Questions tagged [quantum-computing]

Quantum computation and computational issues related to quantum mechanics

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23
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1answer
448 views

Approximately sampling from convex polyhedrons with quantum computers

Quantum computers are very good for sampling distributions that we dont know how to sample using classical computers. For example if f is a Boolean function (from $\{-1,1\}^n$ to ${-1,1}$) that can be ...
12
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2answers
580 views

What is the Relationship between QMA and AM?

I read in S. P. Jordan, D. Gosset, P. J. Love's "$QMA$-complete problems for stoquastic Hamiltonians and Markov matrices" that it is unlikely that $QMA \subseteq AM$. I was surprised about this ...
20
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2answers
767 views

Are there descriptive complexity representations of quantum complexity classes?

The title more or less says it all, but I guess I could add a bit of background and some specific examples I'm interested in. Descriptive complexity theorists, such as Immerman and Fagin, have ...
32
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1answer
1k views

$BQP$ vs $QMA$?

The central problem of complexity theory is arguably $P$ vs $NP$. However, since Nature is quantum, it would seem more natural to consider the classes $BQP$ (ie decision problems solvable by a ...
12
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1answer
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Clifford group quantum operations and classical computation

The Clifford group of quantum operators is generated by the quantum operations: Controlled-Z, Hadamard, and Phase ($= |0\rangle\langle0| + i |1\rangle\langle1|$). A circuit composed only of these ...
9
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2answers
376 views

The complexity of Area-lawed Hamiltonians

I have recently thought about "importing" some physics-related question into quantum CS: The notion of the area-law phenomenon in Hamiltonian systems usually stands for a local Hamiltonian on some ...
20
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2answers
1k 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 ...
30
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2answers
3k views

Quantum matrix multiplication?

It doesn't seem like this is known - but are there any interesting lower bounds on the complexity of matrix multiplication in the quantum computing model? Do we have any intuition that we can beat ...
22
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1answer
1k views

How does the BosonSampling paper avoid easy classes of complex matrices?

In The computational complexity of linear optics (ECCC TR10-170), Scott Aaronson and Alex Arkhipov argue that if quantum computers can be efficiently simulated by classical computers then the ...
10
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1answer
218 views

Dependent corrections in measurement-based Universal Blind Quantum Computation

In Universal Blind Quantum Computation the autors describe a measurement-based protocol which allows an almost classical user to perform arbitrary computations on a quantum server without revealing ...
8
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2answers
611 views

Quantum PCP and hardness of simulating of Hamiltonians

I have a few questions about Quantum PCP conjecture: What is the statement of the quantum PCP conjecture? What implications would Quantum PCP theorem have for simulating of Hamiltonians? Is it ...
22
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1answer
784 views

How much computational power fits into a cubic centimeter?

This question is a followup on the question about DNA algorithms asked by Aadita Mehra. In comments there, Joe Fitzsimmons said, in part: [T]he radius of the system must scale proportionately to ...
18
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4answers
802 views

If P = BQP, does this imply that PSPACE (= IP) = AM?

Recently, Watrous et al proved that QIP(3) = PSPACE a remarkable result. This was a surprising result to myself to say the least and it set me off thinking... I wondered what if Quantum Computers ...
6
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2answers
352 views

Energy cost of adiabatic quantum computation

I'm not sure whether this question is completely on-topic, since it is a physics-related question. But I'll ask anyway and apologize if I'm off-topic. In Adiabatic Quantum Computation is Equivalent ...
18
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7answers
24k views

Universities for Quantum Computing / Information?

Which universities have a strong quantum computing curriculum, and offer some type of quantum computing/information courses/research? The aim here is to collect a useful list for someone considering ...
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16answers
3k views

Physics results in TCS?

It seems clear that a number of subfields of theoretical computer science have been significantly impacted by results from theoretical physics. Two examples of this are Quantum computation ...
8
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2answers
451 views

Understanding QMA

This question comes out of an answer Joe Fitzsimons gave to a different question. Most natural complexity classes have a one-line "intuitive description" that helps characterize core problems in that ...
13
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2answers
584 views

One-shot quantum hitting times

In the paper Quantum Random Walks Hit Exponentially Faster (arXiv:quant-ph/0205083) Kempe gives a notion of hitting time for quantum walks (in the hypercube) that is not very popular in the quantum ...
11
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2answers
2k views

Does the trace norm of the difference of two density matrices being one imply these two density matrices can be simultaneously diagonalizable?

I believe the answer to this question is well-known; but, unfortunately, I don't know. In quantum computing, we know that mixed states are represented by density matrices. And the trace norm of the ...
27
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2answers
891 views

Approximate counting problem capturing BQP

In the black-box model, the problem of determining the output of a BPP machine $M(x,r)$ on input $x$ is the approximate counting problem of determining $E_r M(x,r)$ with additive error 1/3 (say). Is ...
21
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3answers
878 views

Is BQP equal to BPP with access to an Abelian hidden subgroup oracle?

Is BQP equal to BPP with access to an Abelian hidden subgroup oracle?
11
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7answers
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Quantum Computation - Postulates of QM

I have just started (independent) learning about quantum computation in general from Nielsen-Chuang book. I wanted to ask if anyone could try finding time to help me with whats going on with the ...
24
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3answers
863 views

Can we quantify the “degree of quantumness” in a quantum algorithm ?

Entanglement is often held up as the key ingredient that makes quantum algorithms well... quantum, and this can be traced back to the Bell states that destroy the idea of quantum physics as a hidden-...
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2answers
892 views

$\ell_p$-norm preserving Turing machines

Reading some recent threads on quantum computing (here,here, and here), make me remember an interesting question about the power of some kind of $\ell_p$-norm preserving machine. For people working ...
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6answers
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Ternary (and beyond) computation and quantum computing?

Binary math is at the heart of most computing, in large part because of the ease with which two energy states can be achieved. I have always thought that having more states could improve computing ...
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0answers
605 views

Learning quantum CS [duplicate]

Possible Duplicate: What is the quantum computational model? What is the best way to study quantum branch of CS for the person with rather advanced background in classical CS? Does one need to ...
12
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6answers
5k views

Quantum computing project ideas

I'm undergraduate computer science student and I'm currently planning for my graduation project. I need some ideas in quantum computing field. any help?
32
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11answers
2k views

What is the quantum computational model?

I have occasionally heard people talk about quantum algorithms and about states and the ability to consider multiple possibilities at once, but I have never managed to get someone to explain the ...
20
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4answers
666 views

Is there an equivalent to derandomization for quantum algorithms?

With some randomized algorithms you can derandomize the algorithm, removing (at a possible cost in run time) the use of random bits and maximizing some lower bound on the objective (usually computed ...
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3answers
955 views

Graph Isomorphism and hidden subgroups

I'm trying to understand the relationship between graph isomorphism and the hidden subgroup problem. Is there a good reference for this ?
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3answers
732 views

Are there any known implementations for quantum computing constructs?

Quantum Computation is an active area of research that aims to take advantage of quantum physics (e.g. quantum entanglement) to advance the efficiency capabilities of computers (does not alter the ...