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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10
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448 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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2answers
1k views

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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303 views

Time Entangled Quantum Blockchain

This answer cites a paper[$\dagger$] which purposes a quantum blockchain using entanglement in time. "The weakness is that the research only presents a conceptual design." - QComp2018 How could a ...
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1answer
449 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 ...
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4answers
583 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 ...
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866 views

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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3answers
293 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(|...
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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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390 views

Simplest algorithm for intuitively demonstrating quantum speed-up?

What's the simplest algorithm (like Deutsch's algorithm and Grover's Algorithm) for intuitively demonstrating quantum speed-up? And can this algorithm be explained intuitively? Ideally this would be ...
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2answers
1k views

How do you implement the Toffoli gate using only single-qubit and CNOT gates?

I've been reading through "Quantum Computing: A Gentle Introduction", and I've been struggling with this particular problem. How would you create the circuit diagram, and what kind of reasoning would ...
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1answer
552 views

Practical implementation of Hamiltonian Evolution

Following from this question, I tried to look at the cited article in order to simulate and solve that same problem... without success. Mainly, I still fail to understand how the authors managed to ...
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1answer
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Efficiently performing controlled rotations in HHL

This question builds off of this question. In the HHL algorithm, how do you efficiently do the $\tilde{\lambda}_k$-controlled rotations on the ancilla qubit? It seems to me that since you don't know ...
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260 views

Quantum algorithm for linear systems of equations (HHL09): Step 1 - Number of qubits needed

This is a continuation of Quantum algorithm for linear systems of equations (HHL09): Step 1 - Confusion regarding the usage of phase estimation algorithm Questions (contd.): Part 2: I'm not exactly ...
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1answer
300 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 ...
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1answer
82 views

Quantum XOR Cipher Construction

After getting help here with XNOR, RCA & XOR linked lists, I am now curious about quantum XOR ciphers (Google returns "no results"). In cryptography, the simple XOR cipher is a type of ...
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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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1answer
490 views

How to implement a matrix exponential in a quantum circuit?

Maybe it is a naive question, but I cannot figure out how to actually exponentiate a matrix in a quantum circuit. Assuming to have a generic square matrix A, if I want to obtain its exponential, $e^{A}...
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771 views

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) ...
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4answers
1k views

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 ...
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334 views

Quantum algorithm for linear systems of equations (HHL09): Step 2 - What is $|\Psi_0\rangle$?

This is a sequel to Quantum algorithm for linear systems of equations (HHL09): Step 1 - Confusion regarding the usage of phase estimation algorithm and Quantum algorithm for linear systems of ...
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730 views

How can I calculate the inner product of two quantum registers of different sizes?

I found an algorithm that can compute the distance of two quantum states. It is based on a subroutine known as swap test (a fidelity estimator or inner product of two state, btw I don't understand ...
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201 views

Will quantum computers be able to solve the game of chess?

Will it be possible to use quantum computing to one day solve the game of chess? If so, any estimate as to how many qubits it would require? The game of checkers has already been solved through back ...
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1answer
325 views

How to benchmark a quantum computer?

Using a simple puzzle game to benchmark quantum computers is the most clever approach I have seen so far. The author of the aforementioned article, James, makes a nice analogy to buying a laptop ("...
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1answer
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Expected repetitions of the quantum part of Shor's algorithm

Shor's algorithm to factor a number $N$ goes as follows: Pick a random value $b \in (0, N)$. Use a specific quantum computation to a sample a value $v$ that should be close to $2^{m} k/p$ where $m$ ...
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Shor's algorithm caveats when $a^{r/2} =-1 \mod N$

For an integer, $N$, to be factorised, with $a$ (uniformly) chosen at random between $1$ and $N$, with $r$ the order of $a\mod N$ (that is, the smallest $r$ with $a^r\equiv 1\mod N$): Why is that in ...
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How to create a quantum algorithm that produces 2 n-bit sequences with equal number of 1-bits?

I am interested in a quantum algorithm that has the following characteristics: output = 2n bits OR 2 sets of n bits (e.g. 2 x 3 bits) the number of 1-bits in the first set of n-bits must be equal to ...
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1answer
375 views

HHL algorithm — controlled-by-eigenvalues rotations

All the references in this question refer to Quantum algorithm for solving linear systems of equations (Harrow, Hassidim & Lloyd, 2009). The question I have is about the step where they apply ...
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1answer
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Realization of Quantum Shadowgraphy

I recently found out about shadowgraphy and was wondering if a technique like this could be used to: Visually show entanglement Suffice as a measure (e.g. continous partial trace) Most useful ...
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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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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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622 views

Resources for quantum algorithm basics

I have just started to learn about quantum computing, and I know a little bit about qubits. What is a resource where I can learn a basic quantum algorithm and the concepts behind how it works?
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1answer
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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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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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1answer
293 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 ...
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1answer
2k 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 ...
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630 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 ...
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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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1answer
155 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 ...
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1answer
227 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 ...
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1answer
202 views

Quantum Algorithm SAT structure

"Quantum magic won't be enough" (Bennett et al. 1997) If you throw away the problem structure, and just consider the space of $2^n$ possible solutions, then even a quantum computer needs about $\...
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1answer
261 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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523 views

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

I have been trying to understand what could be the advantage of using Grover algorithm for searching in an arbitrary unordered database D(key, value) with N values instead of a classical search. I ...
8
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1answer
348 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 ...
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1answer
116 views

Phononic Quantum Computing

Google returns "About 1 results" for Quantum Computing with Sound. The sole result links to an article entitled "Physicists have designed the building blocks of quantum computer that works using ...
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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 ...
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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 ...
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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: ...
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629 views

Quantum algorithm for linear systems of equations (HHL09): Step 2 - Preparation of the initial states $|\Psi_0\rangle$ and $|b\rangle$

This is a continuation of Quantum algorithm for linear systems of equations (HHL09): Step 2 - What is $|\Psi_0\rangle$? In the paper: Quantum algorithm for linear systems of equations (Harrow, ...