(sec:misconceptions)= # Quantum Misconceptions Quantum mechanics has a reputation of being difficult and the source of many mysterious paradoxes. While there are truly remarkable and perplexing consequences of the quantum formalism, many of the seemingly impossible claims are just that: impossible consequences of misapplying the fundamental principals. Here we list some common misconceptions. Can you see where the presentations have mistakes? ## Quantum Eraser and Retrocausality The delayed-choice quantum eraser seems to violate causality by allowing a measurement in the future to change the result of a previous measurement (retrocausality). There is no real paradox here: quantum mechanics is completely consistent with causality. Can you find the mistakes made in the following presentations that lead the presenters to (incorrectly) conclude that quantum mechanics allows retrocausal effects? * [How the Quantum Eraser Rewrites the Past | Space Time | PBS Digital Studios](https://youtu.be/8ORLN_KwAgs) * [Down The Rabbit Hole Of The Delayed Choice Quantum Eraser | Answers With Joe](https://youtu.be/spKlpexL_Hg) * [The super bizarre quantum eraser experiment | Fermilab](https://youtu.be/l8gQ5GNk16s) ### Explanation Sabine Hossenfelder does a reasonable job of "debunking" these videos in [The Delayed Choice Quantum Eraser, Debunked], as does Sean Carroll in his blog post [The Notorious Delayed-Choice Quantum Eraser]. Before viewing these, try to figure out where the previous expositions get it wrong. [The Delayed Choice Quantum Eraser, Debunked]: [The Notorious Delayed-Choice Quantum Eraser]: ## Quantum Computers are Faster than Classical Computers :::{margin} Incomplete. This section needs some references, both to examples of the misconception, and to careful characterize the speed of quantum computers. ::: Another misconception is that quantum computers will be faster classical computers. This is unlikely to be true. In general, quantum computers will be **slower** than their classical counterparts in order to preserve coherence. ### Explanation Quantum advantage is associated with certain problems where quantum quantum algorithms have an algorithmic advantage over classical computers, and hence will be able to solve certain larger problems than classical computers (if they can be made to be large enough). For example, using Grover's algorithm, quantum computers can perform an unstructured search over $N$ in time $O(\sqrt{N})$, which is provably better than classical algorithms which must at least read each entry, thus taking at least $O(N)$ time. Note that this proof addresses the **asymptotic time complexity** of the algorithms, but specifies nothing about the prefactor. Almost certainty, the (machine-dependent) prefactor for Grover's algorithm will be significantly larger. Thus, once $N$ is large enough, the quantum algorithm is guaranteed to win, but we must make a large enough quantum computer that can maintain sufficient coherence to realize this advantage.