# 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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### Quantum comparator with one fixed input

I currently need to implement efficiently a quantum comparator, with one of the values that is known at generation-time. In other words, I am searching for a quantum routine ...
87 views

### The most important quantum question , how to force a superposition qubit to collapses to an exact value?

Note: forcing a superposition qubit to collapses to 1, means cancel the other value 0 to get 1 appear Question details step by step: ...
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### QAOA and symmetry effects on the angles

In this paper, QAOA on Maxcut shows symmetries that allow them to restrict their search space intervals. But how do they find such intervals knowing that in the original QAOA angles $\gamma,\beta$ are ...
37 views

### What is $\mathbb{Z}_2$ symmetry?

I encountered the notion of $\mathbb{Z}_2$ symmetry in an article. Can someone give a definition?
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### What happens with first phase factor in QFT?

I'm using Mermin's Quantum Computer Science book to understand Shor's algorithm, but I can't figure out why one of the phase factors drops out of the probability for measuring a certain y. This is ...
313 views

### Grover's algorithm: what to input to Oracle?

I am confused about what to input to Oracle in Grover's algorithm. Don't we need to input what we are looking for and where to find what we are looking for to Oracle, in addition to the ...
14 views

### Ansatz Techniques to Multi-Body Physics Problems

I have been reading this paper: https://arxiv.org/abs/1906.01563v1. I am wondering: is it possible to use the idea behind quantum circuits to build classical Hamiltonians represented in the same way?...
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### What does a zero state combined state vector for 2 qubits mean?

I was fiddling with the quantum circuit used for Deutsch's algorithm and I was led to a zero state as a result which is bizarre. I don't know how to explain this result. ***I'm using Nielsen and ...
419 views

### 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 ...
79 views

### Quantum Optimization via Quantum Label Classification in Quantum Circuits

I have been reading Farhi and Neven's paper on quantum neural networks on quantum circuits. I also found an example - albeit not ideal as pointed out by a couple of users - thank you - in here. ...
3k views

### 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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### Why is the second register needed to define bit flip quantum oracles in a way that distinguishes between complementary oracles?

If our input $x \in \{0, 1\}^{n}$ is given as a black box, we usually query an oracle as follows. $$O_{x}|i, b \rangle = (-1)^{b x_{i}} |i, b \rangle$$ $i = \{1, 2, \cdots, n \}$ is the index of the ...
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### Does an oracle use only the eigenstates of the quantum register?

The working of a quantum oracle is still not completely clear to me and I have a few questions: As I understand it, an oracle is a unitary quantum gate and must somehow differentiate between the ...
45 views

Suppose you have a large collection of N numbered copper coins. However, one of them is nickel but looks exactly the same as the rest. How do you find out which number the nickel coin has? Classical ...
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### Phase estimation error analysis

This question is about Lemma $7.1.2$ in Kaye, Laflamme, and Mosca's textbook: Let $\omega = \frac{x}{2^n} = 0.x_1x_2\ldots x_n$ be some fixed number. The phase estimation algorithm applied to the ...
91 views

### Using the HHL algorithm to compute $A |b \rangle$ instead of $A^{-1} |b \rangle$

In the paper "Compiling basic linear algebra subroutines for quantum computers" here, they discuss (page 2 bottom right) using the HHL algorithm to multiply a vector by a matrix. However, after ...
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### The possibility of recovering the matrix $A+B$ from $e^{i(A+B)t}$ for Hermitian $A,B$

In the paper "Compiling basic linear algebra subroutines for quantum computers" here, the introduction seems to imply that the subroutines covered will touch on matrix addition and multiplication, ...
183 views

### Clarification of the “Calculations” section of the (HHL09) paper

I am reading this paper entitled "Quantum algorithm for linear systems of equations" and am trying to understand a portion of the algorithm described on page 2 and in more detail in the appendix ...
49 views

### Eliminating a term of a superposition state

Is there a way of eliminating a term of a superposition state? Let's say I have the state $$\frac{1}{\sqrt 2}|00\rangle + \frac{1}{2}|01\rangle + \frac{1}{2}|10\rangle$$ What operation would I do to ...
163 views

### Quantum counting in Q#

I cannot seem to get an estimate for the number of solutions using the quantum counting algorithm described in Nielsen and Chuang, i.e. phase estimation with the Grover iteration acting as $U$. I try ...
88 views

### Counting in Q#: number of solutions

I have this program derived from Microsoft Quantum Katas for counting (see here): ...
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### Can anybody explain or suggest a good reference on how to make a modular exponentiation circuit for N=15 with any coprime base?

I have read many papers related to it but in every paper, they just show the circuit of order finding algorithm for N=15, but did not explain what is the procedure to make it. It will be great if ...
45 views

### Quantum gate teleportation T gate

I am faced with the problem of teleporting certain gates using modified Bell states. For example, I have solved the problem with the $S$ gate, which is defined as following: Alice and Bob share a ...
59 views

### Why should we use inverse QFT instead of QFT in Shor's algorithm?

Why should we use inverse QFT instead of QFT in Shor's algorithm? When I tried to simulate Shor's algorithm for small numbers, I got an answer even when I used just QFT instead of inverse QFT.
244 views

### Grover's diffusion on subset of input space

Is it possible to run grover's diffusion step on a subset of the possible input space? By this, I mean is it possible to do the diffusion process with a state space isn't in a total superposition of ...
68 views

### Implementation of Grover's Algorithm (minimum spanning tree)

I am trying to solve a minimum spanning tree problem using Grover's Algorithm. To accomplish this I would need to search a list for the minimum weight or edge for each point, for example: Given the ...
53 views

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### How do quantum computers prevent “quantum noise”?

On the Wikipedia page for Shor's algorithm, it is stated that Shor's algorithm is not currently feasible to use to factor RSA-sized numbers, because a quantum computer has not been built with enough ...
350 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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### 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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### How to understand Deutsch-Jozsa algorithm from an adiabatic perspective?

I'm trying to understand the Deutsch-Josza algorithm from an adiabatic perspective as presented in Adiabatic quantum computing A: Review of modern physics, vol 90, (2018) pp 015002-1 (arXiv version). ...