Questions tagged [quantum-computing]

Quantum computation and computational issues related to quantum mechanics

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Oracle separation between coNP and QMA implies oracle separation between NP and QMA

In [this] paper, Aaronson remarks (page 2, footnote) that: From the BBBV lower bound for quantum search [6], one immediately obtains an oracle $A$ such that $coNP^{A} \not\subseteq QMA^{A}$ for ...
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Witness verifiable quantum advantage

Update: A slightly different version of this question has been answered here. As far as I can see, a major issue with Google's recent quantum supremacy claim is that it is hard to verify the results. ...
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Diagonalization arguments for QMA type proof systems

Diagonalization is a very common technique to find oracle separations. For example, it can be used to separate $\cal{P}$ and $\cal{NP}$, with the essential idea being that of constructing an oracle in ...
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Is there an analogue of QMA where Merlin gives Arthur unitaries rather than states?

$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$Is there an analogue to $\mathsf{QMA}$ where Merlin provides to Arthur single-use access to a unitary operator $U$? By ...
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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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What would a very simple quantum program look like?

In light of the announcement of the world's first programmable quantum photonic chip, I was wondering just what software for a computer that uses quantum entanglement would be like. One of the first ...
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Proof that Entanglement Cannot Increase the Capacity of a Noiseless Classical Channel

I am aware that quantum entanglement cannot increase the asymptotic capacity of a noiseless classical channel. However, can anyone provide some type of reference in the literature that contains a ...
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Quantum evasiveness conjecture?

A property of simple $n$-vertex graphs is said to be evasive if its deterministic query complexity is exactly maximal, $\binom{n}{2}$ (that is, the best algorithm must query all $\binom{n}{2}$ ...
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Quantum Grover Algorithm

I have 6 different grover oracles out of which I know the 4th one is an incorrect oracle. 1st Oracle return 01 with 100% probability, 2nd 00 with 100% probability, 3rd, 4th and 5th with 10, 01 and 00 ...
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Oracle Construction for Grover's Algorithm

In Mike and Ike's "Quantum Computation and Quantum Information", Grover's algorithm is explained in great detail. However, in the book, and in all explanations I have found online for Grover's ...
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Approximately sampling from convex polyhedrons with quantum computers

Quantum computers are very good for sampling distributions that we don't know how to sample using classical computers. For example if $f$ is a Boolean function (from $\{-1,1\}^n$ to $\{-1,1\}$) that ...
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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 ...
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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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Quantum Computing: project ideas

I'm an undergraduate computer science student and I'm currently taking a course in the field of quantum computing requiring projects. I've read already a huge number of articles but still cannot come ...
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Proof: Why are MM-1QFA strictly more powerful than MO-1QFA? // Quantum automata

While dealing with quantum finite automata (QFA), I repeatedly come across the statement that measure-many QFA (MM-1QFA, KW97) are strictly more powerful than measure-once QFA (MO-1QFA, MC97). More ...
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Does MIP* = RE algebrize?

Does the MIP* = RE result algebrize? (It doesn’t relativize, as noted here.) If it doesn’t algebrize, is there a more complicated similar notion that it does satisfy?
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What would be the next step after quantum computing? [closed]

Is their anything that would make Quantum computing obsolete in the future? I know a Matrioksha Brain is the most powerful theoretical computer; but it probably won’t ever be realized. Too large and ...
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Is the wording of Google's QC Supremacy valid?

Quantum supremacy using a programmable superconducting processor was published today. Scott Aaronson posted a few weeks ago a post about this paper and it was clear we will see a Nature or Science ...
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Complexity of finding automorphism group of code

What is the computational complexity (may be both classical or quantum) for finding automorphism group of a general linear code? Is there better bound on complexity if structure of code is known for ...
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Are there problems that can be solved in time $2^{n-q^c}$ with $q$ qubits?

