Questions tagged [quantum-advantage]
For questions about schemes to prove that quantum devices can, at least in principle, be exponentially more efficient than their classical ones. Also often referred to as "quantum computational advantage" or "quantum supremacy". Typical examples are sampling problems such as boson sampling and random circuit sampling.
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Create a superposition among the basis states of G for the hidden subgroup problem, implementing $\frac{1}{\sqrt{|G|}}\sum_{g\in G} | g,0\rangle$
I’ve been studying Simon’s problem and developing simulation models using Mathematica to extend the problem to other abelian groups and hidden subgroups of order $\geq 2$. I can now obtain the $h^\...
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Is there some theorem that proves that entanglement is necessary for quantum advantage? [duplicate]
Gottesman-Knill theorem kind of implies that entanglement is not sufficient to produce quantum advantage because it can be simulated in many cases (for Clifford gates combinations). Also it is kind of ...
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Advantage of quantum computers over classical computers in fully modeling interactions between atoms?
I'm trying to better understand the advantage quantum computers offer in terms of their ability to more accurately model chemical reactions. As a way to come to a deeper understanding, my question is:
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What is the state of the art quantum state preparation algorithm?
Encoding classical information into a quantum computer is a bottleneck of quantum machine learning. I want to learn which algorithm for state preparation is the best (in complexity) currently. The ...
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Does the D-Wave hardware show any advantage for academic use-cases, for example in condensed matter physics?
The D-Wave team put out a few papers (like this one and this one) in the last few years describing how their methods can find ground states of certain spin-glass Hamiltonians faster than classical ...
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Did D-Wave show quantum advantage in 2023?
I would like to know your thoughts on whether or not D-Wave has shown a a smoking-gun example of quantum advantage this year. I am genuinely not quite sure what to think, but I believe the answer to ...
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Ansatz for VQE demonstrating Quantum Advantage
What would be a possible ansatz quantum state in VQE (variational quantum eigensolver [1]) that would demonstrate the quantum advantage of VQE over classic computers? More specifically, I see that VQE ...
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Can we obfuscate the identity?
Motivated by Aaronson's call to find simple, verifiable proofs of quantumness, suppose we start off with a random polynomial-length circuit $U$ of, say, Clifford+T gates, and attach $U^\dagger$ to it, ...
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Measure on the unitary space and complexity
I'm currently studying various quantum supremacy protocols and i'm struggling to have a clear and well defined view on the rôle of approximating the Haar-measure (through k-designs ...) and the ...
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Heuristics on Quantum computers
I found the article :
Strengths and Weaknesses of Quantum Computing, 1997
Charles H. Bennett, Ethan Bernstein, Gilles Brassard, Umesh Vazirani
As far as I understand, this one states that quantum ...
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How do researchers know / prove they've achieved quantum supremacy?
I'm currently reading the book Quantum Supremacy: How the Quantum Computer Revolution Will Change Everything by Michio Kaku, and I came upon the following sentence:
Soon after Google made its claim ...
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How to benchmark approximate random unitary sampling
I'm currently studying a specific sampling "quantum advantage" (sorry for the buzzword) protocol wich consist of periodically driving a random Ising chain (https://iopscience.iop.org/article/...
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Quantum algorithms with few T gates?
Many existing quantum algorithms require millions or billions of T gates to reach a scale that is classically hard to simulate. However, existing Clifford + T circuits seem hard even with 100 or so T ...
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Does quantum computing take more computer memory (storage) than classical computing?
Please clarify: Let's say we have 3 bits of memory for classical computation (CC), we can represent any number between 0 and 7. On the other hand, with 3 qubits of memory for quantum computation (QC), ...
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Most promising QML algorithms in the NISQ era
This question was asked in the previous years, but how is 2023 state of the art Quantum Machine Learning ?
Things seem to go fast in this area, for instance I saw Thales used 4 qubits for quantum ...
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Is there something wrong with cross-entropy benchmarking, or is it still considered as a reasonable path towards quantum supremacy?
My question is strongly related with this one. Google's quantum supremacy claim uses Random Circuit Sampling. The principle is the following one: a realistic noise model for random circuits performed ...
