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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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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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177 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 ...
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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 ...
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Quantum Walk: Why the need of adding “tail” nodes to the root?

As stated in the question, I have found in several papers (e.g. 1, 2) that in order to perform a quantum walk on a given tree it is necessary to add some nodes to the root $r$, say $r^{'}$ and $r^{"}$....
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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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Does the GLOA have any advantage over the Solovay-Kitaev algorithm?

The Solvay Kitaev algorithm was discovered long before the Group Leaders Optimization algorithm and it has some nice theoretical properties. As far as I understand, both have exactly the same goals: ...
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Gradient boosting akin to XGBoost using a quantum device

I am currently trying to implement a boosting algorithm akin to XGBoost with a quantum device. The reason is that I want to make use of a quantum device to train weak classifiers. However, as far as I ...
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95 views

Proof of the optimality of Grover's algorithm

I am currently working on the proof of Grover's algorithm, which states that the runtime is optimal. In Nielsen they say, the idea is to check whether $D_k$ is restricted and does not grow faster ...
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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.
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How many qubits and how many gates, are required for finding the eigenvalues of a matrix?

Say I have an $N \times N$ matrix and I want to know the eigenvalues to a precision of $\pm \epsilon$. How many qubits and how many gates do I need?
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Are non-secret-based quantum money mini-schemes susceptable to Jogenfors' “reuse attack?”

Aaronson and Christiano call public-key or private-key quantum mini-schemes $\mathcal M$ secret-based if a mint works by first uniformly generating a secret random classical strings $r$, and then ...
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Quantum SVM Algorithm Error on import

I am experimenting with some Qiskit ACQUA AI algorithms which require the following import statement: from datasets import * However, ...
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How exactly is the stated composite state of the two registers being produced using the $R_{zz}$ controlled rotations?

This is a sequel to How are two different registers being used as "control"? I found the following quantum circuit given in Fig 5 (page 6) of the same paper i.e. Quantum Circuit Design for ...
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Consequences of SAT ∈ BQP

"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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Is there a BQP algorithm for each level of the polynomial hierarchy PH?

Note: Cross-posted on Theoretical Computer Science SE. This question is inspired by thinking about quantum computing power with respect to games, such as chess/checkers/other toy games. Games fit ...
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Correspondence between the Topological model and Quantum Circuit model

For example, given the $R$ & $F$ gates and Toric codes for a given problem, how to convert this code into the conventional circuit model and vice versa. From the literature developed, it seems ...
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How can blackholes be fast information scramblers?

I noticed that there was already a post discussing the fast scrambling property of black holes. But it seems no satisfactory answer was given. As mentioned by L. Susskind et. al, the fast scrambling ...
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Why is there no $N$ in the time complexity of the QLSP algorithm by Childs et al.?

The paper Quantum linear systems algorithms: a primer by Dervovic et al has this table on page 3: I'm not sure why there's no $N$ in the time complexity of the algorithm by Childs et al. i.e. $\...
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Counting in Q#: number of solutions

I have this program derived from Microsoft Quantum Katas for counting (see here): ...
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Does HHL implementation requires a priori eigendecomposition?

I am interested in HHL algorithm and despite all the problems related to current technologies, I am trying to understand how it has to be implemented. I have seen from these two available circuits (...
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What can be some bachelor thesis ideas in quantum random walks?

Note: Cross-posted on Theoretical Computer Science Stack Exchange. I am an undergraduate, reading about quantum information and quantum technology. For about some time, I have been interested in the ...
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What are applications of HHL's “simple example” to determine similar stable states of different quantum processes?

The HHL paper "Quantum algorithm for linear systems of equations" [link] initially describes a "simple example" to illustrate the potential power of their algorithm. They state: Consider a ...
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Quantum addressing scheme

Nielsen explains how a search algorithm can access a classic database. I have a few questions. I hope you can help me a bit :) I work with a few quotes from the book. The principle of operation is ...
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Genetic algorithm does not converge to exact solution

I'm trying to evolve quantum circuits using genetic algorithms as they did in this paper Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians (Daskin &...
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Deutsch Algorithm on a Quantum Turing Machine

I understood how a Quantum Turing Machine works from this lecture. It would be great if someone could give an example of how this machine could be used to solve a real problem though, for example, ...
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108 views

Algorithm to allocate tasks and tools fairly to 2 players

Puzzle I have the following puzzle for which I would like to create a quantum algorithm. There are 2 players that need to complete 3 tasks as fast as possible. There are 3 different types of tasks ( ...
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Grover's algorithm and Battleship solution

I have read that quantum computers are not known to be able to solve NP-complete problems in polynomial time. However, if you consider a game of Battleship with grid size $X, Y$ and represent this by ...
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How to apply unitary coupled cluster to a spin problem?

I understand how to apply UCC to a problem formulated in a second-quantized (fermion) form: you start with some state and then create a unitary operator out of single-body (or double-, triple- and so ...
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Possible results from Shor's algorithm in practice

After reading through Shor's algorithm, I have a few questions about the probability of factoring semiprime number out. Here is some background of the question. To factor a semiprime number $N$ such ...
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What is the complexity of the quantum phase estimation in Grover's algorithm?

Suppose we are using GA (Grover's algorithm) such that we are given it has 2 or more solutions. The search space is of size $N$. We all know Grover's algorithm has, at worst, a time complexity ...
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Optimal sampling strategy for VQE

In VQE we wish to minimize some cost function $F(\vec{x})$ that is dependent on a quantum state $\left| \psi_\vec{x} \right>$ which is prepared by a unitary $U(\vec{x})$ depending on some (...
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Does Brassard's algorithm for calculating the mean make implicit assumptions on distribution?

In An optimal quantum algorithm to approximate the mean and its application for approximating the median of a set of points over an arbitrary distance Brassard presents a quantum algorithm for finding ...
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Speedup Prange ISD using Grover

In his 2009 paper, Grover vs McElicee, Bernstein proposed to use the Grover's algorithm to obtain a quadratic speedup on the Prange ISD. However, it is not quite clear to me in which part of the ...
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Would this quantum algorithm implementation work?

I am trying to implement the order finding algorithm on Cirq finding the minimal positive $r$ for coprime $x$ and $N$ satisfying the equation $x^r \ = \ 1$(mod$ \ N$). In my case, I have set $x \ = \ ...
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Pointer to related research (paper)

Recently, I was reading a paper (arXiv:1804.03719 [cs.ET]), which had the following quote (the most relevant part has been bolded), Quantum algorithms are often grouped into number-theory-based, ...
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Extrapolation of CRISPR

Can quantum computing do a simple simulated extrapolation of CRISPR (clustered regularly interspaced short palindromic repeats) projects using a limited number of variables? I mean something like ...
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188 views

FPGA qubit simulation

This question is regarding the simulation of qubits, using FPGAs. My question is: how does using FPGAs to simulate qubits help us understand or give us an insight into how quantum computers could be ...