Questions tagged [speedup]

For questions about either: comparing the performance of a quantum algorithm with a classical algorithm (or set of classical algorithms) independent of devices; or the ratio of time to solution of a quantum device running a specific algorithm to a classical device running a specific algorithm.

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33
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Is there any general statement about what kinds of problems can be solved more efficiently using a quantum computer?

Is there a general statement about what kinds of problems can be solved more efficiently using quantum computers (quantum gate model only)? Do the problems for which an algorithm is known today have a ...
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Are there problems in which quantum computers are known to provide an exponential advantage?

It is generally believed and claimed that quantum computers can outperform classical devices in at least some tasks. One of the most commonly cited examples of a problem in which quantum computers ...
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Why is a quantum computer in some ways more powerful than a nondeterministic Turing machine?

The standard popular-news account of quantum computing is that a quantum computer (QC) would work by splitting into exponentially many noninteracting parallel copies of itself in different universes ...
26
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Has there been any truly ground breaking advance in quantum algorithms since Grover and Shor?

(Sorry for a somewhat amateurish question) I studied quantum computing from 2004 to 2007, but I've lost track of the field since then. At the time there was a lot of hype and talk of QC potentially ...
24
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2answers
949 views

When will we know that quantum supremacy has been reached?

The term "quantum supremacy" - to my understanding - means that one can create and run algorithms to solve problems on quantum computers that can't be solved in realistic times on binary computers. ...
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3answers
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What makes quantum computers so good at computing prime factors?

One of the common claims about quantum computers is their ability to "break" conventional cryptography. This is because conventional cryptography is based on prime factors, something which is ...
18
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1answer
282 views

Level of advantage provided by annealing for traveling salesman

My understanding is that there seems to be some confidence that quantum annealing will provide a speedup for problems like the traveling salesman, due to the efficiency provided by, ex, quantum ...
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Why can the Discrete Fourier Transform be implemented efficiently as a quantum circuit?

It is a well known result that the Discrete Fourier Transform (DFT) of $N=2^n$ numbers has complexity $\mathcal O(n2^n)$ with the best known algorithm, while performing the Fourier transform of the ...
16
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1answer
319 views

How long does quantum annealing take to find the solution to a given problem?

Quantum annealing is an optimization protocol that, thanks to quantum tunneling, allows in given circumstances to maximize/minimize a given function more efficiently than classical optimization ...
16
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1answer
345 views

How does magic state distillation overhead scale compare to quantum advantages?

I'm interested in the model of quantum computation by magic state injection, that is where we have access to the Clifford gates, a cheap supply of ancilla qubits in the computational basis, and a few ...
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3answers
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What is the current state of the art in quantum sorting algorithms?

As a result of an excellent answer to my question on quantum bogosort, I was wondering what is the current state of the art in quantum algorithms for sorting. To be precise, sorting is here defined ...
14
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1answer
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What exactly is “Random Circuit Sampling”?

Many people have suggested using "Random Circuit Sampling" to demonstrate quantum supremacy. But what is the precise definition of the "Random Circuit Sampling" problem? I've seen statements like "the ...
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1answer
542 views

Is entanglement necessary for quantum computation?

Entanglement is often discussed as being one of the essential components that makes quantum different from classical. But is entanglement really necessary to achieve a speed-up in quantum computation?
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307 views

What is the minimum integer value to make quantum factorization to be worthwhile?

Let us assume that we have quantum and classical computers such that, experimentally, each elementary logical operation of mathematical factorization is equally time-costing in classical and in ...
11
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1answer
260 views

Are there any encryption suites which can be cracked by classical computers but not quantum computers?

Are there any encryption suites that can be cracked by usual computers or super computers, but not quantum computers? If that's possible, what assumptions will it depend on? (Factorizing big numbers, ...
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What can we learn from 'quantum bogosort'?

Recently, I've read about 'quantum bogosort' on some wiki. The basic idea is, that like bogosort, we just shuffle our array and hope it gets sorted 'by accident' and retry on failure. The ...
11
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1answer
848 views

How are magic states defined in the context of quantum computation?

