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9
votes
1answer
370 views

Do quantum “Sure-Shor separators” have a natural Veronese/Segre classification? (question inspired by Gil Kalai and Aram Harrow)

Aram Harrow asked: "Is there any place this is written up?" Update  Partly in answer to Aram's question, the thermodynamical properties of varietal dynamical systems now are written-up in ...
7
votes
1answer
989 views

What is the “Tangle” at the Heart of Quantum Simulation?

The following questions generalize and naturalize the question that was originally asked. Provisional answers largely due to Will Sawin are now included. As was discussed in the question originally ...
12
votes
3answers
595 views

Representing SU(3) with 3 ropes in 3 dimensions

The short question is: how exactly is SU(3) realized with ropes? The long question: There is this idea that deformations of a configuration of three infinitely long, flexible ropes that cross each ...
10
votes
2answers
507 views

Is quantum game theory reducible to classical game theory?

Quantum game theory is an extension of classical game theory to the quantum domain. It differs from classical game theory in three primary ways: Superposed initial states, Quantum ...
10
votes
4answers
861 views

Quantum algorithms for dummies

I want to try my hand at designing quantum algorithms to solve certain problems. I feel like I understand (for example) how Grover's algorithm and Shor's algorithm work, and I'm excited to apply the ...
12
votes
3answers
1k views

Will quantum computing kill cryptography ? [closed]

I apologize as this question is not really mathematical, and therefore perhaps not well-suited for this site. Please feel free to close it if you think it is not. My reason for asking it here is that ...
2
votes
2answers
207 views

How can I get all the good items using quantum search algorithm?

One can get a superposition of all good item using quantum search algorithm in $O$($\sqrt{N}$ ) time, but how one can get all the good items using quantum search algorithm? I found that all the good ...
5
votes
1answer
691 views

How much does a quantum oracle to find a needle in a haystack really cost?

Among the basic algorithms of quantum computations Lov Grover's result on quantum search stands out, both in regards to its intrinsic interest, and for its undisputable elegance. Grover's algorithm ...
5
votes
1answer
268 views

Set of physical states of FQHE on closed Riemann surface = ?

Disclaimer. One might argue that my question is off topic as it is clearly a question about physics... But I'd like a mathematically phrased answer, and I expect that only a mathematician can offer an ...
1
vote
4answers
707 views

Presentation of the Clifford group by generators and relations?

The Clifford group $\mathcal{C}_n$ is a matrix group on $\mathbb{C}^{2^n}$ generated by tensor products of the following matrices: $$ P = \begin{pmatrix} 1 & 0 \\\\ 0 & i\end{pmatrix} \quad H ...
2
votes
1answer
620 views

Bounding the von Neumann entropy of a density matrix with the Hilbert-Schmidt norm

Question Suppose I have a $D$-dimensional density matrix $\rho_0$ $\rho_0^\dagger = \rho_0 \quad, \quad \mathrm{Tr} \rho_0 = 1 \quad, \quad \rho_0 > 0,$ with a known spectrum $\{\lambda_i^0\}$ ...
3
votes
1answer
408 views

Are all quantum cellular automata invertible & representable?

A little background: As far as I know there is no standard definition of a quantum cellular automaton in the literature. Different authors use different definitions. Here I propose my own definition ...
0
votes
2answers
441 views

A non-associative three-valued logic

There are three elements: x, y, z and a relation C: x C y, y C z, z C x, x C x, y C y, z C z. Let us introduce two binary operations with respect to the C: "the leftmost" (L) and "the rightmost" ...
5
votes
1answer
271 views

Standard reference for equivalence of PU(2) action on $\mathbb{C}\mathbb{P}^1$ and SO(3) action on $S^2$

The equivalence I describe below is well-known, but I'd like a simple standard reference for it. Consider $\mathbb{C}\mathbb{P}^1$, the set of one-dimensional subspaces of $\mathbb{C}^2$, which has a ...
3
votes
0answers
606 views

Why isn't Montgomery modular exponentiation considered for use in quantum factoring?

It is well known that modular exponentiation (the main part of an RSA operation) is computationally expensive, and as far as I understand things the technique of Montgomery modular exponentiation is ...
9
votes
2answers
2k views

Quantum PCP Theorem

Although I think I know the answers to these, I'd just like to collect them all in one place. What is the quantum PCP theorem, what implications does its proof have for simulation of Hamiltonians and ...
7
votes
3answers
1k views

Grover's Quantum Search Algorithm

I am confused about an extremely basic point concerning Grover's quantum search algorithm; my confusion suggests to me that maybe I've missed the entire point. My understanding of the algorithm is ...
0
votes
1answer
356 views

Linear Mapping and integration

I have been reading the paper - "Introduction to Quantum Fisher Information". In section 1.2 the author talks about the linear map $\mathbb{J}_D$, which he defines as follows: Let $D \in M_n$ be a ...
3
votes
2answers
740 views

Amplitude amplification as a quantum walk algorithm

This is a followup to an earlier question on a taxonomy for quantum algorithms in which I ultimately concluded in a comment that all known nontrivial quantum algorithm speedups (in Jordan's quantum ...
7
votes
2answers
474 views

What's known about the relationship about EQP and BQP?

EQP is the class of problems solvable deterministically using a quantum computer in polynomial time - that seems to me to be a good analogue to P, whereas BQP is the quantum analogue of BPP. It ...
10
votes
2answers
866 views

Are there any known quantum algorithms that clearly fall outside a few narrow classes?

I'm trying to refresh myself on quantum algorithms and have been skimming Childs and van Dam's 2008 RMP paper among other things. From my preliminary surfing it looks like the known quantum algorithms ...