Questions tagged [quantum-computing]

Quantum computation and computational issues related to quantum mechanics

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Is it possible to design an efficient approximation algorithm for one NP-complete problem based on Shor's algorithm?

Is it possible to design an efficient approximation algorithm for an $\sf{NP\text{-}complete}$ problem based on reductions from Shor's algorithm? Are known any (classical) approximation algorithms ...
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135 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 ...
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Techniques for lower bounding spectral gaps in the quantum adiabatic algorithm

In the quantum adiabatic algorithm, one prepares the ground state of a Hamiltonian $H_{i}$, and then evolves the Hamiltonian slowly over time to a target Hamiltonian $H_{f}$ via the interpolation $H(s)...
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347 views

Quantum cellular automata

This questions is cross-posted from MathOverflow A little background: As far as I know there is no standard definition of a quantum cellular automaton in the literature. Different authors use ...
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160 views

Probabilistic and quantum analog of $FP$ and $FNP$?

Is there any analog of the computational classes $FP$ and $FNP$ with probabilistic or quantum Turing machines? If so, what are the relation with other computational classes?
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Is there a universal gate set for classical probabilistic computing?

We know that NAND gates are universal for deterministic classical circuits, Toffoli gates are universal for reversible deterministic classical circuits, and Clifford+T is universal for quantum ...
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Dequantumizability known and unknown?

Dequantumizable problems have been taking some headlines these days (for example https://www.scottaaronson.com/blog/?p=3880 and https://www.quantamagazine.org/teenager-finds-classical-alternative-to-...
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Why primitive rotation is $53.13^\circ$ in the quantum Turing machine used by Vitanyi for Quantum Kolmogrov Complexity?

Right now I am going through Quantum Kolmogorov Complexity Based on Classical Descriptions by Vitanyi. In the introduction, the author assumed the primitive rotation $\theta = 53.13^\circ$ to have ...
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Two questions on Shor's algorithm

Does Shor's algorithm produce factors of a $n$-bit number and discrete log modulo $n$-bit prime in $O((\log n)^{2+\epsilon})$ bit operations using fast multiplication? I am trying to read from ...
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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 ...
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117 views

Is black box parallel quantum speedup ever nontrivial?

Grover's algorithm is not parallelizable, in that $p$ quantum processors searching over $n$ elements can't do better than $O(\sqrt{n/p})$ queries. Are there any oracle problems where quantum ...
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Consequences of $NP\subseteq P/poly$ to $BQP$

A post here Consequences of $BQP \subseteq P/poly$? queried on Consequences of $BQP \subseteq P/poly$. It is not known if $NP\subseteq BQP$. In general, what are the consequences of $NP\subseteq P/...
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359 views

When is a non-unitary quantum system only theoretical?

Suppose we construct a non-unitary quantum system α in hilbert space. It entails that this system would have no direct parallel in quantum circuitry as it is a requirement that all quantum gates ...
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String theory based computations

I was reading Arora and Barak's book on computational complexity and in the section on 'criticism on Turing machine model and the class P' along with quantum computer it also mentions possibilities of ...
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500 views

Numerical accuracy of superpositions in quantum computers

I am new to the topic of quantum computers (though I am very familiar with both quantum and computers, and I have studied Shor's paper about his eponymous algorithm at some point). Still, I have the ...
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732 views

Continued Fraction Algorithm in Shor's Algorithm

I am just trying to make the final link of Shor's algorithm clear. Here $r$ is the order of $x$ modulo $N$. We have a number $\psi$, which for a rational number $\dfrac{s}{r}$ satisfies \begin{...
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177 views

Efficient generation of permutational invariant quantum states

Starting from $|00\cdots 0\rangle$, can permutational invariant quantum states, i.e. the following one: $$ |\psi_n\rangle = \frac1{n!} \sum \prod_{\pi\in S_n} |\pi(0)\rangle|\pi(1)\rangle\cdots|\pi(n-...
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465 views

Is the D-Wave architecture a close implementation of quantum interactive proof?

A very high level architecture is, as mentioned here, shown in this picture. The component on the left is classical while the one on the right is the D-Wave box. I understand that in QIP, Arthur is ...
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308 views

How does one determine if a mixed bipartite quantum state is entangled or not?

My question is based on the structure of the NP-hardness proof in section 6 (page 17) of this paper, http://arxiv.org/pdf/quant-ph/0303055v1.pdf Mathematically one can think of being given a positive ...
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160 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 \...
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95 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 ...
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What is 'circuit problem' mentioned in Kempe-Kitaev-Regev's local hamiltonian problem paper

I have been going through Kempe-Kitaev-Regev's paper The Complexity of the Local Hamiltonian Problem. In the first paragraph of page 3, the authors point out that: To the best of our knowledge, ...
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Papers on using resource states to implement QFT efficiently

I recently stumbled onto the idea of using a pre-existing re-usable phase gradient to implement the QFT, instead of having to keep re-applying exponentially precise phase gates. I'm looking for papers ...
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Clarification for argument in proof of search in N^1/3 queries with hidden variables/non-collapsing measurements

Let $N=2^n$. In Aaronson's Quantum Computing and Hidden Variables (1) and the recent follow up by Aaronson, Bouland, Fitzsimons, and Lee The space "just above" BQP (2), we consider models of ...
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258 views

Background Required to understand Quantum Monte Carlo techniques?

