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1500 questions
7
votes
1 answer
How to generate all stabilizer states numerically?
I would like to obtain a list of all stabilizer states in the given dimension (not necessarily qubit systems). What is an efficient way of generating this list numerically?
Ver
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7
votes
1 answer
What is the probability of finding the second qubit as $0$ in the state $|\psi\rangle=\frac1{\sqrt2}|00\rangle+\frac12|10\rangle-\frac12|11\rangle $?
Assuming two qubits start in the state:
$|\psi\rangle = \frac{1}{\sqrt 2}|00\rangle + \frac{1}{2}|10\rangle- \frac{1}{2}|11\rangle $
What is the probability of measuring the second qubit as 0? And what is the new state of the system after measuring…
Lizzo
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7
votes
3 answers
What can I conclude about $\langle \phi|\pi_1\pi_2|\phi\rangle$ if $\langle \phi|\pi_i|\phi\rangle\ge e$?
If I have two projectors $\pi_1, \pi_2$ such that for some $|{\phi}\rangle$:
$\langle {\phi}| \pi_1 |{\phi}\rangle \geq e$ and $\langle {\phi}| \pi_2 | {\phi}\rangle \geq e$
What can I conclude about the following quantity?
$\langle {\phi} | \pi_1…
islamfaisal
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7
votes
2 answers
Shor's algorithm: initialization of second register
I am trying to understand Shor's algorithm. I am not quite sure why the initialization, indicated as $|1\rangle$ in the below image at the bottom left is chosen as it is? I understand the modular exponentiation method in principle, but I am not sure…
user823
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7
votes
3 answers
How to learn parameters in a quantum circuit, given an interference pattern?
Using cirq, I have the following quantum circuit, with three parameters: phi, alpha and beta:
q0 = cirq.GridQubit(0,0)
q1 = cirq.GridQubit(0,1)
phi = sp.Symbol('phi')
alpha = sp.Symbol('alpha')
beta = sp.Symbol('beta')
circuit = cirq.Circuit([
…
Calum Macdonald
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7
votes
1 answer
Could random quantum circuits be efficiently approximately simulated?
Google's landmark result last year was to compute a task with a quantum computer that a classical computer could not compute, and they chose random circuit sampling. Part of their justification was complexity-theoretic reasons that, if one can…
Sam Jaques
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7
votes
2 answers
What is a maximal number factored by Shor's algorithm so far?
With reference to a similar question here, I would like to know what is the maximal number which has been factored with Shor's algorithm so far on actual quantum hardware.
The reason I am asking a similar question as the link is that this question…
Martin Vesely
- 15,244
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7
votes
1 answer
Bob applies a projector - what happens to eigenvalues of Alice's reduced state?
Suppose Alice and Bob share a state $\rho_{AB}$. Let us denote the reduced states as $\rho_A = \text{Tr}_B(\rho_{AB})$ and $\rho_B = \text{Tr}_A(\rho_{AB})$. Bob applies a projector so the new global state is
$$\rho'_{AB} = (I_A\otimes…
user1936752
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7
votes
1 answer
What is the intuition behind "states with support on orthogonal subspaces"?
I'm sure I don't fully understand the concept of support, but I am having trouble seeing how it connects to things like density operators. I have an idea that it means, according to Wikipedia:
"In mathematics, the support of a real-valued function…
BADatThis
- 73
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7
votes
2 answers
How is the quantum relative entropy $S(\rho\|\sigma)$ defined when $\sigma$ is a pure state?
I want to evalualte the quantum relative entropy $S(\rho|| \sigma)=-{\rm tr}(\rho {\rm log}(\sigma))-S(\rho)$, where $\sigma=|\Psi\rangle\langle\Psi|$ is a density matrix corresponding to a pure state and $\rho$ is a density matrix corresponding to…
Confinement
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7
votes
1 answer
(Why) does every CSS code allow for transversal measurement?
I recently encountered the statement that
any CSS code [that encodes single-qubit logical states] has a property that measurements can be performed qubit-wise, but the measurement outcome of every qubit must be communicated classically to obtain…
jgerrit
- 161
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7
votes
2 answers
Is there a circuit to compare two quantum states?
Lets have two quantum states (single qubits ones for simplicity) $|\psi\rangle$ and $|\phi\rangle$:
$$
|\psi\rangle = \alpha_\psi|0\rangle+\mathrm{e^{i\varphi_\psi}}\beta_\psi|1\rangle
$$
$$
|\phi\rangle =…
Martin Vesely
- 15,244
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7
votes
4 answers
What is the quantum circuit to prepare a Bell state?
I was watching some lectures on qubits. They were talking about how to generate a Bell state. They described it as follows:
Prepare state 00:
$$\left |0 \right> \otimes \left |0 \right>$$
Apply the Hadamard:
$$ (H \otimes I)(\left |0 \right>…
STOI
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7
votes
1 answer
Reducing the depth of quantum circuits with ancilla qubits
This question is two-fold and considers general $n$-qubit operations on a quantum computer.
First, can a general $n$-qubit operation be implemented on a quantum computer without the use of ancilla qubits?
Second, can ancilla qubits help in reducing…
nippon
- 1,609
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7
votes
1 answer
How would Blockchain technologies change to survive a post-quantum world?
Reading this entertaining piece of a QC enthusiast mining bitcoins with a Quantum Computer (although efficiently mining bitcoins with the current state of QCs is far-fetched, it is quite possible to be done in the next few years), I wonder how…
nj2237
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