## Unstructured quantum search algorithm for unknown solutions

This code was tested on IBM’s 5-Qubit processor as an implementation of Grover’s search algorithm, but for an unknown number of solutions. This code is based on Arthur Pittenger’s book, “An Introduction to Quantum Computing Algorithms” and the mathematical structure was posted as a proof-verification question here. h q; h q; x q; s q; … Read more

## Quantum random number generator

I’m working on a Quantum Random Number Generator and wanted to get some feedback on the project so far. I’m using PyQuil to generate machine code for the quantum computer, first to create a bell state placing our random bit into a superposition, then I measure the bit to collapse the superposition and repeat the … Read more

## Grover algorithm when element not present in the array/database

I’ve been reading about the Grover algorithm for finding elements in an unstructured database by the means of quantum computing, and even done some exercises. What I don’t understand (and can’t find anywhere) is what is supposed to happen if the element is NOT present in the database. The oracle would never flip any qubit, … Read more

## Computational power of quantum finite automata

I am preparing some lecture notes on the computational power of quantum finite automata (QFA). I am a bit confused about which models of QFA are stronger and which models are weaker than standard finite automata (FA). There is one-way QFA (1QFA) and two-way QFA (2QFA). For each model, we can either have “measure-once” (MO) … Read more

## Use Less Qubits to simulate More Qubits

Lots of (quantum) applications need thousands of qubits. But suppose we are short of stable qubits, is it possible (in general) using more time (or classical computation resources) to made up this shortage? Or is there any lower bound for this proving it can’t be done? Apology for phrasing the problem in just a few … Read more

## How is the modular multiplication matrix unitary in Shor’s Algorithm?

I have been reading papers about the construction of this matrix in Shor’s Algorithm all night. The behavior of the controlled modular multiplication matrix is described as CUa2(|c⟩|y⟩)=|c⟩|(a2i)cymod in this paper. It’s described similarly here The issue I have is this does not seem to be unitary, since N<2^n, we can get stuff like this: … Read more

## Questions about Seth Lloyd’s Programming the Universe?

I have been interested in Seth Lloyd’s cosmological model (which proposes that the universe is a computer: https://en.wikipedia.org/wiki/Programming_the_Universe, https://arxiv.org/abs/quant-ph/0501135) since long ago. While I was “researching” about this topic, I found an interesting article that hungarian author Zoltán Galántai wrote (https://arxiv.org/pdf/1501.01754.pdf) I was wondering if you would answer a few questions I have about the … Read more

## What is the complexity class of exponential parallelism?

Consider the class of problems that can be computed when you have access to exponentially many processors working in parallel. How does one capture that in a proper formalism? Is there some literature on it already? Would it be true that such a class would be a superset of BQP? Answer AttributionSource : Link , … Read more

## Which is harder, an NP-complete problem or the Raz-Tal oracle problem?

This is a (hopefully) sharper version of a question that I asked previously. Which of these algorithms is believed to have a longer asymptotic runtime? The optimal algorithm guaranteed to solve some NP-complete problem using a standard Turing machine. The optimal algorithm guaranteed to solve the problem described by Raz and Tal using a Turing … Read more

## Why are MM-1QFA strictly more powerful than MO-1QFA?

While dealing with quantum finite automata (QFA), I repeatedly come across the statement that measure-many QFA (MM-1QFA, KW97) are strictly more powerful than measure-once QFA (MO-1QFA, MC97); both models are sufficiently described in this Wikipedia article. So far, I found a proof in L19 (p.5, prop.1) which shows that, for any MO-1QFA and any input … Read more