I'm trying to decide whether or not to do a project for a professor. The project involves writing a survey paper (of high enough quality to get his research group up to speed for a peripheral project)...
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310 views

The relationship between QCMA and QMA in the Turing and Communication model

First my background about computational complexity is still beginner. Recent paper published by Klauck and Podder [KP14] show that for the first time an exponential gap between computing partial ...
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139 views

Complexity class for quantum computer with commutative gates

BQP is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances. In quantum computer allowed operations can be ...
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169 views

Why spectral norms are used for computing the complexity of adiabatic Hamiltonian?

In the context of adiabatic quantum computation the spectral norm was first used in the first adiabatic paper by Farhi et. al. when he demonstrated the relation of it to the conventional quantum ...
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482 views

Quantum complexity of maximum inner product search

Given two matrices $X \in \mathbb{R}^{m \times k}$, $Y \in \mathbb{R}^{n \times k}$, maximum inner product search (MIPS) asks for the largest $l$ entries of $X Y^T$. Typically $k \ll m, n$ (many ...
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186 views

Understanding efficient classical simulation of quantum computing

I want to understand the Gottesman-Knill theorem, which basically says that using some subclass of unitary transformations (from the Clifford group) there is no quantum speed-up ie. we can simulate ...
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60 views

Hardness of ancilla free quantum circuit extraction from circuit with ancillas

Is there any known result regarding the hardness of the following problem: Given a quantum circuit with ancillae implementing a unitary, find a quantum circuit that does not use any ancillae that ...
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230 views

Convexity argument in QMA Amplification

I'm interested in the basic amplification procedure for QMA: the prover sends $O(r)$ copies of his witness to the verifier, which decreases the error probability to $2^{-O(r)}$ (Chernoff bound). The ...
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103 views

Quantum annealing or adiabatic quantum optimization with continuous optimization problems

How do quantum annealing or adiabatic quantum optimization deal with continuous optimization problems such as SDP?
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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 ...
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Are NQP and QMA comparable?

Both definitions try to create a quantum analog for NP. NQP's definition comes from non-deterministic algorithms: it contains languages for which a Quantum Algorithm accepts with non-zero probability ...
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Why is Shor's algorithm in $BPP^{BQNC}$ when needing to uncompute subprocedure call?

Why is Shor's algorithm in $BPP^{BQNC}$? It's true the quantum Fourier transform is in $BPP^{BQNC}$, but the algorithm needs to call a number theoretic function f which has period p which is a factor ...
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201 views

Environment-assisted quantum transport computation

The paper below and the news story based on it describe a new form of computation based on what they call environment-assisted quantum transport (ENAQT). ENAQT involves a combination of quantum and ...
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Impacts of quantum computing on Theoretical Computer Science [closed]

Using quantum computers we can do calculations very fast. However from a layman's view, I want to know the impact of quantum computers have on Theoretical computer science.
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Polynomial Quantum Algorithm for Graph Isomorphism? [duplicate]

Possible Duplicate: NP-intermediate problems with efficient quantum solutions Many suspect that quantum computers will not be able to efficiently solve NP-complete problems and thus focus on the ...
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372 views

Time-entanglement phenomenon

Please let me mention certain idea here, although it is probably vague (and new, at least as related to experiment mentioned below, as far as I know). The general notion of algorithm is model of ...
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2k views

Differences between Quantum Computing and Parallelism [closed]

What are the differences between Quantum Computing and Parallelism? thanks in advance
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105 views

Is it possible to encrypt quantum states under reasonable assumptions?

Is it possible to encrypt a quantum state, such that a $BQP$ attacker who does not know the secret key cannot obtain any information about the original state, but a $BQP$ decryptor with the key can ...
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1answer
2k views

Is quantum annealing faster than simulated annealing/genetic/other state-of-the-art optimization algorithms?

There's the idea of quantum annealing being used to solve optimization problems in terms of a QUBO problem for D-Wave's quantum algorithm. I understand that the advantage of quantum annealing as ...
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1answer
91 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 ...
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133 views

Lower bound on alternations needed in $BQP$ versus $PH$ result?

What is the fastest $f(n)$ the relatively new result of oracle separation of $\mathsf{BQP}$ from $\mathsf{PH}$ provides such that ${\#\mathsf{SAT}}\not\subseteq\mathsf{FP}^{\mathsf{PH}[O(f(n))]}$ ...
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222 views

Why are sub-normalized states studied in quantum computation?

By basic postulates of QM, any state of a system is described by a normalised density operator. Now i fail to see why people study sub-normalized states ( e.g.: In generalised fidelity etc). I'd be ...
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2k views

Using MATLAB's CVX Package for Semidefinite Programming in Quantum Information

I'm attempting to formulate the semidefinite programs used in the paper "Hedging Bets with Correlated Quantum Strategies" (specifically those on page 7) into CVX so that I can play around with the ...
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408 views

Simulating quantum measurements by unitaries

I have seen many papers in which quantum measurements are assumed to be replaced by unitaries. See this quotation from [KW00] for instance: Often we will describe quantum circuits in a high-level ...
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62 views

QPIP minimal client quantum capabilities

It is conjectured that classical (BPP) client blind quantum computing is implausible according to Aaronson et al: https://www.researchgate.net/publication/...
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Is graph automorphism Karp-reducible to graph isomorphism under hidden subgroup representation?

The classical representations of the graph automorphism problem is Karp-reducible to the classical representation of the graph isomorphism problem. The sketch of proof for this can be written as ...

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