Questions tagged [algorithm]

For questions on quantum algorithms. That is, algorithms which in theory can be executed by quantum computers, usually the computers providing 'universal' quantum computation.

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32
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The algorithm of the new quantum factoring record 1,099,551,473,989

According to the New Scientist News, the Zapata team is able to factor 1,099,551,473,989 into its factors 1,048,589 and 1,048,601. According to the New Scientist: A quantum computing start-up company ...
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2answers
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How is the oracle in Grover's search algorithm implemented?

Grover's search algorithm provides a provable quadratic speed-up for unsorted database search. The algorithm is usually expressed by the following quantum circuit: In most representations, a crucial ...
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4answers
2k views

Introductory material for quantum machine learning

In the past few days, I have been trying to collect material (mostly research papers) related to Quantum machine learning and its applications, for a summer project. Here are a few which I found ...
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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 ...
26
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3answers
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Is there a layman's explanation for why Grover's algorithm works?

This blogpost by Scott Aaronson is a very useful and simple explanation of Shor's algorithm. I'm wondering if there is such an explanation for the second most famous quantum algorithm: Grover's ...
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Is quantum cryptography safer than classical cryptography?

Quantum computing allows us to encrypt information in a different way compared to what we use today, but quantum computers are much more powerful than today's computers. So if we manage to build ...
20
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2answers
1k views

What could be the possible future applications for HHL algorithm?

Note on the vocabulary: the word "hamiltonian" is used in this question to speak about hermitian matrices. The HHL algorithm seems to be an active subject of research in the field of quantum ...
19
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2answers
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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 ?...
18
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1answer
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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 ...
18
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1answer
310 views

Quantum Bitcoin Subdivision

Background Recently I was reading the article "Quantum Bitcoin: An Anonymous and Distributed Currency Secured by the No-Cloning Theorem of Quantum Mechanics" which demonstrates how a quantum bitcoin ...
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4answers
975 views

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 ...
17
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0answers
602 views

Quantum machine learning after Ewin Tang

Recently, a series of research papers have been released (this, this and this, also this) that provide classical algorithms with the same runtime as quantum machine learning algorithms for the same ...
16
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1answer
523 views

Hamiltonian simulation is BQP-complete

Many papers assert that Hamiltonian simulation is BQP-complete (e.g., Hamiltonian simulation with nearly optimal dependence on all parameters and Hamiltonian Simulation by Qubitization). It is easy ...
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Will deep learning neural networks run on quantum computers?

Deep Learning (multiple layers of artificial neural networks used in supervised and unsupervised machine learning tasks) is an incredibly powerful tool for many of the most difficult machine learning ...
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3answers
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What applications does Grover's Search Algorithm have?

Grover's Search algorithm is usually talked about in terms of finding a marked entry in an unsorted database. This is a natural formalism that lets it be applied directly to searching for solutions to ...
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2answers
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How does the Grover diffusion operator work and why is it optimal?

In this answer, Grover's algorithm is explained. The explanation indicates that the algorithm relies heavily on the Grover Diffusion Operator, but does not give details on the inner workings of this ...
15
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1answer
261 views

Are there results from quantum algorithms or complexity that lead to advances on the P vs NP problem?

On the surface, quantum algorithms have little to do with classical computing and P vs NP in particular: Solving problems from NP with quantum computers tells us nothing about the relations of these ...
14
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Is the common Computer Science usage of 'ignoring constants' useful when comparing classical computing with quantum computing?

Daniel Sank mentioned in a comment, responding to (my) opinion that the constant speed-up of $10^8$ on a problem admitting a polynomial time algorithm is meager, that Complexity theory is way too ...
14
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3answers
507 views

How to permute (reshuffle) an n-bit input?

I am interested in a quantum algorithm that gets as input an n-bit sequence and that produces as output a reshuffled (permuted) version of this n-bit sequence. E.g. if the input is 0,0,1,1 (so n=4 in ...
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5answers
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How would I implement the quantum oracle in Deutsch's algorithm?

I am trying to simulate Deutsch's algorithm (elementary case of Deutsch-Josza algorithm), and I am not entirely sure how I would go about implementing the quantum oracle necessary for the algorithm to ...
13
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2answers
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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 ...
13
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3answers
570 views

Can a quantum computer easily determine the mixing time of the Rubik's cube group?

Officials in Rubik's cube tournaments have used two different ways of scrambling a cube. Presently, they break a cube apart and reassemble the cubies in a random order $\pi\in G$ of the Rubik's cube ...
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Quantum circuits explain algorithms, why didn't classical circuits?

When explaining a quantum algorithm, many revert to 'circuit-speak' by drawing a diagram of how qubits split off into transformations and measurements, however, rarely if not never would someone ...
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3answers
971 views

General construction of $W_n$-state

Two of the most well known entangled states are the GHZ-state $|\psi\rangle = 1/\sqrt{2}\left( |0\rangle^{\otimes n} + |1\rangle^{\otimes n}\right)$ and the $W_n$-state, with $W_3 = 1/\sqrt{3}\left(|...
12
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2answers
681 views

Does a study guide exist that starts from a “purely CS background” and advances towards “making a new quantum programming language”?

I am from a computer science background and I find it difficult to decide on the resources I should focus on while learning quantum computing, since there is so much to read/watch. My ultimate goal is ...
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How is the Grover-Algorithm applied to a database?

