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votes
3 answers
What exactly are anyons and how are they relevant to topological quantum computing?
I have been trying to get a basic idea of what anyons are for the past couple of days. However, the online articles (including Wikipedia) seem unusually vague and impenetrable as far as explaining topological quantum computing and anyons goes.
The…
Sanchayan Dutta
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27
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4 answers
Why is it crucial that the initial Hamiltonian does not commute with the final Hamiltonian in adiabatic quantum computation?
I've read in many sources and books on adiabatic quantum computation (AQC) that it is crucial for the initial Hamiltonian $\hat{H}_i$ to not commute with the final Hamiltonian $\hat{H}_f$, i.e. $\left[\hat{H}_i,\hat{H}_f\right]\neq 0$. But I've…
Turbotanten
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27
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2 answers
Who first proposed the idea of quantum computing using qubits?
As I understand it, the field of quantum mechanics was started in the early 20th century when Max Planck solved the black-body radiation problem. But I don't know when the idea of computers using quantum effects spread out.
What is the earliest…
User that hates AI
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26
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4 answers
Is error correction necessary?
Why do you need error correction? My understanding is that error correction removes errors from noise, but noise should average itself out. To make clear what I'm asking, why can't you, instead of involving error correction, simply run the…
auden
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26
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4 answers
How to calculate circuit depth properly?
Is the circuit depth the longest sequence of gates applied on one of the qubits?
Or is it something more complicated?
C-Roux
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26
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Explicit Conversion Between Universal Gate Sets
I'm interested in the conversion between different sets of universal gates. For example, it is known that each of the following sets is universal for quantum computation:
$\{T,H,\textrm{cNOT}\}$
$\{H,\textrm{c}S\}$, where $S=T^2$ and $S^2=Z$, and…
DaftWullie
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26
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3 answers
What is the argument that practical quantum computers cannot be built?
An answer to another question mentions that
There are arguments that suggests that such machines ["quantum Turing machines"] cannot even be built...
I'm not sure I fully understand the problem, so perhaps I'm not asking the right question, but…
BurnsBA
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26
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1 answer
Explicit Lieb-Robinson Velocity Bounds
Lieb-Robinson bounds describe how effects are propagated through a system due to a local Hamiltonian. They are often described in the form
$$
\left|[A,B(t)]\right|\leq Ce^{vt-l},
$$
where $A$ and $B$ are operators that are separated by a distance…
DaftWullie
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26
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2 answers
Why can't quantum annealing be described by a gate model?
This is a question I was inspired to ask based on this question, which notes that quantum annealing is an entirely different model for computation than the usual circuit model. I've heard this before, and it's my understanding that the gate-model…
Emily Tyhurst
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25
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What's the difference between T1 and T2?
I learned that T1 is relaxation time (time from $|1\rangle$ to $|0\rangle$) and T2 is coherence time.
The relaxation is a specific case of decoherence.
What's the difference between them and what's the exact meaning of coherence time T2?
peachnuts
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25
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4 answers
Intuition about Knill-Laflamme QEC conditions
The Knill Laflamme QEC conditions are stated this way:
We consider a code space $C$ and its associated projector $P_C$.
We consider a noise acting on our system: $E(\rho)=\sum_a E_a \rho E_a^{\dagger}$
A necessary & sufficient condition for the…
Marco Fellous-Asiani
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25
votes
5 answers
How would I implement the quantum oracle in Deutsch's algorithm?
I am trying to simulate Deutsch's algorithm (elementary case of Deutsch-Jozsa algorithm), and I am not entirely sure how I would go about implementing the quantum oracle necessary for the algorithm to function, without defeating the purpose of the…
Jack Ceroni
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6 answers
Counterexamples in quantum information theory
As was already asked about in this phys.SE question many years ago—which, sadly, got closed and never received an answer—is there a collection of counterexamples in quantum information theory, "in the spirit of books like [...] Counterexamples in…
Frederik vom Ende
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25
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1 answer
How to interpret a quantum circuit as a matrix?
If a circuit takes more than one qubit as its input and has quantum gates which take different numbers of qubits as their input, how would we interpret this circuit as a matrix?
Here is a toy example:
PiMan
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25
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2 answers
What is the status of confirming the existence of anyons?
In a comment on my answer to the question: What exactly are anyons and how are they relevant to topological quantum computing? I was asked to give specific examples of occurrence of anyons in nature. I've spent 3 days searching, but every article…
user1271772 No more free time
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