Questions tagged [quantum-computing]

Quantum computation and computational issues related to quantum mechanics

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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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201 views

Quantum oracle for non-negative vector

I was wondering if anyone knew on whether it is possible to construct a quantum oracle that was able to detect whether a given state vector was "non-negative"? Essentially I have a classical problem ...
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703 views

Qubits and permutation symmetry

To put it straight - are qubits fermions, bosons or else? For example, the Bell states that are frequently used in quantum computations have different symmetry (00 + 11 is symmetric, 10 - 01 is ...
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218 views

Results comparing BQP and NEXP

Are there oracle results with $$P=NP\neq BQP=NEXP\mbox{ and }P=NP\neq BQP\neq NEXP?$$ Also is there a $PCP$ characterization of $BQP$ like $$PCP(O(poly(n)),1)=PCP(O(poly(n)),O(poly(n)))=NEXP?$$
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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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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 ...
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466 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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151 views

Given a subset of of the hypercube and an affine transform of it, find the affine map

This is a follow up to this resolved question. Suppose we are given a set of bitvectors $A\subseteq\mathbb{F}_2^d$ and an invertible affine transformed copy of it $$B=\{Mx + s\mid x\in A\}$$ for some ...
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theorems for universal set of quantum gates for SU(d)

It seems that there is a theorem that for prime dimension d, the set of Clifford gates and one non-Clifford gate together forms a universal set of quantum gates for SU(d). It also seems that for a ...
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Is it possible to MAC a quantum state with a classical key under reasonable assumption?

Assume that classical one-way functions secure against quantum adversaries exist. Is it possible, given a quantum state $Q$ and classical secret key $k$, produce a quantum state $AuthQ$ such that: ...
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247 views

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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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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192 views

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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335 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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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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161 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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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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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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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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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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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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370 views

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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362 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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Differences between Quantum Computing and Parallelism [closed]

What are the differences between Quantum Computing and Parallelism? thanks in advance
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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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852 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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521 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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161 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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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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264 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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145 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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173 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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490 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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187 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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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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234 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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104 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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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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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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379 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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1answer
116 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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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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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

How exactly is solving the random circuit sampling problem a computation in the Church-Turing thesis sense? [closed]

Note: This has been cross-posted to Quantum Computing SE. If we assume $\mathsf{BQP} \neq \mathsf{BPP}$, then we can say with reasonable certainty that Google's random sampling experiment falsifies ...

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