Questions tagged [quantum-advantage]
"Quantum advantage" or "quantum supremacy" is the potential ability of quantum computing devices to solve problems that classical computers practically cannot.
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Feynman method and polynomial time algorithm for XQUATH
Consider the Feynman algorithm for simulating quantum circuits, as given here.
Consider the XQUATH conjecture for random quantum circuits from here, given by
(XQUATH, or Linear Cross-Entropy Quantum ...
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Relation between approximate counting and sampling
Consider the following statement of Stockmeyer counting theorem.
Given as input a function $f:\{0, 1\}^{n} \rightarrow \{0, 1\}^{m}$
and $y \in \{0, 1\}^{m}$, there is a procedure that runs in ...
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When is a Quantum Computer Slower Than a Classical Computer?
Someone offhandedly mentioned to me that quantum computers are sometimes significantly (I guess they meant asymptotically) slower than classical computers.
Unfortunately, I didn't get any arguments ...
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Can I use Grover's algorithm on overlapping sets of qubits?
Let's say I have 3 qubits: $q_1,q_2,q_3$.
I want to apply Grover's algorithm on q1,q2, such that q1,q2 $\neq$ 10 and do the same for q2,q3, so that q2,q3 $\neq$ 11. The final possible combinations of ...
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How are quantum computers more powerful than classical computers? [duplicate]
I feel the answer to this question is just out of reach - I "understand" the implication that a quantum computer uses all combinations of bits simultaneously compared to a classic computer, ...
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Quantum hardness of XQUATH conjecture
Consider the XQUATH conjectures, as defined here (https://arxiv.org/abs/1910.12085, Definition 1).
(XQUATH, or Linear Cross-Entropy Quantum Threshold Assumption). There
is no polynomial-time ...
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What is the main advantage of using the Variational Quantum Eigensolver over a classical algorithm?
What is the main advantage of using the Variational Quantum Eigensolver (quantum computing) over a classical algorithm? I know a key fact is the speed-up, but how is this speed-up quantised.
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Has any analogue quantum simulator showed quantum advantage yet?
Quantum advantage/supremacy was achieved by Google using a quantum computer and more recently by Pan Jianwei's group using photons. So I was wondering, has any analog quantum simulator showed quantum ...
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Is it possible to design a Quantum Computing Advantage to deploy an application on the web?
I need to understand the frontier and practical applications of quantum computing.
Is it possible to design a Quantum Computing Advantage to deploy an application on the web, such as a browser, ...
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Generally speaking, are quantum speedups always due to parallelization of a given problem?
We know that quantum computers use the wave-like nature of quantum mechanics to perform interference. Sometimes we can use this interference to perform specific algorithms that will cause enough ...
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Quantum supremacy: shallow depth Haar random circuits and unitary designs
I had a confusion about shallow depth Haar random quantum circuits. In this paper, in Section B (related works), it is mentioned that Haar random quantum circuits form approximate $2$-designs only ...
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Q-means, QRAM and how it helps algorithmic speedup
I am trying to understand how QRAM will help improve algorithm performance. I am reading a paper on Q-means classification, but I have noticed that some other algorithms (Grovers) seem to have a ...
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Why does QAOA achieve quantum supremacy in an algorithmic sense?
In the paper Quantum Supremacy through the Quantum Approximate Optimization Algorithm the authors claim (last sentence of page 15):
"If [...] the QAOA outperforms all known classical algorithms ...
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Confusion about the output distribution of Haar random quantum states
Consider a Haar random quantum state $|\psi \rangle$. I was confused between two facts about $|\psi \rangle$, which appear related:
Consider the output distribution of a particular $n$-qubit $|\psi \...
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List of practical quantum computing algorithms that have speed-up higher than quadratic speed-up?
From this link (provided by @KAJ226's comment in this question), it appears as though current error correction methods are not enough to get practical speedup out of algorithms that have quadratic ...
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Can quantum computers speed up parsing?
Can quantum computers offer Grover-like speed ups in parsing of context-free languages? For instance, general CFLs can be parsed in $O(n^3)$ with standard algorithm like https://en.wikipedia.org/wiki/...
