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2answers
168 views

Is true randomness and the physical Church-Turing thesis incompatible?

As follow up to Does the physical Church-Turing thesis imply that all physical constants are computable?, I ask if true randomness (as predicted by QM) and the physical Church-Turing thesis are ...
3
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2answers
290 views

Does the physical Church-Turing thesis imply that all physical constants are computable?

The physical Church Turing thesis is a conjecture that any physically computable algorithm can be computed by a Turing machine. Let us create a machine that, for example, outputs the digits of the ...
8
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4answers
558 views

Stephen Hawking's impact on computer science

In light of Stephen Hawking passing away today, I was wondering whether any of his results have direct impact on cs? The obvious candidate would be in quantum computing, or rather the construction ...
3
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1answer
180 views

How to study the thermodynamics of 2 problems if reduction from $B$ to $A$ exists?

Peter Shor commented on this post: years of experience in theoretical computer science says that the thermodynamic behavior of two NP complete problems are in general not similar. What do we know ...
5
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2answers
694 views

Isn't it trivial to represent any classical Physics problem in a Spin-Glass format which is NP-Complete?

In the late 80's there were several efforts to use Spin-Glass models to formulate other computational problems such as: Protein Folding and Neural Networks. Wouldn't it be straight forward to reduce ...
4
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1answer
208 views

The Maxwell's Demon and Computer Science

What is the best source -in terms of quality- that would explain the argument that uses computations concepts to demonstrate that the Maxwell's Demon does not break the second law of thermodynamics? I ...
7
votes
1answer
293 views

Applications of Takens' theorem to TCS?

My apologies if the question is a tad vague—I did try to search the literature for more, but didn't find anything (the similarity between the keywords "Takens" and "taken" on Google may be partly to ...
11
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1answer
343 views

What does a tangible Quantum-Gate look like?

I'v read published books, articles and papers about Quantum-Computing. I found that all the materials I've seen are, instead of describing quantum gate from basic physics to abstraction, trying hard ...
2
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1answer
148 views

Complexity of computing generalised determinants. (P - #P transition)

Computing the determinant of a matrix can be done in polynomial time, while computing the permanent is known to be #P-hard. Let $A$ be an $n \times n$ matrix. Define a generalised determinant function ...
6
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1answer
242 views

Which areas of computer science have lots of overlap with physics?

I'm an undergrad in computer science but I've always loved physics and its ability to constantly amaze and surprise us about our world. I am wondering if there are areas in graduate level computer ...
2
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1answer
84 views

Why is it impossible to work with polylog length encoding schemes for quantum circuits?

I am going through Quantum Computational Complexity by John Watrous. On page $12$, he said: The encoding disallows compression: it is not possible to work with encoding schemes that allow for ...
1
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1answer
59 views

How the hardness of hidden subgroup problem in $S_n$ changes as the order of the subgroup grows?

In Normal Subgroup Reconstruction and Quantum Computation Using Group Representations by Hallgren et al. In this paper it is showed that no hidden subgroup algorithm can distinguish the trivial ...
3
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2answers
113 views

Is there any hidden subgroup of a symmetric group which can be efficiently determined?

There have been a number of cases where efficient hidden subgroup algorithms have been found for specific non-Abelian groups with very specific structures. Why haven't we found any efficient quantum ...
3
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0answers
83 views

Why hidden subgroup problem is easy for very large subgroup?

I am going through QUANTUM MECHANICAL ALGORITHMS FOR THE NONABELIAN HIDDEN SUBGROUP PROBLEM by Grigni et al. On page 2, it is said that solving the hidden subgroup problem becomes very easy when the ...
2
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0answers
144 views

Are ill-posed inverse problems in NP?

I'm a physicist who works on inverse problems; I'll explain what these are by means of an example. Consider an object whose refractive index is known; then, the problem of computing scattered ...
-3
votes
1answer
133 views

Dimension of the Fourier transform for $S_5$ [closed]

My question: What is the dimension of the Fourier transform for $S_5$? My effort: The dimensions of the seven irreps of $S_5$ are $1,1,4,4,5,5,6$. According to the notes of Andrew Childs, the ...
5
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1answer
225 views

How Much Computing Power would be Required to Fully Simulate a Cubic Meter?