Quoting from this blog post by Earl T. Campbell: Magic states are a special ingredient, or resource, that allows quantum computers to run faster than traditional computers. One interesting example ...
11
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1answer
602 views

Quantum Algorithm for God's Number

God's number is the worst case of God's algorithm which is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles ...
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451 views

Can we use quantum parallelism to calculate many functions at once?

It is well-known that by utilizing quantum parallelism we can calculate a function $f(x)$ for many different values of $x$ simultaneously. However, some clever manipulations is needed to extract the ...
9
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1answer
683 views

HHL algorithm — why isn't the required knowledge on eigenspectrum a major drawback?

This question is a continuation of Quantum phase estimation and HHL algorithm - knowledge on eigenvalues required?. In the question linked above, I asked about the necessity for HHL to have ...
9
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1answer
252 views

Does quantum computing provide any speedup in evaluation of transcendental functions?

With the integer factorisation problem, Shor's algorithm is known to provide a substantial (exponential?) speedup compared to classical algorithms. Are there similar results regarding more basic maths,...
9
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1answer
447 views

Barren plateaus in quantum neural network training landscapes

Here the authors argue that the efforts of creating a scalable quantum neural network using a set of parameterized gates are deemed to fail for a large number of qubits. This is due to the fact that, ...
9
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1answer
2k views

What is the difference between QAOA and Quantum Annealing?

Edward Farhi's paper on the Quantum Approximate Optimization Algorithm introduces a way for gate model quantum computers to solve combinatorial optimization algorithms. However, D-Wave style quantum ...
8
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What is the actual power of Quantum Phase Estimation?

I have some perplexity concerning the concept of phase estimation: by definition, given a unitary operator $U$ and an eigenvector $|u\rangle$ with related eigenvalue $\text{exp}(2\pi i \phi)$, the ...
8
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1answer
211 views

New algorithm for faster QC simulation by IBM

This new algorithm for QC calculation was introduced recently (2017 4Q) by IBM/ Pednault et al. to great fanfare. The paper seems more couched in the language of physics. Are there any basic ...
8
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1answer
102 views

Are Genetic Programming runtimes faster on QCs than on classical computers?

If this isn't known, would they theoretically be? I'm particularly interested in knowing whether a QC would be faster at evaluating the fitness function of the possible solutions than a classical ...
8
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1answer
626 views

What are the implications of Bremermann's limit for quantum computing?

The title says most of it: What are the implications of Bremermann's limit for quantum computing? The Wikipedia page says that the limit applies to any self-contained system, but in the last few lines ...
8
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1answer
203 views

Quantum algorithms for problems outside NP

What is known about quatum algorithms for problems outside NP (eg NEXP-complete problems), both theoretically like upper & lower speedup bounds and various (im)possibility results, as well as ...
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174 views

What kind of boolean functions are faster to compute on qc?

Deutsch-Jozsa algorithm can compute if some function $f : \{0,1\}^n \rightarrow \{0,1\} $ is constant. This goes exponentially faster than on classical computers. If we consider the set of all boolean ...
7
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2answers
465 views

Can classical algorithms be improved by using quantum simulation as an intermediary step?

I'm wondering whether even if we cannot create a fast quantum computer, simulating quantum algorithms can be a reasonable method for classical algorithms. In particular, I'd like to see any results ...
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120 views

Empirical Algorithmics for Near-Term Quantum Computing

In Empirical Algorithmics, researchers aim to understand the performance of algorithms through analyzing their empirical performance. This is quite common in machine learning and optimization. Right ...
6
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3answers
1k views

Why do classical bits perform calculations at a scale that expands linearly and qubits at exponential scale in the number of (qu)bits?