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Grover Algorithm vs Classical Search Algorithms
If Grover algorithm has a better speed than classical search algorithms, would it be an example of where Quantum computers outruns classical computers?
Can we use Grover Algorithm in real world ...
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Is Gaussian boson sampling (used for showing quantum advantage) a subcategory of the continuous variable approach?
I read about the photonic QC Jiŭzhāng that showed quantum advantage by Gaussian boson sampling. I read that boson sampling itself is a sub-universal technique of QC (where they use single-photon ...
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Could a new benchmark of quantum processors Q-Score by Atos be more useful than quantum volume?
A few days ago, Atos company published new benchmark for quantum computers. The benchmark is called Q-Score and it is defined as follows:
To provide a frame of reference for comparing performance ...
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Question regarding integration of Haar random state
I am trying to understand the integration on page 4 of this paper. Consider a Haar random circuit $C$ and a fixed basis $z$. Each output probability of a Haar random circuit (given by $|\langle z | C |...
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Comparing QSVM & Classic SVM on BigData. Quantum Supremacy
I work on comparing QSVM and Classic SVM (SKlearnSVM) with using Qiskit. I have to show
quantum supremacy at 400000-500000 samples but I don't get good results. I have problem with long time training ...
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Could random quantum circuits be efficiently approximately simulated?
Google's landmark result last year was to compute a task with a quantum computer that a classical computer could not compute, and they chose random circuit sampling. Part of their justification was ...
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How do quantum bits increase computational power?
I'm new to quantum computing, I'm learning how to use Qiskit. I'm trying to understand better how exactly the quantum characteristics of quantum computer help to increase its computational power. I ...
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Dirichlet distribution: posteriors and priors of distribution
Let $|\psi\rangle \in \mathbb{C}^{2n}$ be a random quantum state such that $ |\langle z| \psi \rangle|^{2} $ is distributed according to a $\text{Dirichlet}(1, 1, \ldots, 1)$ distribution, for $z \in \...
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What is the reason for the exponential speed-up of quantum computers? [duplicate]
In quantum computers the following two effects should be seen:
If an operator acts on an arbitrary qubit $Q_n$ of a quantum system $S$ consisting of several qubits than we get a new quantum system $S'...
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What is the advantage of quantum machine learning over traditional machine learning?
Why exactly is machine learning on quantum computers different than classical machine learning? Is there a specific difference that allows quantum machine learning to outperform classical machine ...
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When we do a linear fit, what is the correlation coefficient of the estimated parameters?
In Google's quantum supremacy experiment, supplementary Section VIIIH, they calculate the correlation coefficient of the linear fit coefficients $p_0$,$p_1$. I can't figure out the definition of this ...
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Does quantum computers give any advantage over classical computers in Sudoku?
To my basic knowledge I know that solving a generalized Sudoku problems is an NP-complete problem so, is there any possible way quantum computers give an advantage over classical computers in this ...
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Is the BB84 protocol an example of “quantum supremacy”?
This is a fairly broad question, I hope it fits here. I am wondering if the BB84 protocol is an example of "quantum supremacy", ie. something a quantum computer can do but something that is assumed a ...
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How does Deutsch Oracle shows quantum supremacy?
I learnt from this lecture (at 33:20) that Deutsch Oracle is way faster on quantum computers than on classical computers. However, it seems to me that this is just due to smart structuring of input ...
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Why Google has used $\sqrt{X}$ and $\sqrt{Y}$ instead of $X$ and $Y$ in supremacy experiment?
In supremacy experiment Google has used $\sqrt{X}$ and $\sqrt{Y}$ as two of their single qubit gates (paper).
So My questions are:
Is there any specific reason for choosing these gates and not $X$...
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Is there quantum advantage to be had with a D-Wave computer in 2020?
I've seen a lot of excitement in the popular press about the computers made by D-Wave Systems, but when I dig deep the only practical things that I can figure out that one can do with the computer are ...
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What is the role of choosing the single-qubits randomly in Google quantum supremacy experiment?
In supremacy paper and part D of section VII of supplementary information (below), it is said that there is a pseudo-random number generator that is initialized with a seed called $s$; And then the ...
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What did exactly Google do in simulating a random quantum circuit on a classical computer in supremacy experiment?
