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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HHL algorithm for linear systems with a real matrix and a real right side

HHL algorithm can be used for solving linear system $A|x\rangle=|b\rangle$. If we put $|b\rangle$ (to be precise its normalized version) into the algorithm and measuring ancilla to be $|1\rangle$ we ...
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 ...
2answers
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 ...
1answer
77 views

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.
2answers
87 views

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 ...
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 ...
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 ...
0answers
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 ...
3answers
3k views

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 ...
2answers
7k views

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 ...
0answers
39 views

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/...
1answer
59 views

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 ...
0answers
102 views

Can hash functions speed up quantum simulation? (Generalizing May and Schlieper's idea)

Recently May and Schlieper have published a preprint (https://arxiv.org/abs/1905.10074) arguing that the modular exponential register in Shor's algorithms can be replaced with a universally hashed ...
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587 views

Could quantum computing improve chess engines?

Could and how quantum computing improve chess engines? Will it be able to think much faster and better than a classical chess computer? Will a quantum computing chess engine be drastically better ...
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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 ...
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 ...
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, ...
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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 "...
2answers
49 views

Could a quantum computer simulator be faster than a normal computer when running on a normal computer?

I'm very new to quantum computing. I was just wondering if a quantum computer simulator could be faster than a normal computer when running on a normal computer. Could it?
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How can we apply Quantum Algorithms (Grover's to be specific) to edge coloring problem?

I am a novice in the Quantum Computing field. Recently we were discussing NP-complete problems in Algorithms class and a question arose in my mind which I have stated above, can anyone help me with ...
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Meaning of “Running” time field in Results and correlation with the “shots” choosen number

I've created a same circuit that I've executed two different ways on the same computer (ibmq_16_melbourne); First with 1024 Shots and secondly with 8096 Shots For the first (1024), I got in results, ...
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36 views

Why does quantum computing only offer faster computational times for certain, specific types of problems? [duplicate]

Quantum computing has gained media attention about the exponential increase in computational speeds but only when dealing with specific problems which are prone to a quantum computational approach (...
1answer
99 views

Where will I find necessary math to understand HHL algorithm?

How can we show that HHL algorithm achieves exponential speedup?
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 ...
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, ...
3answers
151 views

How many probabilities does the number of qubits represent?

If $2$ qubits together provide the states 00, 01, 11 or 10 simultaneously which represent $4$ probabilities in total, how many probabilities do $N$ qubits represent? Does the formula for this somehow ...
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 ...
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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/...
2answers
1k views

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 ...
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 ...
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 $\sim \sqrt{N}$ ...
1answer
4k views

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 ...
0answers
330 views

Comparing CPU to QPU In terms of processing power

The current processors are limited by the speed of the electrons but quantum processors take advantage of the properties of subatomic particles. But the question is how to compare the processing power ...
4answers
1k views

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 ...
1answer
112 views

Lesser qubit computer doing the parts of Shor's against e.g., RSA-2048 sized prime

After posting this question to Physics, it became pretty clear I should have posted here. So: How might a (e.g.) 72-bit crypto-relevant quantum computer attack RSA-2048? Bonus: how might that be ...
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 ...
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?
2answers
199 views

What is the actual mechanism behind quantum computing?

I was redirected from theoretical computing to quantum computing for this question. I've been mildly researching quantum computers to figure out how entanglement and superposition are utilized for ...
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 ...
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 ...
3answers
3k views

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 ...
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.
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 ...
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 ...
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?
2answers
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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 ...
4answers
3k views

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 ...
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 ...
0answers
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Physics World - Questioning quantum speed [closed]

My question is definitely regarding quantum-speedup but the quantum-speedup tag is confined to algorithms... and my question is definitely not on algorithms. So, this is just my best shot at tagging. ...
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 ...