Questions tagged [quantum-computing]

Quantum computation and computational issues related to quantum mechanics

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22
votes
1answer
786 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 ...
42
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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 ...
27
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2answers
2k views

NP-intermediate problems with efficient quantum solutions

Peter Shor showed that two of the most important NP-intermediate problems, factoring and the discrete log problem, are in BQP. In contrast, the best known quantum algorithm for SAT (Grover's search) ...
14
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1answer
655 views

Reading up on $BQP = BPP^{BQNC}$

What should I read to understand this problem? The power of small-depth quantum circuits. Is $BQP = BPP^{BQNC}$? In other words, can the "quantum" part of any quantum algorithm be compressed ...
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 ...
13
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6answers
6k 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?
14
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2answers
874 views

Quantum analogues of SPACE complexity classes

We often consider complexity classes where we are bounded in the amount of space our Turing machine can use, for example: $\textbf{DSPACE}(f(n))$ or $\textbf{NSPACE}(f(n))$. It seems that early in ...
10
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4answers
634 views

Bounding the gap between quantum and deterministic query complexity

Although exponential separations between bounded-error quantum query complexity ($Q(f)$) and deterministic query complexity ($D(f)$) or bounded-error randomized query complexity ($R(f)$) are known, ...
10
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1answer
562 views

What is the proof that quantum computers can efficiently simulate arbitrary quantum mechanical systems?

JBV suggested I turn some comments into a question, so here goes. Another question [1] asks about applications of QM computing. One answer [2] was "efficiently simulating quantum mechanics". ...
5
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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 ...
79
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2answers
9k views

Was the reduction in Shor's algorithm originally discovered by Shor?

This is a "historical question" more than it is a research question, but was the classical reduction to order-finding in Shor's algorithm for factorization initially discovered by Peter Shor, or was ...
18
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7answers
25k 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 ...
19
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3answers
5k views

Is there any connection between the diamond norm and the distance of the associated states?

In quantum information theory, the distance between two quantum channels is often measured using the diamond norm. There are also a number of ways to measure distance between two quantum states, such ...
20
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1answer
555 views

Consequences of $BQP \subseteq P/poly$?

While Adleman's theorem shows, that $\mathsf{BPP} \subseteq \mathsf{P}/\text{poly}$, I'm not aware of any literature investigating the possible inclusion of $\mathsf{BQP} \subseteq \mathsf{P}/\text{...
20
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4answers
667 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 ...
17
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5answers
3k views

Real world applications of quantum computing (except for security)

Let's assume that we have built an universal quantum computer. Except for security-related issues (cryptography, privacy, ...) which current real world problems can benefit from using it? I am ...
27
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5answers
853 views

Quantum proofs of classical theorems

I'm interested in examples of problems where a theorem which seemingly has nothing to do with quantum mechanics/information (e.g. states something about purely classical objects) can nevertheless be ...
20
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2answers
898 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 ...
19
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1answer
857 views

Why does Odlyzko improvement of Shor's Algorithm reduces the number of trials to $O(1)$

In his 1995 paper Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer, Peter W. Shor discusses an improvement on the order-finding part of his ...
14
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1answer
670 views

What is known about multi-prover interactive proofs with short messages?

Beigi, Shor and Watrous have a very nice paper on the power of quantum interactive proofs with short messages. They consider three variants of 'short messages', and the specific one I care about is ...
9
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2answers
802 views

Is adiabatic quantum computing as powerful as the circuit model?

Much of the quantum computing literature focuses on the circuit model. Adiabatic quantum computing is not based on applying a sequence of unitary operators, but on changing a time-dependent ...
50
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3answers
1k views

Rigorous security proof for Wiesner's quantum money?

In his celebrated paper "Conjugate Coding" (written around 1970), Stephen Wiesner proposed a scheme for quantum money that is unconditionally impossible to counterfeit, assuming that the issuing bank ...
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 ...
14
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1answer
705 views

Is there a quantum NC algorithm for computing GCD?

From the comments on one of my questions on MathOverflow I get the feeling that the question regarding GCD being in $\mathsf{NC}$ vs. $\mathsf{P}$ is akin to the question regarding Integer ...
10
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2answers
378 views

Restricting entries of unitary operators to real numbers and universal gate sets

In Bernstein and Vazirani's seminal paper "Quantum Complexity Theory", they show that a $d$-dimensional unitary transformation can be efficiently approximated by a product of what they call "near-...
23
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5answers
644 views

Universal sets of gates for SU(3)?

In quantum computing we are often interested in cases where group of special unitary operators, G, for some d-dimensional system gives either the whole group SU(d) exactly or even just an ...
19
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3answers
742 views

Is there a Quantum equivalent of the Time hierarchy theorem ?

My favourite theorem in complexity theory is the Time hierarchy theorem. However, this was done in 1965. I wanted to know then if there was anything similar for Quantum Computing. Also, if not ...
10
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1answer
420 views

Span programs, witness size, and certificate complexity

A span program is a linear-algebraic way of specifying a boolean function introduced here. Recently, this model was used to show that the negative adversary method provides a tight characterization (...
7
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2answers
319 views

Given a subset of the hypercube and a copy translated by s, find s

Problem: Suppose we are given an $n$ element subset $A\subseteq\{0,1\}^d$ of the $d$ dimensional hypercube and a translated copy $B= A+s$ by some secret $s\in\{0,1\}^d$. Find $s$ as fast as possible ...
8
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2answers
453 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 ...
1
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1answer
108 views

Is unbounded quantum fanout operation experimentally feasible?

It is known that the "unbounded quantum fanout operation" is very powerful: (See, for example, Hoyer et al. : http://theoryofcomputing.org/articles/v001a005/v001a005.pdf). In particular, it is known ...
10
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1answer
236 views

Lower bounds for quantum circuits using the geodesic framework

Some of us have been reading Michael Nielsen's paper on a geometric approach to using quantum lower bounds (in brief, the construction of a Finsler metric on $SU(2^n)$ such that the geodesic distance ...
7
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2answers
448 views

Quantum query complexity and certificate complexity

A certificate for an input $x$ is a subset of bits $S \subseteq \{1,...,n\}$ such that for all inputs $y$, $(\forall i \in S \quad y_i = x_i) \rightarrow f(y) = f(x)$. Then $C_x(f)$ is the minimum ...
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 ...
4
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0answers
184 views

Do the quantum communication complexity lower bounds hold when parties can send a “duplicated” qubits?

This question continues from the previous question where I mistakenly asked a question that is too general. In quantum communication complexity, we always assume that Alice and Bob have unlimited ...
4
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6answers
5k views

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 ...
3
votes
1answer
92 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 ...
3
votes
1answer
154 views

How well can an arbitrary (unknown) quantum state be imperfectly cloned?

How well can an arbitrary unknown (quantum) state $\rvert \psi \rangle = \alpha\rvert 0 \rangle + \beta \rvert 1 \rangle$, be imperfectly/approximately cloned? Given an unknown state ${\rvert \psi \...
0
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2answers
338 views

Are Alice and Bob allowed to copy qubits in quantum communication complexity model?

In quantum communication complexity, we always assume that Alice and Bob have unlimited computational power and are still prove lower bounds such as the $\Omega(n)$ lower bounds of parity. What ...