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Are there some cases where Grover's algorithm was used to improve machine learning performance?
Grover algorithm showing quantum advantage, are there some cases where it was used to improve Machine Learing performance ?
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Does Google's error correction paper invalidate Gil Kalai's arguments?
In his paper "The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims", Gil Kalai argues that quantum advantage will never be reached. For NISQ ...
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What problems can quantum computers solve right now which classical computers cannot solve? [duplicate]
I know that an error-corrected quantum computer with unlimited amount of qubits can provide a significant speed up compared to classical computers for specific kind of problems, e.g. searching in an ...
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Are there problems where quantum computers are faster (in practice!) than classical ones? [duplicate]
Today's Quanta Magazine article says "But it’s proved difficult to find examples of any algorithms with a clear “quantum advantage” that enables performance beyond the reach of classical machines....
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What is the fastest quantum computational algorithm by which quantum computer speed up than classic one?
What is the fastest quantum computational algorithm by which quantum computers speed up than classic one? Of course, those speedup algorithms have to be proven.
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Can we use cryptocurrency mining to verify claims of quantum advantage?
Beginning with the earlier works of work of Brakerski et al. or the more recent results of Kahanamoku-Meyer et al., interactive proofs of quantum advantage entail a classical verifier (Vicky) ...
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Any simple description of a circuit for Yamakawa-Zhandry algorithm?
Recently, popular sources (including Aaranson's blog and Quanta Magazine) have made it look like the recent Yamakawa-Zhandry algorithm is akin to Shor's algorithm, in the sense that it could ...
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Status of Google's quantum supremacy claim 2022
More than a year ago a couple of scientists made a splash by presenting a classical algorithm that took less than a week to simulate Sycamore's circuits on a small GPU cluster. Also, their simulations ...
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What arguments point towards D-Wave devices being potentially useful?
I'm looking for any evidence pointing towards D-Wave's approach to quantum computation being promising to achieve any sort of computational advantage with respect to classical devices.
Note that I'm ...
glS♦
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What are quantum computers actually doing today?
I am curious about what are quantum computers actually doing today. I seem to only be able to find information online about what they could be used for in the future (i.e. breaking encryption, quantum ...
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Understanding the supremacy regime plot in Google's "Quantum supremacy using a programmable superconducting processor"
I was going through the Google's 2019 paper & had difficulties regarding some details.
How are they calculating XEB in quantum supremacy regime? To calculate the XEB,we also need the ideal ...
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Is there any rigorous proof that Quantum Annealing provides a quantum advantage?
Is there any rigorous proof that Quantum Annealing (QA) is of any benefit (e.g. in terms of time to optimal solution, convergence rate, etc.) for a specific problem? Or any empirical evidence for the ...
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Why do we need physical qubit if qubit can be simulated?
I do not see any advantage in constructing very costly and imperfect physical qubit while this qubit can be simulated with using conventional computer memory (noise-free).
So what is the purpose when ...
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I have question about cost of 'modular multiplication unitary' in Shor's algorithm
Here modular multiplication unitary means $U_a : |s\rangle \to|as\mod N\rangle$.
My main question is, can the modular multiplication unitary $U_a$ can be constructed in time polynomial in the number ...
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What tasks are quantum computers good at that classical computers are not?
At this stage, a large number of theoretical proofs have made us vaguely aware of the particularity of quantum computers. But what tasks are quantum computers good at that classical computers are not? ...
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Exponential advantage with Hadamard test
My question is the following:
Let's assume that the only algorithm a quantum computer would be able to implement is the Hadamard test, which circuit is represented below, would we say that compared to ...
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Quantum advantage without phase?
I'm wondering if one can (potentially) get any quantum advantage with $R_y$ single-qubit rotations and $CNOT$s only?
(Note that I don't care about having a universal quantum computer.)
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Are qubits just analog, continuous classical bits? [duplicate]
Topologically, classical bits (cbits) are essentially special cases of qubits restricted to the poles of the Bloch sphere. However, this restriction doesn't seem to be classical per se, but is simply ...