I've been working on Google quantum supremacy paper for quite some time now and I have a problem in understanding how exactly they simulate their actual random quantum circuit on a classical computer.
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Decomposing Hamiltonian into qubit model representation
One of the main applications of VQE is its application to find the approximation to the ground state energy (smallest eigenvalue of the Hamiltonian) for a particular molecule through an iterative ...
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In Google's Quantum Supremacy experiment, what if we use $\theta=45°$ for two-qubit $f_{sim}$ gates?
In Google's Quantum Supremacy experiment, they use $f_{sim}$(fermionic-simulation) gates with $\theta=90°$ and $\phi=30°$ as their two-qubit gates. What if we use $\theta=45°$ for the two-qubit $f_{...
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What is the difference between classical and quantum computers as well as computing (permuting) itself?
Theoretically and for sure physically (I know the quantum physics behind it) I know something about it. But not that much. That's why I ask the question here. I'm very interested. The only answer to ...
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Interpretations of quantum computing power [closed]
Over the years I encountered different explanations of quantum computing advantage over classical computers. But I am not sure which explanations are in fact valid and which are not.
Quantum ...
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Boson Sampling with a single beamsplitter
In Boson Sampling as first proposed by Aaronson and Arkhipov in arxiv.org/abs/1011.3245, the interferometer is made up of phase shifters and beamsplitters. As these gates are universal, drawing the ...
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How to distinguish quantum random from classical random?
Given two sets of $N$ uniformly random binary bitstrings of size $m$, such as $$(x_0,x_1,...,x_m) \space \forall x_i \in \{0,1\}.$$
One generated from a quantum device and the other generated by ...
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What is the problem in demonstrating quantum supremacy?
I am new to the quantum world and it's computing. But it accidentally hit in my mind that DWave built a quantum computer with 2000 qubits which can be use to simulate the whole observable universe or ...
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How exactly is solving the random circuit sampling problem a computation in the Church-Turing thesis sense?
Note: This has been cross-posted to CS Theory SE.
If we assume $\mathsf{BQP} \neq \mathsf{BPP}$, then we can say with reasonable certainty that Google's random sampling experiment falsifies the ...
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How does successfully sampling from a random quantum circuit invalidate the Extended Church-Turing Thesis?
According to these lecture notes from Berkeley, the Extended Church-Turing Thesis (ECT) asserts that:
...any "reasonable" model of computation can be efficiently simulated on a standard model such ...
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Making sense of the Sycamore's computing prowess - power consumption
I came here after reading about the announcement regarding the Sycamore processor and Google's Quantum Supremacy claim. I am hung up on several key things and I am hoping that I could find those ...
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What does Google's claim of “Quantum Supremacy” mean for the question of BQP vs BPP vs NP?
Google recently announced that they have achieved "Quantum Supremacy": "that would be practically impossible for a classical machine."
Does this mean that they have definitely proved that BQP ≠ BPP ?...
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Why does Google's quantum processor outperform IBM's?
I understand that both have 53 qubit devices, yet it is Google that has demonstrated quantum supremacy (although IBM refutes this!). I'm not sure if this is true but it seems like IBM cannot replicate ...
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Why do the IBM and Google processors both have 53 qubits?
As I understand from this IBM post both the IBM and Google teams have independently built 53-qubit processors. What is the significance of the number 53? It is purely coincidental, or is there a ...
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Are 20 repetitions of Sycamore's one- and 2-qubit gates sufficient to produce a uniformly random state?
In the answer to this question about random circuits, James Wootton states:
One way to see how well we [fully explore the Hilbert space] is to focus on just randomly producing $n$ qubit states. ...
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Quantum Supremacy: Some questions on cross-entropy benchmarking
I was skimming through the Google quantum supremacy paper but got stuck on this section:
For a given circuit, we collect the measured bit-strings $\{x_i\}$ and compute the linear XEB fidelity [24-26, ...
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Number of qubits to achieve quantum supremacy?
Google's Sycamore paper describes achieving quantum supremacy on a $53$-qubit quantum computer. The layout of Sycamore is $n=6\times 9=54$ nearest neighbors, with one qubit nonfunctional. They apply ...
