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17 votes
Accepted

What does a tangible Quantum-Gate look like?

You seem to have the idea that a quantum gate is a physical thing rather than just a conceptual thing. It doesn't necessarily work that way. While CMOS gates are usually actual physical devices, ...
16 votes

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

P and BQP are decision-problem classes, i.e. the correct output is always a deterministic functions of the inputs. The only question is whether randomness helps "along the way" to speed up computing ...
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13 votes
Accepted

Quantum algorithms for QED computations related to the fine structure constants

The general belief seems to be that the expansion in $\alpha$ is an asymptotic series but not a convergent series. The handwaving estimate is that in $\sum_k c_k \alpha^k$, the scaling for the ...
  • 558
12 votes

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

The questions touches on some very interesting issues regarding quantum computation (and randomness). BQP is the class of decision problems that can be solved efficiently (in polynomial time) but it ...
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10 votes

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

If quantum computers can simulate in polynomial time the Standard Model, which is a quite complicated quantum field theory, then probably the Standard Model does not provide any extra computational ...
9 votes
Accepted

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

I extend my comment in an answer. By rewriting $e^{i \cdot sgn(\mu)\theta} = \cos(sgn(\mu)\theta)+i\sin(sgn(\mu)\theta) = \cos(\theta)+i \cdot sgn(\mu)\sin(\theta)$ we have: $Det_\theta(A) = \cos(\...
  • 1,854
9 votes

Isn't it "trivial" to represent/reduce any classical physics problem into a Spin-Glass which is NP-Complete?

Classical physical problems often involve real-number positions or parameter values rather than values from a discrete set (such as the integers) which would be more typical of NP-complete problems. ...
9 votes
Accepted

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

I'm not 100% sure what the question is about, but the title seems to ask about computation that allows failure. There is a lot of work on noisy (erroneous) computation in the sense that I think you ...
9 votes

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

You appear to be positing a universe where (a) the fine-structure constant has an exact value and (b) we can measure as many digits of it as we want. Thus, if a Turing machine cannot compute the exact ...
8 votes
Accepted

Quantum annealing vs adiabatic quantum computation

Adiabatic quantum computing (AQC) is a computational model (as Peter said in the comments). Compare AQC with other models of computation such as: circuit-based quantum computing (CBQC) Adleman-...
8 votes

Stephen Hawking's impact on computer science

He didn't have any major impact on computer science. His writing in computer science are limited to popsci and more recently raising public concerns about AI.
8 votes
Accepted

Quantum Money where not even the Bank can counterfeit

There are proposals for quantum money where it appears that not even the bank can produce two copies of a quantum money state with the same serial number. See Farhi et al's paper Quantum Money from ...
7 votes

Stephen Hawking's impact on computer science

The Black Hole Information Paradox seems relevant to me, as it concerns information theory, which can be seen as close to computer science. To sum up, the paradox in question is that when objects or ...
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7 votes
Accepted

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

Yes, if you somehow had a scheme that allows to compute/measure more and more digits of the fine-structure constant $\alpha$ then $\alpha$ should be Turing computable according to the Church-Turing ...
6 votes
Accepted

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

Clearly you can work with abstract compressed representations of circuits. You can reason about them and manipulate them and turn them into concrete lists of gates. We do it all the time. But in ...
  • 1,468
6 votes

Is it possible to infer on the thermodynamics of two problems if a reduction from $B$ to $A$ exists?

With thermodynamics you have to be careful with the kind of reductions you allow, or (as Peter Shor pointed out) there can be essentially no thermodynamic relationship implied by a reduction. For ...
5 votes

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

[The following is more an extended comment with pointers than a real answer.] If you were in France, a good answer would be combinatorial physics. I say "if you were in France" because, for reasons ...
5 votes
Accepted

Dimension of the Fourier transform for $S_5$

A quantum Fourier transform is a unitary operation, so the number of basis states of the input and output must be the same. The number of basis states before the Fourier transform is 120, the number ...
5 votes

Stephen Hawking's impact on computer science

Not a direct answer but something : He is mentioned 19 times in these lecture notes of Scott Aaronson, https://www.scottaaronson.com/barbados-2016.pdf That says something, I guess? :D
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4 votes
Accepted

The Arrow of Time in a Non-Physical Realm

For the consequences of such transmission to theoretical computer science (the only aspect of your question that is on-topic here) see Aaronson and Watrous's "Closed Timelike Curves Make Quantum and ...
4 votes
Accepted

The Maxwell's Demon and Computer Science

A good place to start looking at these ideas is this paper, though it talks about the (related) idea of information and thermodynamics. It relates fundamental computational tasks (eg. editing a bit) ...
4 votes
Accepted

Applications of Takens' theorem to TCS?

Takens himself did some CS work although not TCS work. He did some attractor reconstruction stuff with neural networks, for example (https://clgiles.ist.psu.edu/papers/NC-2000-learning-chaos-nn.pdf) ...
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4 votes

Stephen Hawking's impact on computer science

He gave a little indirect concrete (not theoretical) contribution to assistive technologies: Stephen Hawking's speech tech released by Intel: "... Software that helps Prof Stephen Hawking to speak ...
4 votes

Is it proved that error rate of quantum computation is bounded by constant rather than a function dependent on time and environment by quantum theory

As far as I know, nobody has come up with a convincing physics reason that fault-tolerant quantum computing is fundamentally impossible. However, it is a formidable engineering task, which is why we ...
3 votes
Accepted

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

From what I understand, it is partially because we don't have any techniques currently that take advantage of structure of the hidden subgroup itself. Weak Fourier sampling solves the problem whenever ...
3 votes

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

Rabie introduced the model of "Rusted Turing Machines" in his thesis: The Power of Weaknesses:What can be computed with Populations, Protocols and Machines (Chapter 7). The idea is that there is a ...
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3 votes

How could God authenticate in one message?

God could (a) provide a proof that factorization was hard and (b) use the idea of the OP to show us that He can factor large numbers. (Of course, this doesn't work if you think factorization is easy ...
2 votes

Physics results in TCS?

I know some examples in machine learning. It is very common for thermodynamic ideas to be used in this area: Boltzmann machine, Hopfield network, Wake-sleep algorithm. Markov Chain were initially used ...
2 votes
Accepted

Isn't it "trivial" to represent/reduce any classical physics problem into a Spin-Glass which is NP-Complete?

It was only recently (2016) that it was proved mathematically that all of classical spin physics can be reproduced by the 2D Ising Model with linear terms (what physicists call "fields") with at most ...
2 votes

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

The Church-Turing thesis is about (partial) functions $\mathbb{N} \to \mathbb{N}$ (or $\Sigma^* \to \Sigma^*$ for a finite alphabet $\Sigma$). How do you define a definite value based on some random ...

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