18 votes
Accepted

When will we know that quantum supremacy has been reached?

The term quantum supremacy doesn't necessarily mean that one can run algorithms, as such, on a quantum computer that are ...
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18 votes

Why do the IBM and Google processors both have 53 qubits?

It's just a coincidence. I can speak from personal recollection on the Google side. Google originally intended to use a 72 qubit chip (Bristlecone) where qubits were essentially directly connected to ...
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15 votes
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What countries are leading this "Global Quantum Computing Race"?

There are several countries that are actively participating in the "Quantum Race", most of which are making significant investments. The estimated annual spending on non-classified quantum-technology ...
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  • 519
15 votes
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What does Google's claim of "Quantum Supremacy" mean for the question of BQP vs BPP vs NP?

Google's paper/results are kind of sideways to questions in computational complexity about the relation between $\mathrm{BPP}$ and $\mathrm{BQP}$ (and even further from questions about whether $\...
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  • 6,767
14 votes

What exactly is "Random Circuit Sampling"?

There are a continuous set of possible states for $n$ qubits, each of which can be expressed as a superposition of the $2^n$ basis states. Mostly of these states are highly entangled, and would ...
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12 votes
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Quantum machine learning after Ewin Tang

I am not an expert in the field but there are a few points that I am aware of: There are proofs that certain quantum machine learning algorithms cannot be efficiently simulated on a classical ...
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12 votes

Are there problems in which quantum computers are known to provide an exponential advantage?

Not sure if this is strictly what you're looking for; and I don't know that I'd qualify this as "exponential" (I'm also not a computer scientist so my ability to do algorithm analysis is ...
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12 votes
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Are there quantum algorithms showing a double exponential advantage?

Classical computers can simulate quantum computers with an exponential overhead. Thus, there cannot be a doubly exponential speedup (unless maybe in some blackbox setting, cf Deutsch-Jozsa).
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11 votes
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Are there problems in which quantum computers are known to provide an exponential advantage?

Suppose a function $f\colon {\mathbb F_2}^n \to {\mathbb F_2}^n$ has the following curious property: There exists $s \in \{0,1\}^n$ such that $f(x) = f(y)$ if and only if $x + y = s$. If $s = 0$ is ...
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10 votes
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Quantum advantage with only Clifford gates (Gottesman Knill theorem)

Are there examples of quantum algorithms only composed of Clifford operations that show [...] A reduction in the "same spirit" of the $n^{800}→n$ for instance. No. An $n$ qubit Clifford+...
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9 votes

What exactly makes quantum computers faster than classical computers?

"What feature of a quantum algorithm makes it better than its classical counterpart?" First, a classical algorithm can be thought of as a quantum algorithm that makes no use of quantum ...
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9 votes

What are the real advantages of superdense coding?

TL;DR: While two qubits must be transmitted in total, in the instant where two bits are to be communicated, only one qubit has to be sent. The information being sent is masked, but it is not truly ...
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  • 46.1k
9 votes

Quantum Supremacy: How do we know that a better classical algorithm doesn't exist?

For all we know, it is extraordinarily hard to prove that a problem which can be solved by a quantum computer is classically hard. The reason is that this would solve an important and long-standing ...
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9 votes

Are there problems in which quantum computers are known to provide an exponential advantage?

The complexity class of decision problems efficiently solvable on a classical computer is called BPP (or P, if you don't allow randomness, but these are suspected to be equal anyway). The class of ...
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  • 2,057
8 votes
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Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 2): simplifiable and intractable tilings

TL/DR: The two-qubit gates are going by the moniker "Sycamore gates" in the paper, and it appears that they would ideally want to explore more of the $(\phi, \theta)$ phase-space but for ...
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  • 6,767
8 votes

What is the advantage of quantum machine learning over traditional machine learning?

As so often, and especially in young research areas, the answer depends quite a lot on how you break down the question. Let me try a few examples: Does quantum mechanics change what is theoretically ...
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8 votes
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Why does QAOA achieve quantum supremacy in an algorithmic sense?

"but for me quantum supremacy would mean that no classical algorithm can exist at all that solves the problem in a better way than a quantum algorithm." If that were the case, then "...
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  • 11.9k
7 votes

When will we know that quantum supremacy has been reached?

The term quantum supremacy, as introduced by Preskill in 2012 (1203.5813), can be defined by the following sentence: We therefore hope to hasten the onset of the era of quantum supremacy, when we ...
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  • 18.1k
7 votes

Quantum Supremacy: How do we know that a better classical algorithm doesn't exist?

How do we know no better classical algorithm exist? We can know thanks to computational complexity theory, which studies the complexity of solving different problems with different computational ...
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  • 18.1k
7 votes
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Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 3): sampling

What does "obtaining samples" mean in this context? The same thing it means in a more classical context. Consider the probability distribution of the possible outcomes of a (possibly biased) coin ...
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7 votes
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Making sense of the Sycamore's computing prowess - power consumption

They say in Section X.H of the supplement that the Summit supercomputer has a power capacity of 14 megawatts. They compare that to their own setup. Their power consumption is mainly their dilution ...
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7 votes

Quantum advantage with only Clifford gates (Gottesman Knill theorem)

Quantum advantage using Clifford gates Gottesman-Knill theorem applies to stabilizer circuits only, not to all circuits consisting of Clifford gates. The former satisfy the stronger requirements of ...
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6 votes

Grover algorithm for a database search: where is the quantum advantage?

The problem is with your initial assumption: the oracle for Grover's is based on a function f(value)=0/1, where 1 indicates that the value meets your search criteria and 0 indicates that it doesn't. ...
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6 votes

Grover algorithm for a database search: where is the quantum advantage?

You are right to recognize the complexity of building the oracle to use it with Grover's search - it is indeed the tricky part of solving the problem, and indeed a lot of sources don't consider this ...
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6 votes
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What is the HOG test and how would it help proving quantum supremacy?

There are a couple variants of the HOG test. "Old HOG" computed the proportion of unique samples whose probability is larger than the median probability of the distribution. It then compares that ...
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  • 21.8k
6 votes

Interpretations of quantum computing power

1 and 2 have elements of truth, but are only partially correct, with big caveats. 3 and 5 are complete nonsense. You can choose to read 4 the right way to make some sense out of it, but it doesn’t ...
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  • 46.1k
6 votes
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Why Google has used $\sqrt{X}$ and $\sqrt{Y}$ instead of $X$ and $Y$ in supremacy experiment?

While Craig Gidney (from Google) is correct in his comment which says that $X$ and $Y$ do not create superpositions on states that are not in superposition, such as $|0\rangle$ and $|1\rangle$; even ...
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  • 11.9k
6 votes

Why exactly are variational algorithms considered promising?

"As far as I understand there aren't many rigorous results on performance of these algorithms, similar to many classic machine learning approaches." You are correct in that, unlike Grover's ...
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  • 11.9k
5 votes
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Grover algorithm for a database search: where is the quantum advantage?

Grover's algorithm does not have an advantage when searching an unordered database, because encoding the oracle into a circuit requires $\tilde \Omega(n)$ operations. You can prove this with a simple ...
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  • 21.8k
5 votes
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What is the problem in demonstrating quantum supremacy?

D-Wave's 2000Q is a quantum annealer, not a circuit-based quantum computer like Google's Sycamore. The qubits in D-Wave's system are much noisier, less controlled and perform a fundamentally ...
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