Questions tagged [quantum-algorithms]

For questions about quantum algorithms, that is, sequences of quantum gates, operations, and measurements, whose purpose which achieve some goal. Standard examples are Shor's and Grover's algorithms.

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Comparing BQM and CQM solving for a tree-path problem

I'm currently working on a project for my thesis regarding BQM and CQM optimisation for a path problem. Without going too much on the details, here's some info: the structure is a tree, where all the ...
Amedeo Bertuzzi's user avatar
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An unexpected result of the Implementation of a finding minimum values algorithm using a qRAM

Motivated by the article Quantum algorithm for finding minimum values in a Quantum Random Access Memory, I'm training to implement a simplified version of the proposed algorithm. But the output isn't ...
j__j's user avatar
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What is the initial state in the second register in Shor's algorithm?

Following up on this question, can someone help me clear up the notation we're using for states in Shor's algorithm? It's very unclear what the sentence "where the second register is $|1\rangle$ ...
Jackson Walters's user avatar
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Complexity of the quantum circuits that are needed to implement communication protocol?

Consider the following simultaneous communication problem. Alice and Bob do not share any entanglement or any common randomness, and cannot communicate directly with each other. As inputs, x is given ...
Ruben Hoba's user avatar
2 votes
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Quantum computation of classical Fisher information

Consider a pure $n$-qubit quantum state $|\psi_\theta\rangle$ prepared by some parametrized quantum circuit. There exist well-known algorithms to efficiently estimate the quantum Fisher information ...
phonon's user avatar
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Can D-Wave presently solve real-world problems that conventional computers cannot solve?

There are number of threads on this site about the ability of QCs solving real-world problems (see for example What are the practical applications of quantum computing in engineering by the year 2030?,...
Max's user avatar
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How to calculate number of qubits required for Grover Algorithm while constructing it's oracle and diffuser for any Specific Algorithm or Hash?

I am reading a paper titled, " (Towards Post-Quantum Secure Symmetric Cryptography: A Mathematical Perspective)". Here, I am able to understand the gate counts and T-depth calculations. ...
Syed Shahmir Kazmi's user avatar
5 votes
1 answer
163 views

What is the hidden subgroup in Deutsch-Jozsa?

It is noted by several sources (e.g. this paper) that the problem solved by the Deutsch-Jozsa (DJ) algorithm is an instance of the Hidden Subgroup Problem (HSP). However, I fail to see this for $n>...
smitke6's user avatar
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How can I derive the very basic formulas used in Grover's algorithm?

I have been studying the Grover's algorithm for quite some time. I have used David McMohan (Quantum Computing Explained), M. Suhail Zubairy (Quantum Mechanics For Beginners) and some research papers. ...
Syed Shahmir Kazmi's user avatar
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1 answer
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Pennylane variational classifier demo - need for padding

In the variational classifier demo from Pennylane, the data loading is performed with ...
Sarvapriya Tripathi's user avatar
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What is the total number of qubits required for the Harrow-Hassidim-Lloyd algorithm?

I am fairly new to Quantum Computing and I know a bit of Linear Algebra. I am currently working on the HHL algorithm, I'm having confusion as to how many qubits are actually required in the circuit ...
Subhradeep Sarkar's user avatar
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How to best implement this algorithm?

I am trying to design an algorithm to find a solution to a certain problem. I have N qubits which encode the problem (let's call them the problem qubits) and one check_qubit (which is flipped to |1>...
Q.Ask's user avatar
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The possibility of a Quantum image classifier

I want to create an exhaustive database of all possible contour images(B&W) with their image tags, for a given resolution. By classifying every single image possible for the resolution, I want to ...
LithiumPoisoning's user avatar
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If you had a 100 qubit fully fault-tolerant quantum computer, what would you do?

As quantum computers improve, eventually we may have error-corrected devices that have very low error rate. However, many applications (Shor's algorithm, quantum chemistry) appear to require thousands ...
shixian105's user avatar
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1 answer
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Simulating Sparse Hamiltonians: help understanding query complexity bounds

tl;dr: How can I show that $e^k/k^k$ is less than $\epsilon^2/2$ when $k=\Omega\left(\frac{\log(1/\epsilon)}{\log \log(1/\epsilon)}\right)$, where $k,\epsilon\in \mathbb{R}$ and > 0? Context: Berry ...
muru's user avatar
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When is it justified to have an oracle in a quantum algorithm?

I've always been confused as to when a quantum algorithm is allowed to have an oracle and what kind of a function the oracle can have. For instance, I know in Hamiltonian simulation algorithms, you ...
confusion's user avatar
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Visual the qubit state after amplitude encoding

I trying to visualize qubits state after amplitude encoding. I have the following code which takes the 8 feature [1/2, 1/2, 1/2, 1/2,1/2, 1/2,1/2,1/2] and encodes into 3 qubits. I now get the output [...
kannan quantum's user avatar
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The possibility of an image classifier using quantum computer architecture?