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Proven quantum advantage (in the algorithmic sense) without error correction (for specific algo, or noise models)
I would like to know if there are some specific class of quantum algorithms, under some hypotheses about the noise model behind the quantum gates for which we know that there is an exponential ...
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Derivation of the linear cross entropy
I'm looking at cross-entropy benchmarks and there's much that I'm reading at the moment but I'm stuck on one detail: how to derive the linear cross-entropy formula from the cross-entropy formula.
The ...
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Are there quantum algorithms showing a double exponential advantage?
I would like to know if there are known quantum algorithms that provide a double exponential advantage compared to the best known classical algorithms.
More precisely, if the characteristics of the ...
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What exactly makes VQE faster than classical optimization?
I have been trying to understand Variational Quantum Eigensolver (VQE), particularly from the non-linear binary programming perspective. But after reading a few resources I'm still confused about ...
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What is the explicit best known quantum algorithm for LWE?
Consider the learning with errors(LWE) problem which is known to be hard for quantum computers.
Let $q \geq 2$ be a prime integer. Consider us being given (polynomially many samples of) either:
$$A, ...
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Schmidt vectors for random quantum states
Consider a random quantum circuit $U$ over $n$ qubits, drawn from the Haar measure. Consider the quantum state
$$|\psi\rangle = U |0^{n}\rangle.$$
Now, partition $n$ into two and consider the Schmidt ...
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Anticoncentration for two independent random quantum circuits in parallel
Consider two Haar random $n$ qubit unitaries, $U_1$ and $U_2$. Consider the quantum state
$$|\psi\rangle = (U_1 \otimes U_2) |0^{2n}\rangle. $$
Let $p_x = |\langle x| \psi \rangle|^{2}$, for $x \in \{...
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Reduced density matrix of a Haar random state and its Schmidt decomposition
Consider a Haar random quantum state $|\psi\rangle$. Note that
$$\rho =\mathbb{E}[|\psi\rangle\langle \psi|] = \frac{\mathbb{I}_{n}}{2^{n}}.$$
$\mathbb{I}_n$ is the identity operator on $n$ qubits. ...
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Random quantum states and Schur-Weyl duality
Consider the following density matrix over $n$ qubits, with $C$ being a single qubit operator:
$$
\rho_{n} = \int_{C \sim \text{Haar}} \big(C|0\rangle\langle0|C^\dagger\big)^{\otimes n} dC.
$$
Let's ...
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Optimality of the SWAP test versus weak Schur sampling for testing unitarily invariant properties
Consider the following setting.
I am either given the density matrix $|\psi\rangle \langle \psi|^{\otimes k}$ or the density matrix $\frac{\mathbb{I}^{\otimes k}}{2^{nk}}$, where $\mathbb{I}$ is the $...
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At what depth and for what architecture are random quantum circuits $1$-designs?
I was confused about something related to quantum $1$ designs.
Let us recap two facts we know about random circuit ensembles that form a $1$ design.
$1$ design, for a quantum circuit over $n$ qubits, ...
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Quantum advantage with only Clifford gates (Gottesman Knill theorem)
Let's say I want to solve a computational task which input can be encoded in $n$ bits of information.
The look for a quantum advantage is (usually) asking to find a quantum algorithm in which there ...
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How does a quantum computer execute a process by leveraging superposition?
I understand in plain terms superposition and entanglement, but I'm very unclear how either of these could work as a means to increase computation power.
A helpful metaphor is that of the maze. A ...
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Random quantum circuits and general efficient POVM measurement
Let's consider a random quantum circuit $C$, applied to the $n$ qubit initial state $|0^{n}\rangle$, producing the state $|\psi\rangle$.
Consider a general efficiently implementable $m$-outcome POVM ...
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How can one define contextuality within the circuit model?
It is in general believed that contextuality is one of the quantum resource that provides the quantum advantage. A context is usually defined in terms of a set of commuting observables. The quantum ...
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Average output state of random quantum circuits
Let $|\psi\rangle = C_1 |0^{n}\rangle$ be a quantum state, such that $C_1$ is a Haar random unitary circuit. Consider a density matrix $\rho$ as follows
\begin{equation}
\rho_1 = \mathbb{E}[|\psi\...
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