What does one mean by saying that classical bits perform operations at the scale of $2n$ and quantum computers perform operations at the scale of $2^n$? In both cases, $n$ = Number of bits/qubits.
6
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1answer
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Assessing speed-up via Quantum-Stochastic correspondence

You can make a natural correspondence between a quantum state vector and a classical probability vector, and between a quantum unitary operator and a classical stochastic matrix. There is also a ...
6
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1answer
203 views

Quantum speedup without entanglement

Is there an instance of a quantum algorithm that is faster than its classical counterpart, but doesn't use entanglement, only superposition?
6
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1answer
33 views

List of problems in the query complexity model with no super-polynomial quantum speedup

Similar to this list over at cstheory, I'm looking for a list of computational problems in the query complexity model for which it is known that no super-polynomial quantum speedups exist. What are ...
6
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1answer
625 views

Travelling salesman problem on quantum computer

Recently a pre-print of article Efficient quantum algorithm for solving travelling salesman problem: An IBM quantum experience appeared. The authors use a phase estimation as a core for their ...
6
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1answer
305 views

Requirements for Achieving a Quantum Speedup

We usually talk about the power of a quantum computer by examining the separation between sets of gates that we know we can efficiently simulate on a classical computer (i.e. problems in the class BPP)...
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2answers
370 views

Are there many practical problems for which Grover's algorithm beats the best heuristic classical algorithm?

It's well known that, given an oracle for a function $f$ from a very large set $S$ (of order $N \gg 1$) to $\{0, 1\}$, Grover's algorithm can find an element of $S$ that maps to 1 with $\sim \sqrt{N}$ ...
5
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1answer
183 views

Compact encoding of Boolean formula as oracle

As in the title, I have a doubt regarding the implementation of a boolean formula used as an oracle for a quantum algorithm. The problem is that so far I could reproduce the formula as a quantum ...
5
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0answers
180 views

Could quantum computing help solving the Eternity II puzzle?

First of all, since I am not a specialist, sorry if this question does not make sense. But, I can't resist to ask as I have not found any direct information while googling. I hope some of you know/...
5
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1answer
560 views

How to compare a quantum algorithm with its classical version? [closed]

The Quantum Algorithm Zoo includes a host of algorithms for which Quantum Computing offers speedups (exponential, polynomial, etc). However, those speedups are based on asymptotic computational ...
4
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2answers
667 views

Can classical linear algebra solvers implement quantum algorithms with similar speed-ups?

A quantum algorithm begins with a register of qubits in an initial state, a unitary operator (the algorithm) manipulates the state of those qubits, and then the state of the qubits is read out (or at ...
4
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2answers
690 views

Is running a large random brute force on quantum computer possible at the moment?

I want to run a experiment like this: Generate a bunch of random 12-character passwords like $``\texttt{<Bb\{Q,r2Qp8`}".$ Write an algorithm to randomly generate & compare value on quantum ...
4
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1answer
71 views

Low-dimensional data and quantum machine learning

Ewin Tang says to not expect exponential speed-ups from quantum machine learning using low-dimensional data because, in such cases, quantum analogues of classical algorithms will not provide ...
4
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1answer
74 views

Are applications with only polynomial speedup worth chasing after? (since error correction adds a heavy overhead)

A number of ML algorithms have demonstrated to have polynomial speed-up: But this (I'm assuming) is without error correcting qubits. How practical are algorithms that only exhibit polynomial speed-up ...
4
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1answer
91 views

The relationship between problem structure and exponential speedups under the query model

What problem structure(s) are required to admit an exponential speedup in the universal quantum model of computation under the query model? Intuitively, it would seem that much of the benefit of the ...
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37 views

Bound on quantum speedups under various models of complexity

What are the bounds on quantum speedups under the various models of complexity? How big or small can they be? Under the query model, my understanding is that the lower bound is $\Omega(\sqrt{N})$ as ...
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35 views

Is either the adiabatic or the diabatic version of quantum annealing known to be theoretically more powerful than the other?

Quantum annealing can be considered either in the perfectly adiabatic "slow" limit (in which case it's usually referred as "adiabatic quantum computing" (AQC) instead of "...
3
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1answer
451 views

Quantum speedup in Bayesian machine learning on NISQ computers

It is well known that in Bayesian learning, applying Bayes' theorem requires knowledge on how the data is distributed, and this usually requires either expensive integrals or some sampling mechanism, ...
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Are there already hypothetical durations of how long a continuous-variable gate would take on a continuous-variable quantum computer?

I've heard that you run up against the very large constant factors when comparing run times of quantum and classical computers -- things simply take much longer in a carefully controlled quantum setup ...