Consider an exhaustive database of all contour images that can ever be created on a 16x16 grid. Out of the $2^{256}$ unique possibilities, could a quantum computer classify all the resulting images ...
LithiumPoisoning's user avatar
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Help to make the equations of state of qubits?

.., and find their cofacents, after H(q1) ->CNOT(q1,q2) -> H(q2) On the website https://algassert.com/ The preparation is like this. I understand so far The preparation is like this. I ...
Даниил Данилов's user avatar
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What's an example of a superposition $\sum_i \sqrt{p_i}|i\rangle$ that cannot be prepared efficiently?

As also discussed in (How does the induction step in the Grover-Rudolph scheme to prepare superpositions from probabilities work? and How does the uncomputation step work in the Grover-Rudolph scheme ...
glS's user avatar
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How does the uncomputation step work in the Grover-Rudolph scheme to prepare $\sum_i\sqrt{p_i}|i\rangle$?

In https://arxiv.org/abs/quant-ph/0208112, the authors discuss a scheme to, given a discrete probability distribution $\mathbf p\equiv (p_i)_i$, under some assumptions on $\mathbf p$, prepare the ...
glS's user avatar
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How does the induction step in the Grover-Rudolph scheme to prepare superpositions from probabilities work?

In https://arxiv.org/abs/quant-ph/0208112, the authors discuss a scheme to, given a discrete probability distribution $\mathbf p\equiv (p_i)_i$, under some assumptions on $\mathbf p$, prepare the ...
glS's user avatar
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In Deutsch–Jozsa algorithm, why one can safely ignore the last qubit of oracle output?

Wikipedia article about Deutsch-Jozsa algorithm says, under the section Algorithm, that: At this point the last qubit, $$\frac{|0\rangle - |1\rangle}{\sqrt{2}}$$ may be ignored. Does it mean that, ...
ElleryL's user avatar
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The Qiskit code's output doesn't seem to be what I expected

...
Anees Ur Rehman's user avatar
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What are the quantum algorithms available for Monte Carlo sampling?

What are the quantum algorithms available for performing Monte Carlo sampling. Is there any implementation of these algorithms. Any kind of resources would be helpful
Rag's user avatar
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3 answers
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Seeking Programming Projects and Tools for Quantum Gate Decomposition Implementations

The Solovay-Kitaev theorem shows that "this approximation can be made surprisingly efficient, thereby justifying that quantum computers need only implement a finite number of gates to gain the ...
138 Aspen's user avatar
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Is the QFT optimal in the quantum phase estimation algorithm?

We can concisely summarise the quantum phase estimation (QPE) algorithm as follows: Generate the state $\sum_{k=0}^{2^n-1} \lambda^k |k\rangle$ efficiently using a series of controlled-unitary ...
glS's user avatar
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1 answer
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Does subtraction circuit have a class like full or half Carry adder circuit in qiskit? one subtraction circuit code-example in qiskit?

I need a subtraction circuit to calculate Laplacian in edge processing, but I didn't find any class in qiskit.Do I have to write the code myself?
f h's user avatar
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Two-way quantum computers (like in Ising model) - are they possible? Could solve general NP problems? [closed]

Standard one-way quantum computers (1WQC) allow for e.g. Shor, Grover algorithms, however, general NP problems seem too difficult for them(?) - bringing an open question if they could be somehow ...
Jarek Duda's user avatar
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Exponential modulation on qiskit, Shor algorithm [duplicate]

I´m trying to code the shor algorithm for any N and any a but i always find examples of code for the N=15. My first question is how is this funtion( provided by qiskit ) does the exponential ...
Diogo Chikhi's user avatar
6 votes
0 answers
71 views

Is amplitude estimation optimal?

Amplitude estimation requires $O(1/\epsilon)$ measurements if we want to estimate an amplitude to absolute precision $\epsilon$. Is this optimal? Why can't we do better than this? I'm trying to see if ...
confusion's user avatar
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3 votes
1 answer
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Determining the number of qubits to represent the eigenvalues in HHL algorithm?

I am trying to understand how well the HHL algorithm would scale. Therefore my first inquiry is how the number of qubits scale with the size of the problem ie the size of the Matrix A in the linear ...
Noé Bosc-Haddad's user avatar
2 votes
1 answer
153 views

What quantum algorithms can be used to solve for eigenstates and eigenvalues of a hermitian matrix?

I am working with a tight binding model. I am looking for a way I can efficiently find the eigenvalues and eigenvectors of the Hamiltonian using a quantum algorithm. Can someone suggest some good ...
Cheshta Joshi's user avatar
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37 views

Why are the other qubits affected by a phase flip in Shor's 9-qubit code?

