The Quantum Zeno Effect: From the Arrow Paradox to Freezing Qubits
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- Опубліковано 10 січ 2023
- If an arrow flying through the air is stationary at every instant of time, how can it ever be moving?
Zeno's arrow paradox was resolved by calculus many years ago, but recently our intuition has been challenged by the quantum Zeno paradox. It turns out you can freeze a qubit's state by continuously measuring it!
In this video, Oxford PhD student Maria Violaris shows you how to use the quantum Zeno effect on a real quantum computer, how to code a quantum freezer game using Qiskit, and how to upgrade this game to freeze entangled qubits, as the latest addition to our Quantum Paradoxes series.
Learn more at the Qiskit Blog: / the-quantum-zeno-effec...
Find all the code at this Jupyter Notebook: github.com/maria-violaris/qua...
#learnquantum #ibmquantum #qiskit - Наука та технологія
10/10 opening, need to see more bow shooting in qiskit videos!
Haha glad you liked it! It’s not easy to fire arrows in the British breeze unfortunately 😅
Interesting!
Mind blowing
Is this why clocks feel slower when I look at them?
Can you also consider that the arrow is never stationary but moving infinitesimally over an infinite distance then adding these up infinitely we get a finite answer (like integral calculus). Then the arrow will be moving as we perceive it.
Perhaps the Quantum Zeno Effect explains why we have our Newtonian Classical Reality, for example, why macroscopic objects are in one place instead of a super position of places.
Thank you for the interesting comment. The appearance of a single macroscopic reality emerging from underlying quantum dynamics can be explained by decoherence: quantum systems are projected into the computational basis when they interact with / are measured by their environment. The quantum Zeno effect can actually protect against decoherence, maintaining superposition and entanglement, see the section "Zeno lends a hand to quantum computing" in the Blog post (linked in the video description above) for more detail. Hope that helps!
@@maria_violaris Thanks for those clarifications, I appreciated a lot this video.
So, the permanent re-collapse prevents the state from evolving?
If my brother is upset with his computer, he permanently presses reset button so it never comes up. That's "Zeno-effect" in classical computing.
Does this mean, the term "Zeno-Effect" is now reserved for the Arrow-Paradox, and can't be used for the "Achilles and the tortoise"-Paradox any more?
Seems that Zeno didn't know the time derivative to express motion. Or infinitely small intervals "dt", "dx", ...
In that sense, it's more astonishing that ancient people could calculate volumes like the sphere, without knowledge of infinitesimals.
They used some kind of "cavalieri principle", later rediscovered by cavalieri. And some of these paradoxes may led to analysis.
However, 2:05 Marian Rejewski cracked the enigma, not Turing!
The "quantum Zeno effect" specifically refers to the quantum thought experiment I explain in the video, with its name inspired by Zeno's arrow paradox. Some people may use "Zeno effect" as a shorthand for the "quantum Zeno effect". In general, the phrase "Zeno's paradox" outside the quantum context could refer to any of his paradoxes, including the Achilles and the tortoise paradox. Hope that helps!
we all forgot the name "sofism"
Really enjoyed the video. However, it appeared that on the real device, the probability was moving towards the experiment without the Zeno effect though bounded by it. (at 9:36)
Glad you liked the video! Yes, on the real device the errors introduced by the hardware (including in the mid-circuit measurements) build up with more timesteps, leading to a greater effect from the noise, so the Zeno effect becomes less effective.
But the first measurement on the qubit will turn it into classical. How will that help with later operations??
The first measurement projects the qubit into a computational basis state, so either 0 or 1. However, the qubit is still a quantum system, and so its state can continue to evolve into a superposition of 0 and 1, demonstrated by a rotation gate after the measurement in my Qiskit implementation. Frequent measurements are required to keep projecting a qubit whose state is evolving over time back into the computational basis state it started in, with high probability. Hope that helps with your question!
@@maria_violaris Thankyou for your reply. So after I am done maintaining the state in 1 over time, if I want I can apply other operations on it??
@@SushantRanjan143 Yes, the quantum Zeno effect does not stop you applying operations to a qubit, if you want to change its state. For example, if an X gate was applied to the qubit in my Qiskit demonstration at some point in the quantum circuit, it would flip from the 1 to the 0 state, and the subsequent measurements would maintain a 0 state with high probability.
So does the Quantum Zeno effect itself prove that time is not made of individual instants
Or is it based on the assumption that time is not made of individual instants?
With the invention of calculus, it was realised that to understand motion, we should consider the behaviour of an object in the infinitesimal limit of some time-interval rather than consider motion at individual instants of time - using that knowledge, we can resolve the original Zeno's arrow paradox. The quantum Zeno effect was named after the original Zeno's arrow paradox because the phenomenon of freezing a quantum state by observing sounding similar to the philosophical idea that an arrow would never fly through the air if you kept observing it (and seeing it frozen at each instant of time). The quantum Zeno effect does not actually tell us anything about time being split into instants, and that problem was already resolved with calculus. Hope that makes sense!
@@maria_violaris ah neat.
Although from the sound of it calculus itself only states that motion should be viewed in time intervals, rather than time instants. I dont imagine it empirically proves time isnt made of instants does it. Simply that it's much more convenient to not view it as instants but as time-intervals.
@@nairda55555 Calculus tells us how to calculate properties of motion at instants of time, by taking the limit of a time interval as that interval becomes zero. So yes in that sense it is more accurate to say that calculus enables us to understand what is happening at individual instants of time, rather than proving something about the nature of time itself.
Maria, if you don't want to run out of gas in your car, keep driving.
Did you just apply X gate to Maria's Demo?
I think it's not good practice to measuring the qubit multiple times (ua-cam.com/video/vfUn8cR-eXw/v-deo.html), because it will keep reset the qubit status, or I am missing something here.
In this context, the aim of the repeated measurement is to "freeze" the qubit in its original state with high probability. For an example of a situation where it is useful to do these repeated measurements, see how the quantum Zeno effect is used to make an up to 100% effective quantum bomb tester in our quantum minesweeper video: ua-cam.com/video/fus1nJ6JaTk/v-deo.html.
The missile knows where it is at all times. It knows this because it knows where it isn't. By subtracting where it is from where it isn't, or where it isn't from where it is, whichever is greater, it obtains a difference, or deviation. The guidance subsystem uses deviations to generate corrective commands to drive the missile from a position where it is to a position where it isn't and, arriving at a position where it wasn't, it now is. Consequently, the position where it is, is now the position that it wasn't, and it follows that the position that it was is now the position that it isn't. In the event that the position that it is in is not the position that it wasn't, the system has acquired a variation; the variation being the difference between where the missile is and where it isn't. If variation is considered to be a significant factor, it, too, may be corrected by the GEA. However, the missile must also know where it was. The missile guidance computer scenario works as follows: because a variation has modified some of the information the missile has obtained, it is not sure just where it is, however it is sure where it isn't, within reason, and it knows where it was. It now subtracts where it should be from where it wasn't, or vice versa. And by differentiating this from the algebraic sum of where it shouldn't be and where it was, it is able to obtain the deviation and its variation, which is called error.
Is this missile position paradox?
@@amiprasis totally. Search UA-cam for 'the missle knows'
I didn't understand a one damn word you said. 😕