This is another attempt to formalize my former question on the topic. I'm looking for a problem for which all known classical algorithms take exponential time, but given ANY number of few qubits (...
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Quantum Money where not even the Bank can counterfeit

The Quantum Money system proposed in "Quantum Copy-Protection and Quantum Money" has the following properties: The bank can produce bank notes in the form of quantum states. Anyone can verify that ...
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Quantum advantage beyond the black-box model

Question Aaronson wrote in his thesis that “essentially all quantum algorithms that we know today—from Shor’s algorithm, as discussed previously, to Grover’s algorithm, to the quantum adiabatic ...
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PPAD and Quantum

Today in New York and all over the world Christos Papadimitriou's birthday is celebrated. This is a good opportunity to ask about the relations between Christos' complexity class PPAD (and his other ...
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Qubit gates in google supremacy

The gates in quantum supremacy experiment are nearest-neighbor and have spatial locality. Would this additional information help bolster IBM's argument to perhaps simulate quantum supremacy experiment ...
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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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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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Oracular separations between poly- and log-depth quantum circuits

The following problem appears in Aaronson's list Ten Semi-Grand Challenges for Quantum Computing Theory. Is $\mathsf{BQP}=\mathsf{BPP}^{\mathsf{BQNC}}$ In other words, can the "quantum" part of any ...
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Hidden subgroup problems in a tower of subgroups

Let $H$ be a hidden subgroup of $G_1$ that is indistinguishable from subgroup $H^{\prime}$ by quantum Fourier sampling. Now take a larger group $G_2$ such that it contains $G_1$. Now if I do quantum ...
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Quantum security of cryptosystems

One of the main candidates for PQ cryptography is code based cryptography (other than lattice based). The Niederreiter cryptosystem based on goppa codes is shown to be resistant to hidden subgroup ...
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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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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 ...
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Grover's algorithm, M out of N, when M is large

The more general version of Grover's algorithm searches for one of $M$ entries that match a criterion, out of $N$ total entries. I have seen it written that this takes $O(\sqrt{N/M})$ iterations, to ...
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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 there any quantum analog of the VP vs. VNP problem?

From Wikipedia: $\mathsf{VP}$: The class VP is the algebraic analog of P; it is the class of polynomials $f$ of polynomial degree that have polynomial size circuits over a fixed field $K$. $\...
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Why exactly are complexity theorists interested in closed timelike curves?

Context: There are several papers that study the implications of closed timelike curves (CTCs) to quantum complexity. In 2008, Aaronson and Watrous published their famous paper on this topic which ...
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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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List of quantum-inspired algorithms

Advances in quantum computing have led to the development of new classical algorithms. Notable recent examples are quantum-inspired algorithms for linear algebra: A quantum-inspired classical ...
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What can be some bachelor thesis ideas in Quantum random walks?

Note: Cross-posted on Quantum Computing Stack Exchange. I am an undergraduate, reading about quantum information and quantum technology. For about some time, I have been interested in the ...
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Notation for a Conditional Hamiltonian Evolution Operator

I am reading Harrow, Hassidim, and Lloyd's paper Quantum algorithms for linear systems of equations. On the third page of that paper, they write Next we apply the conditional Hamiltonian evolution $...
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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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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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whether two sets of stabilizer generators are related by a Clifford circuit

I have two stabilizer models each specified with a given set of generators. Let's call the two generating sets $S_1$ and $S_2$. By stabilizer model, I mean putting the generators on unit cells of a ...
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QMA definition of difference between probabilities intuition

I'm reading about the complexity classes related to quantum computation, currently I'm studying QMA class. A language is in QMA(c,s) if there exists a polynomial time verifier and polynomial $p(n)$ ...
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BQNC and Abelian Hidden Subgroup Problem

We know integer factorization is in $BPP^{BQNC}$ from Cleve and Watrous. Is Abelian Hidden Subgroup Problem also in $BPP^{BQNC}$? In particular is Discrete Logarithm in $BQNC$ or at least in $BPP^{...
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Complexity of enumerating over promise problems and circuits?

Given an enumeration over all Turing Machine which run with increasing length, is there a ``complexity class'' which describes the complexity of determining whether a given TM satisfies the promise ...
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Why is finding the ground state of a Hamiltonian in QMA?

Why is finding the ground stte of a Hamiltonian in QMA? It's in QMA to figure out if a hamiltonian has any energy eigenvalue within a certain window range which is at least inverse polynomial in size....
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Complexity class of approximating perfect match count

We know we can approximate perfect matching count of bipartite and approximate volume of convex bodies in randomized polynomial time. Is there any evidence these approximations could be in Nick's ...
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Relatively low ambitious frontiers

What are some of the current "relatively" low ambitious frontiers for MA/PhD thesis in complexity theory class separations/containment or quantum computing? For example: In the draft version of Arora ...
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Efficient quantum algorithm for CLASSICAL FFT

Is there a known improvement on the current O(n*log(n)) algorithm for CLASSICAL FFT using quantum computation? 'n' is the number of samples. I need to find the amplitude and phase of the K dominating ...

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