We have the following "concatenated" initial state in the 9-qubit Shor code: $\alpha{(|000\rangle+|111\rangle)(|000\rangle+|111\rangle)(|000\rangle+|111\rangle)}/{2\sqrt{2}}+\beta{(|000\...
Alan Whitteaker's user avatar
12 votes
1 answer
692 views

How are quantum algorithms devised?

This is a soft question, but I find it to be a very pertinent one... Algorithms for Grover's search and Simon's problems seem to come completely out of the blue, and I find it very hard to understand ...
Alan Whitteaker's user avatar
2 votes
3 answers
331 views

How do we measure the probability of outcomes in a quantum computer if qubits collapse when measured?

I understand the idea behind Quantum Computing being that we superpose all possible states of a system of qubits and amplify the probabilities of whatever it is that we want depending on the circuit ...
Omeglac's user avatar
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1 vote
1 answer
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General Grover's search showing wrong results on a particular instance

I am trying to implement a general Grover's search for n qubits searching for m marked elements. I happened to observe that for ...
abirbhav's user avatar
2 votes
1 answer
72 views

Is there something like error-suppression codes?

My question is a bit on the soft side, and basically asks if there is something between error mitigation and full error correction? On the one hand, as far as I understand, trying to increase the ...
Nikita Nemkov's user avatar
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Heuristics on Quantum computers

I found the article : Strengths and Weaknesses of Quantum Computing, 1997 Charles H. Bennett, Ethan Bernstein, Gilles Brassard, Umesh Vazirani As far as I understand, this one states that quantum ...
deb2014's user avatar
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Why can Shor code fix arbitrary errors?

This is taken from Page 434 of Nielsen and Chuang: To simplify the analysis, suppose noise of an arbitrary type is occurring on the first qubit only; we’ll come back to what happens when noise is ...
Alan Whitteaker's user avatar
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1 answer
55 views

Why is "this" particular decomposition/regouping of states observed?

This question is motivated from this as well as the regrouping of terms in Shor code. The setup is not important, but it is being provided for context. $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$ $|...
Alan Whitteaker's user avatar
0 votes
2 answers
164 views

Is there a quantum algorithm for the closest vector problem on a 2-dimensional lattice?

Is there a standard quantum algorithm (adiabatic or density matrix based) that can output the answer to a 2-dimensional closest vector problem: ie. find the closest lattice point (the blue one) that ...
James's user avatar
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1 answer
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How to read the result of this HHL algorithm circuit output?

I have computed the final states of a 1-qubit HHL circuit using initial conditions $$ A|x\rangle = |b\rangle$$ $$\begin{bmatrix} 8 & 6+i \\ 6-i & -1\end{bmatrix} |x\rangle = \begin{bmatrix} \...
James's user avatar
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1 answer
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Verification for calculation on Shor's code

Here I have tried to determine the end result for the qubit states, when we apply an arbitrary gate on the first qubit in the 9 qubit code. I have followed this diagram: U's operation on a qubit can ...
Alan Whitteaker's user avatar
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0 answers
49 views

Random variable as tensor product of its components

Consider a finite random variable $X: \Omega \rightarrow \mathbb{R}^d$ on a probability space $(\Omega, 2^{\Omega}, P)$. Let $H_{\Omega}$ and $H_E$ be two Hilbert spaces with basis states $ \{| \omega ...
Simon's user avatar
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2 votes
0 answers
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GPU Support for Qiskit's SPSA Optimization Algorithm

I am using Qiskit's SPSA optimization algorithm to find the ground state energy of various lattices (fermi-Hubbard model) by running different circuits through it and having the algorithm modify the ...
Nidhish Sharma's user avatar
-1 votes
1 answer
136 views

4-cities traveling salesman quantum algorithm (QUBO)

A quantum version of the traveling salesman algorithm is discussed here: There is a reference to QUBO, Ising, and some matrix constructions, and the output in the end: Is anyone able to run through ...
James's user avatar
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2 votes
2 answers
279 views

What is period finding useful for in Shor's algorithm?

Could someone help me to understand the concept behind period finding in Shor algorithm?. I'm a beginner in quantum computing. I want to know why we use Shor's algorithm to find the period and what is ...
Karthick Raja's user avatar
1 vote
0 answers
19 views

How does Functional Completeness look like in the quantum world?

Can Post's theorem help to elucidate the nature of quantum logic or other non-classical logics? Quantum logic uses a different set of logical connectives than classical logic, which makes questions of ...
Pole_Star's user avatar
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1 answer
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Quantum algorithms and binomial distributions and probabilities

Qubits in a quantum computer are mostly spins of quantum particles.But since spin can take up to 2 values does this mean quantum algorithms are applied mathematics which make use of binomial ...
Volpina's user avatar
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