Question I want to use the Grover-Algorithm to search an unsorted database for an element $x$. Now the question arises, how do I initialize index and value of the database with the qubits? Example ...
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2answers
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How would a quantum computer be used to solve Partial Differential Equations?

Say you have a PDE you want to solve. What kind of quantum algorithms would you use to solve it? How do we input our problem on a quantum computer? What will be the output and in what form? I know ...
12
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355 views

Jones Polynomial

There are many fairly standard quantum algorithms that can all be understood within a very similar framework, from Deutsch's algorithm Simon's problem, Grover's search, Shor's algorithm and so on. ...
12
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1answer
432 views

What is the quantum circuit equivalent of a (delayed choice) quantum eraser?

Quantum computers are efficiently able to simulate any other quantum system. Hence there must be some sort of equivalent of a (possibly simulated) quantum eraser setup. I would like to see such an ...
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2answers
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Are there any examples of anyone applying quantum algorithms to problems in computational biology?

As the title suggests, I'm searching for published examples of quantum algorithms being applied to problems in computational biology. Clearly the odds are high that practical examples don't exist (yet)...
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2answers
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How many operations can a quantum computer perform per second?

I want to know what time complexity is considered efficient/inefficient for quantum computers. For this, I need to know how many operations a quantum computer can perform per second. Can anyone tell ...
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2answers
520 views

Rigorous security proof for Wiesner's quantum money

In his celebrated paper "Conjugate Coding" (written around 1970), Stephen Wiesner proposed a scheme for quantum money that is unconditionally impossible to counterfeit, assuming that the issuing bank ...
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4answers
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Quantum Computing Journals

Can anyone give me a list of different research journals that has quantum computing articles that I can use.
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280 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
700 views

What is the Helstrom measurement?

I have been reading the paper Belief propagation decoding of quantum channels by passing quantum messages by Joseph Renes for decoding Classical-Quantum channels and I have crossed with the concept of ...
11
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1answer
307 views

Advantage of simulating sparse Hamiltonians

In @DaftWullie's answer to this question he showed how to represent in terms of quantum gates the matrix used as example in this article. However, I believe it to be unlikely to have such well ...
11
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1answer
397 views

What kind of real-world problems (excluding cryptography) can be solved efficiently by a quantum algorithm?

This question is very similar as Is there any general statement about what kinds of problems can be solved more efficiently using a quantum computer? But the answers provided to that questions mainly ...
11
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2answers
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Quantum algorithm for linear systems of equations (HHL09): Step 1 - Confusion regarding the usage of phase estimation algorithm

I have been trying to get my head around the famous(?) paper Quantum algorithm for linear systems of equations (Harrow, Hassidim & Lloyd, 2009) (more popularly known as the HHL09 algorithm paper) ...
11
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1answer
208 views

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

As the name already suggests, this question is a follow-up of this other. I was delighted with the quality of the answers, but I felt it would be immensely interesting if insights regarding ...
11
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1answer
251 views

Quantum walk with binary tree

I’m trying to grok quantum walks, and would like to create an example that walks a perfect binary tree to find the one and only marked leaf node. Is this possible? If so, suppose the depth of the tree ...
11
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0answers
582 views

Is there a list of accessible open problems in quantum computing from a theoretical computer science perspective?

(Classical) theoretical computer science (TCS) has a number of outstanding open problems that can easily be instantiated in a manner that is accessible to a wider general public. For example, ...
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2answers
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Classical Memory enough to store states up to 40 qubits quantum system?

As a part of a discussion with my 'classical' friend, he insisted that making a a state machine for calculating the outcome of quantum computer is possible; so, simply calculate the outcomes of (known)...
10
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3answers
415 views

Does Shor's algorithm end the search for factoring algorithms in the quantum world of computation?

In other words, will factoring research remain solely in the classical world or are there interesting research on-going in the quantum world related to factoring?
10
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2answers
409 views

Circuit construction for Hamiltonian simulation

I would like to know how to design a quantum circuit that given a Hermitian matrix $\hat{H}$ and time $t$, maps $|\psi\rangle$ to $e^{i\hat{H}t} |\psi\rangle$. Thank you for your answer.
10
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1answer
433 views

How is Grover's algorithm used to estimate the mean and median of a set of numbers?

On the Wikipedia page for Grover's algorithm, it is mentioned that: "Grover's algorithm can also be used for estimating the mean and median of a set of numbers" So far I only knew how it can be ...
10
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1answer
124 views

Is there any source which tabulates quantum computing algorithms for simulating physical systems?

I was wondering if there is a source (online or review article) which tabulates recent algorithms, and their complexities, used in simulating various physical systems. Something along the lines of: ...
10
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3answers
262 views

Can one interrogate black boxes for quantum coherence?

This question is based on a scenario that is partly hypothetical and partly based on the experimental features of molecule-based quantum devices, which often present a quantum evolution and have some ...
10
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1answer
5k 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 ...
10
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1answer
818 views

Quantum phase estimation and HHL algorithm - knowledge of eigenvalues required?

The quantum phase estimation algorithm (QPE) computes an approximation of the eigenvalue associated to a given eigenvector of a quantum gate $U$. Formally, let $\left|\psi\right>$ be an ...
10
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1answer
386 views

Why is an oracle qubit necessary in Grover's algorithm?

I am a bit confused about the necessity of an oracle qubit in Grover's algorithm. My question is, does it depend on how you implement your oracle whether you need an oracle qubit or not? Or, it there ...

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