Imagine you want to simulate a cubic meter down to the particle. By following the Standard Model and other basic physical equations, how much computing power would be required to do this, in say, a ...
3
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0answers
59 views

Does simulating chiral gauge theories lie within BQP?

In theoretical physics, there is a branch of quantum field theory dealing with chiral gauge theories. It has been conjectured by Feynman [1] and others that all quantum field theories can be simulated ...
7
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3answers
257 views

Is there a theory of computation that takes failure and decay of the computation substrate into account?

There are obvious differences between a Turing machine and a real computer. Not only is the latter finite in size, it is also prone to failures and it is made from decaying matter. The kind of ...
8
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1answer
339 views

Is it conceivable at all that the standard model of physics can outperform a quantum computer in any sense?

The Standard Model of physics (the mathematical model which predicts the Higg's boson) is, as far as I understand, our most complete model of the universe. That is to say, it is the best description ...
6
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2answers
411 views

Suppose $\mathbf{P} = \mathbf{BQP}$. Then what is randomness? Would it even exist at all?

DISCLAIMERI do apologize in advance if this question turns out to be silly, for some trivial reason that I may be overlooking in this moment. Suppose for a moment that $\mathbf{P} = \mathbf{BQP}$ ...
1
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0answers
32 views

Coset state of $3$-node graph isomorphism problem

The hidden subgroup representation of a $3$-node graph isomorphism problem is defined over the symmetric group, $G = S_6$. So, any hidden subgroup algorithm that wishes to solve the problem should ...
2
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1answer
576 views

Complexity: simulated annealing vs. quantum annealing

How do I compare the performance of simulated annealing against the performance of quantum annealing algorithms? In Convergence theorems for quantum annealing by Morita and Nishimori, it has been ...
10
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1answer
557 views

Quantum algorithms for QED computations related to the fine structure constants

My question is about quantum algorithms for QED (quantum electrodynamics) computations related to the fine structure constants. Such computations (as explained to me) amounts to computing Taylor-like ...
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4answers
481 views

How could God authenticate in one message? [closed]

Thought experiment: Which data could convince experts, beyond reasonable doubts, about their origin outside our universe? From which margin should an expert consider such claim seriously? For example,...
2
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0answers
114 views

Calculating the ground state of an Ising model with $\sigma_i = (0,1)$ spin state assignments (do Barahona & Istrail's NP-hardness results hold?)

In a typical Ising model, one has possible spin assignments of $\sigma_i = \pm 1$. However, one can also imagine a $q = 2$ Potts model generalization with spin assignments $\sigma_i = (0,1)$. Is ...
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1answer
91 views

The Arrow of Time in a Non-Physical Realm [closed]

Could there be a logically consistent theory supporting the transmission of non-physical information to a point in time previous to the time it was sent using a computer network (quantum theory, etc)? ...
0
votes
1answer
88 views

References to learn more about graph laplacian.

I have vaguely heard of this connection between random matrix theory and graphs (the spectral gap of their laplacians) on compact Riemann surfaces. Can someone give a pedagogic reference which helps ...
2
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0answers
53 views

How the errors of the measured quantities of an adiabatic Hamiltonian are inversely proportional to the square root of the number of measurements?

I am going through the paper, Solving the graph-isomorphism problem with a quantum annealer, by Hen et. al. In the last line of the second paragraph of the second column of page 2, it says, Since ...
4
votes
2answers
321 views

Simulation of every physical quantum system on quantum computer

Let me quote from the section 9.3 of Classical and Quantum Computation by Kitaev, Shen and Vyalyi. With high confidence, we may claim that every physical quantum system can be efficiently ...
19
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1answer
250 views

Is there a geometrical picture for adiabatic quantum computation?

