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1500 questions
8
votes
2 answers
How is the ground state of a Hamiltonian defined?
I'm studying VQE, but there is something I don't get.
We know (I think) that for a given Hamiltonian the minimum eigenvalue is associated with the ground state. But if we take the Hamiltonian to be Pauli Z, then it has two eigenvalues: 1 associated…
Sorin Bolos
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8
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2 answers
What is a separable decomposition for the Werner state?
Consider the two-qubit Werner state, defined as
$$\rho_z = z |\Psi_-\rangle\!\langle \Psi_-| + \frac{1-z}{4}I,
\quad |\Psi_-\rangle\equiv\frac{1}{\sqrt2}(|00\rangle-|11\rangle),$$
for $z\ge0$.
Using the PPT criterion, one can see that this state is…
glS
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8
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1 answer
What are the differences between the different transpiler optimization levels in qiskit
I am currently running a simple algorithm using Qiskit and I am running it for various transpiler optimization levels (0-3). I wish to know what exactly occurs differently when for example I run the algorithm with optimization level 1 as compared to…
Generic_dp
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- 5
8
votes
2 answers
How can I fill a unitary knowing only its first column?
I have a unitary matrix that I want to construct. I only care what happens to the first computational state, so the first column is specified. So far, I've been assigning each question mark to a variable and solving $UU^T = I$ analytically. But this…
psitae
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8
votes
1 answer
Physical implementation of gates on IBM Q
There is a lot of quantum gates in IBM Q Composer, however, only few are implemented physically while others can be composed of them.
When one looks at description of a quantum processor in IBM Q interface, there is a list of basis gates. For…
Martin Vesely
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7
votes
3 answers
What is meant with "shot" in quantum computation?
What is a "shot" in relation to quantum computing? I heard it is repeating time, but I don't understand it. Additionally, why is the default number of shots 1,024 in the IBM Q Experience?
One more question - I saw the sentence for each value of the…
김동민
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7
votes
2 answers
Why can the QFT be replaced by Hadamard gates?
I'm studying Shor's Algorithm.
In the book, author explains QFT can be replaced by Hadamard gates?
Why this process is possible??
Thank you everybody. This is QPE. I attach part of book!!
유도경
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7
votes
2 answers
The relationship between problem structure and exponential speedups under the query model
What problem structure(s) are required to admit an exponential speedup in the universal quantum model of computation under the query model?
Intuitively, it would seem that much of the benefit of the quantum model, as is often suggested, is due to…
Greenstick
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votes
3 answers
How to run a qasm file on IBMQ device?
I can find many qasm examples.
How can I run them on different IBMQ devices?
peachnuts
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7
votes
2 answers
Constructing a circuit for $C^1(U)$ for rotation operators with TWO single qubit gates and CNOT gate
This is the exercise 4.23 from Nielsen and Chuang, asking that if it is possible to construct $C^1(U)$ for $U=R_{x,y}(\theta)$ with TWO single qubit gates and CNOT gate. My answer is no, and I would like to argue in the following way.
First, we do…
fagd
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7
votes
1 answer
Non-unitary matrix decomposition as a sum of unitary matrices
Several quantum algorithms that deals with linear algebra and matrices that are not necessarily unitary circumvent the problem of non-unitary matrices by requiring a decomposition of the non-unitary matrix as a sum of unitary matrices.
A widely…
Adrien Suau
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7
votes
4 answers
Are there Bell-like violations that can be observed without collecting statistics?
Observing the violation of Bell inequalities, be it in their original formulation, or in the nowadays more commonly used CHSH formulation, involves computing averages of specific experimentally measurable quantities. In the CHSH formulation, these…
glS
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7
votes
1 answer
Uncomputation in quantum implementation of a classical algorithm
In Nielsens and Chuangs book, they present a way to implement a reversible version of any classical algorithm (section 3.2.5).
In short, they use Fredkin and other simple reversible gates to implement a circuit doing $(x, 0, 0, y) \rightarrow (x,…
Leander Behr
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7
votes
1 answer
Could quantum computers be useful for sending encrypted information over a classical channel?
A quantum computer running Shor's algorithm would be famously useful for decrypting information encrypted by many classical public-key cryptography algorithms. Is there any reason (either a specific proposed protocol or a general heuristic argument)…
tparker
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7
votes
1 answer
Decomposing a $(w+1)$-qubit permutation gate into $w$-qubit permutation gates, SWAPs and NOTs
Say I have a quantum circuit of $w+1$ qubits with a permutation gate (mapping computational basis states to computational basis states) that does the permutation $(i, i+1)(i+4, i+5)$ on $w+1$ qubits if $i$ is odd and the permutation $(i+1, i+2)(i+3,…
Sanchayan Dutta
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