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1500 questions
8
votes
3 answers
Is there any method of adding two operators in a circuit?
I am trying to reconstruct the time evolution of a Hamiltonian on the quantum computing simulator, quirk. Ideally I would like to generalise this to any simulator. The unitary matrix is
$$U(t)=e^{-iHt}$$
and I've found a way to decompose the…
Cameron
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8
votes
1 answer
What are XX, YY, YZ etc. couplings?
The D-wave quantum computer allows us to be able to minimize Ising models. In reading other questions and responses, particularly What would be the simplest addition that would make the D-Wave architecture universal?, XX couplings (and others have…
Jacob Wise
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8
votes
1 answer
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 that they tackle fairly different kinds of problems for…
user5438
8
votes
2 answers
Why it is hard to simulate a quantum device by a classical devices?
I was recently watching a talk by Urmila Mahadev on "Classical Verification of Quantum Computations" (see this). I am not new to quantum computation just have a familiarity with the qubit and some part of quantum mechanics. I even did not get the…
new_bee
- 183
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8
votes
1 answer
Isomorphism between the Clifford group and the quaternions
How do I find an explicit isomorphism between the elements of the Clifford group and some 24 quaternions?
The easy part:
The multiplication of matrices should correspond to multiplication of quaternions.
The identity matrix $I$ should be mapped to…
knot
- 83
- 4
8
votes
4 answers
Non-layperson explanation of why a qubit is more useful than a bit?
I have a computer science and mathematics degree and am trying to wrap my head around quantum computing and it just doesn't seem to make sense from the very beginning. I think the problem is the definitions out there are generally watered down for…
Lee Cascio
- 81
- 4
8
votes
2 answers
How to obtain Y rotation with only X and Z rotations gates?
Let's say you have a system with which you can perform arbitrary rotations around the X and Z axis. How would you then be able to use these rotations to obtain an arbitrary rotation around the Y axis?
I have seen somewhere that rotation around an…
PhysicsMan
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8
votes
3 answers
Why is the state of multiple qubits given by their tensor product?
How did we derive that the state we get by $n$ qubits is their tensor product? You can use $n=2$ in the explanation for simplicity.
Archil Zhvania
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8
votes
2 answers
Understanding (theoretical) computing power of quantum computers
I am very new to quantum computing and just try to understand things from a computer scientist's perspective.
In terms of computational power, what I have understood,
100 ideal qubits ... can equate to [$2^n$ pieces of information]
Now Rigetti…
J. Doe
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8
votes
2 answers
Transformation of a Bell state
I am relatively new and interested in quantum computing.
Specifically, I am interested in transforming an equation that I found on Wikipedia. But I did not quite understand the transformation.
$…
P_Gate
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8
votes
1 answer
How to prevent future loops using a control qubit?
I am trying to construct a quantum multiplier using the method described here: https://arxiv.org/abs/quant-ph/0403048. However, it seems that the control qubit would only disable the following gates for one iteration. Afterward, the $|y\rangle$…
nikojpapa
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8
votes
1 answer
Understanding the Group Leaders Optimization Algorithm
Context:
I have been trying to understand the genetic algorithm discussed in the paper Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians (Daskin & Kais, 2011) (PDF here) and Group Leaders…
Sanchayan Dutta
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8
votes
1 answer
Efficiently performing controlled rotations in HHL
This question builds off of this question.
In the HHL algorithm, how do you efficiently do the $\tilde{\lambda}_k$-controlled rotations on the ancilla qubit? It seems to me that since you don't know the eigenvalues a priori, you would have to…
Paradox
- 337
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8
votes
2 answers
Simulation vs Construction of Fredkin gate with Toffoli gates
I'm working my way through the book "Quantum computation and quantum information" by Nielsen and Chuang. (EDIT: the 10th anniversary edition).
On chapter 3 (talking about reversibility of the computation) exercise 3.32, it is possible to see that…
Davide_sd
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8
votes
3 answers
$R_z$ gate representations
Why is the $R_z$ gate sometimes written as:
$$
R_{z}\left(\theta\right)=\begin{pmatrix}1 & 0\\
0 & e^{i\theta}
\end{pmatrix},
$$
while other times it is written as:
$$
R_{z}\left(\theta\right)=\begin{pmatrix}e^{-i\theta/2} & 0\\
0 &…
Bella
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