In adiabatic quantum computation (AQC), one encodes the solution to an optimization problem in the ground state of a [problem] Hamiltonian $H_p$. To get to this ground state, you start in an easily ...
0
votes
1answer
89 views

Confusion with the proof of constraints for a particular adiabatic quantum evolution

[This might be related to one of my previous unanswered questions.] This proof belongs to the paper, How to Make the Quantum Adiabatic Algorithm Fail by Edward Farhi, Jeffrey Goldstone, Sam Gutmann ...
3
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1answer
91 views

Questions about Farhi's pre-Adiabatic paper

I have been going through Eddie Farhi's 6-pages long pre-Adiabatic paper, An Analog Analogue of a Digital Quantum Computation. I guess I understand most of the math and physics but I am struggling ...
6
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0answers
172 views

Local Hamiltonian and combinatorial search problems

I was going through the PhD thesis of Daniel Nagaj. At the beginning of chapter two he indicated a relation between the local Hamiltonian perspective of adiabatic quantum computation and combination ...
7
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0answers
259 views

Implication of Bell test loopholes on Vazirani-Vidick random sequence generation scheme

I am trying to imagine what would be the implications of the loopholes on Bell test on the random sequence generation scheme proposed by Vazirani and Vidick (VV protocol) in the paper titled '...
7
votes
2answers
862 views

Application of methods from dynamical system to the study of k-SAT and similar problems

I am looking for literature (survey and non-survey papers) about transforming the k-SAT problem (or similar problems) into a system of Ordinary Differential Equations (ODEs) and study the solution ...
3
votes
1answer
3k views

Quantum annealing vs adiabatic quantum computation

I had this impression that quantum annealing is an optimization technique which may or may not produce exact solutions. On the other hand adiabatic quantum computation always gives exact solutions ...
22
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1answer
398 views

Exact planar electrical flow

Consider an electrical network modeled as a planar graph G, where each edge represents a 1Ω resistor. How quickly can we compute the exact effective resistance between two vertices in G? ...
29
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7answers
8k views

Should we consider $\mathsf{P} \neq \mathsf{NP}$ a law of nature?

Many experts believe that the $\mathsf{P} \neq \mathsf{NP}$ conjecture is true and use it in their results. My concern is that the complexity strongly depends on the $\mathsf{P} \neq \mathsf{NP}$ ...
0
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1answer
246 views

What's the nature of hypercomputing and relativity?

Somewhere I read something like "a hypercomputer rotating around a rotating black hole" would have some esoteric properties e.g. would produce other answers than other hypercomputers and other ...
7
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3answers
3k views

Are Shannon entropy and Boltzmann entropy mutually convertible?

Are Shannon entropy and Boltzmann entropy mutually convertible, much like mass and energy according to Einstein's formula?
16
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1answer
1k views

Feasibility of Gödel machines

Recently I stumbled upon quite an interesting theoretical construct. A so called Gödel machine It's a general problem solver which is capable of self-optimization. It's suitable for reactive ...
10
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3answers
355 views

Reductions of hard problems to physical models

I am looking for examples of hard problems (in NP or harder) from computer science which can be reduced to models of physical processes. For example, max-2-sat can be reduced to energy minimization ...
6
votes
3answers
1k views

Physical realization of nonlinear operators for quantum computers.

I have read in a paper where nonlinear operators for quantum computers implies the solving of problems in #P time. See http://arxiv.org/pdf/quant-ph/9801041 . What would be the simplest realization of ...
18
votes
1answer
600 views

Does cryptography have an inherent thermodynamic cost?

Reversible computing is a computational model that only allows thermodynamically reversible operations. According to Landauer's principle, which states that erasing a bit of information releases $kT ...
5
votes
1answer
315 views

How efficiently can a 1-sparse Hamiltonian be simulated (quantum mechanically)?

In quantum computation there is a fair amount of interest in the task of simulating quantum physics. One instance of this is the problem of simulating the evolution of a system under the action of ...
32
votes
2answers
1k views

Consequences of $SAT \in BQP$

As a TCS amateur, I'm reading some popular, very introductory material on quantum computing. Here are the few elementary bits of information I've learned so far: Quantum computers are not known to ...
16
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3answers
900 views

Is there a name for “physical things out of which one can build a Turing machine”?

One of the amazing things about computer science is that the physical implementation is in some sense "irrelevant". People have successfully built computers out of several different substrates -- ...
5
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2answers
550 views

Isolation in Turing-complete reversible cellular automata

I don't know much about the terminology and the results on cellular automata, but I would like to ask a question about an conjecture I thought. Consider Turing-complete reversible cellular automata. ...
9
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5answers
504 views

Natural computation based on fundamental forces

Well-known examples of computation inspired by natural phenomenon are quantum computers and DNA computers. What is known about the potential and/or limitations of computing with Maxwell's laws or ...