even better. In general, no vizualization of quantum computation is perfect, they all have some flaws – I guess, this is due to the very abstract nature of the concepts :)

• Q7: When you say we do "multiple shots" are we measuring each shot?

  • A: Yes :) one execution of a quantum circuit on a quantum computer doesnt take that long gladly
    • Follow up: how do we measure a shot without destroying the superposition?
      • We do destroy the superposition, we recreate it by applying the same gates again

• Q8: What is the reason that the gates(H, C, T, etc.) are designed that way? Is there any other sets of gates could be used in QC?

  • A: In principle you can define a lot of different gates, however actual quantum computer hardware will (similiar to a classical computer) only support a so called universal gate set that allows to execute any operation. E.g. for IQM machines it is the PRX gate (Phased X rotation) and the CZ gate (Controlled-Z gate).

• Q9: Regarding Q4 in sheet, didn't want to clutter there so writing here. So phase is somewhat an artifact that we can't measure and two results are indeed entirely different states? Was it intentionally not represented in Bloch sphere (limitations of 3D etc.)? Finally, going from one state to another is it a path dependent process? Is it important that how we got to that state (applying 2 X gate returns back to initial state, is it identical with before)

  • We need to differentiate between the absolute phase and relative phase. The relative phase is the rotation around the Z axis (e.g. by applying a T-gate –> I encourage you to try out the sequence H->T starting from |0>.). Both can't be measured, but relative phase differences can be converted to amplitude differences (|a|, |b|,…) that can be measured. The absolute phase does not matter at all, it is esentially a factor x such that x(a|0>+b|1>)

• Q10: What is absolute phase?

  • A: The absolute phase does not matter at all, it is esentially a factor x such that x(a|0>+b|1>).

• Q11: I still didn't understand, why were we able to read out the secret code just by applying hadamard gates?

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