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Does there exists an algorithm to construct a quantum circuit given an arbitrary unitary?
Suppose there exists an algorithm that takes as input an arbitrary unitary matrix and produces as output a quantum circuit representing that matrix. Then in theory that algorithm could construct any quantum circuit. This would be quite…
treks2448
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Why does quantum phase estimation complexity scale with maximum representable energy?
In Quantum simulation of chemistry with sublinear scaling in
basis size Ryan Babbush and other authors from Google Quantum team argue, when talking about performing Quantum Phase Estimation in 1st quantization, that
The reason for our greatly…
Pablo
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7
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How to create a quantum algorithm that produces 2 n-bit sequences with equal number of 1-bits?
I am interested in a quantum algorithm that has the following characteristics:
output = 2n bits OR 2 sets of n bits (e.g. 2 x 3 bits)
the number of 1-bits in the first set of n-bits must be equal to the number of 1-bits in the second set. E.g.…
JanVdA
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7
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What are the vertices of the no-signalling set $\mathcal{NS}$?
Consider the standard 2-2 Bell scenario, with two parties each one choosing between two measurement settings, with each measurement setting leading to one of two possible measurement outcomes.
Consider the space of possible corresponding behaviours,…
glS
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7
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Derivation of Efficiency of Phase Estimation Algorithm
In the section Performance and requirements of the phase estimation algorithm of Page 224, Quantum Computation and Quantum Information by Nielsen and Chuang
Let $b$ be the integer in the range $0$ to $2^t − 1$ such that $b/2^t = 0.b_1\cdots…
SOORAJ SOMAN
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7
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How did the authors manage to simulate and get the error estimate for a neural network with greater than 7840 qubits?
In the paper A quantum-implementable neural network model (Chen, Wang & Charbon, 2017), on page 18 they mention that "There are 784 qurons in the input layer, where each quron is comprised of ten qubits."
That seems like a misprint to me. After…
Sanchayan Dutta
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7
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What is the no-signaling set and how can it be related to other types of correlations?
The paper Bell nonlocality by Brunner et. al includes a striking diagram on page 7:
This is fascinating to me because it suggests a framework of categorizing correlations that encompasses classical, quantum, "no-signaling", and maybe full…
ahelwer
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7
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Can we use Hadamard test to estimate phases?
There have been some questions discussing the Hadamard test and quantum phase estimation (QPE), but I did not find the answer to the following question. Suppose we are given $|\psi\rangle$, which is an eigenstate of $U$ such that $U|\psi\rangle =…
fagd
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What do commuting quantum channels look like?
Consider two channels, $\Phi,\Psi\in\mathrm C(\mathcal X)$ acting on some space $\mathcal X$, and suppose they commute, that is,
$$\Phi(\Psi(\rho))=\Psi(\Phi(\rho))$$
for all states $\rho$. Can anything be said about the structure, e.g. in terms of…
glS
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7
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How is Quantum Phase Estimation useful for simulating dynamics of a many-body system?
I am quite aware of the Quantum Fourier Transform (QFT) as well as the very closely related topic of Quantum Phase Estimation (QPE). The latter is usually motivated as follows:
Given a unitary $U$ and a state $|\psi \rangle$ that is promised to be…
Marion
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7
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Tripartite quantum marginal problem
Consider a tripartite quantum system with the three subsystems labeled $A, B,$ and $C$. Now take two states $\rho_{AB}$ on the joint system $AB$ and $\rho_{BC}$ on the joint system $BC$. Under what conditions are these compatible with the same…
biryani
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Does the controlled Pauli Z gate cause entanglement?
I'm trying to understand the relationship between the factorability of a 2 qubit gate and that gate's ability to cause entanglement.
I've begun by considering the controlled Pauli Z gate. After playing around with the computational basis inputs and…
Flipper
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How can I run a VQE on one of IBMQ's Quantum Computers
I have implemented a VQE based on Qiskit's VQE function and want to run that on an actual quantum computer. My understanding was, that an IBMQ backend can be passed into the function as a Quantum Instance. But this doesn't seem to work.
Here is the…
Tom
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Why do we care about the number of $T$ gates in a quantum circuit?
When reading this question and quickly reading some of the linked papers, I wondered why was the number of $T$ gates specified along the number of controlled-$X$ gates.
I've often read that implementing a controlled-$X$ gate was more costly than…
Tristan Nemoz
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7
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Why is the decomposition of a qubit-qutrit Hamiltonian in terms of Pauli and Gell-Mann matrices not unique?
If I have the $X$ gate acting on a qubit and the $\lambda_6$ gate acting on a qutrit, where $\lambda_6$ is a Gell-Mann matrix, the system is subjected to the Hamiltonian:
$\lambda_6X=
\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0\\
0…
user1271772 No more free time
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