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1500 questions
31
votes
3 answers
What is the difference between superpositions and mixed states?
My understanding so far is: a pure state is a basic state of a system, and a mixed state represents uncertainty about the system, i.e. the system is in one of a set of states with some (classical) probability. However, superpositions seem to be a…
Norrius
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30
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2 answers
When will we know that quantum supremacy has been reached?
The term "quantum supremacy" - to my understanding - means that one can create and run algorithms to solve problems on quantum computers that can't be solved in realistic times on binary computers. However, that is a rather vague definition - what…
blalasaadri
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30
votes
5 answers
How can I implement an n-bit Toffoli gate?
I want to create a Toffoli gate controlled by n qubits, and implement it in QISKit. Can this be done? If so, how?
Ali Javadi
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30
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5 answers
Are there any organised resources available from where I can begin my quantum computing studies?
I am a computer science student and am currently searching for resources from where I can learn about quantum computers, quantum computing models, their working principles, their gates and some simple quantum algorithms.
Aman Gupta
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30
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2 answers
What is the difference between quantum annealing and adiabatic quantum computation models?
From what I understood, there seems to be a difference between quantum annealing and adiabatic quantum computation models but the only thing I found on this subject implies some strange results (see below).
My question is the following: what is…
Adrien Suau
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30
votes
3 answers
How does measurement of one qubit affect the others?
To represent a quantum computer's state, all the qubits contribute to one state vector (this is one of the major differences between quantum and classical computing as I understand it). My understanding is that it's possible to measure only one…
auden
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29
votes
2 answers
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 $e^{\frac{i\hat{H}t}{\hbar}} |\psi\rangle$ with $\hbar =1$.
Thank you for your answer.
Gradius
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29
votes
4 answers
Are quantum computers just a variant on Analog computers of the 50's & 60's that many have never seen nor used?
In the recent Question "Is Quantum Computing just Pie in the Sky" there are many responses regarding the improvements in quantum capabilities, however all are focussed on the current 'digital' computing view of the world.
Analog computers of old…
Philip Oakley
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29
votes
5 answers
Does Moore's law apply to quantum computing?
Plain and simple. Does Moore's law apply to quantum computing, or is it similar but with the numbers adjusted (ex. triples every 2 years). Also, if Moore's law doesn't apply, why do qubits change it?
Alex Jone
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29
votes
3 answers
Is there any potential application of quantum computers in machine learning or AI?
A lot of people believe that quantum computers can prove to be a pivotal step in creating new machine learning and AI algorithms that can give a huge boost to the field. There have even been studies that our brain may be a quantum computer, but so…
Piyush Kathuria
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28
votes
4 answers
Why can't there be an error correcting code with fewer than 5 qubits?
I read about 9-qubit, 7-qubit and 5-qubit error correcting codes lately. But why can there not be a quantum error correcting code with fewer than 5 qubits?
Aleph
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28
votes
2 answers
Why does the "Phase Kickback" mechanism work in the Quantum phase estimation algorithm?
I've probably read the chapter The quantum Fourier transform and its applications from Nielsen and Chuang (10 th anniversary edition) a couple of times before and this took this thing for granted, but today, when I looked at it again, it doesn't…
Sanchayan Dutta
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28
votes
2 answers
Why is it important to eliminate the garbage qubits?
Most reversible quantum algorithms use standard gates like Toffoli gate (CCNOT) or Fredkin gate (CSWAP). Since some operations require a constant $\left|0\right>$ as input and the number of inputs and outputs is equal, garbage qubits (or junk…
Be Brave Be Like Ukraine
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27
votes
1 answer
How to understand the Haar measure from a quantum information perspective?
I found it a little difficult to understand it using Wikipedia and some mathematical documents. How to understand the Haar measure from a quantum information theory perspective? Are there any materials that explain it?
raycosine
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27
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1 answer
What are examples of Hamiltonian simulation problems that are 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 to see that Hamiltonian simulation is BQP-hard…
groupsgroupsgroups
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