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7
votes
2 answers
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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7
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Simon's algorithm: Number of equations
During the classical pre-processing stage of Simon's algorithm, we repeat the quantum operations $n-1$ times to get
$$
\begin{alignat}{7}
y_{1} \cdot s & \phantom{\vdots} =~ && 0 \\ y_{2} \cdot s & \phantom{\vdots}=~ && 0 \\ & \phantom{=} \vdots \\…
BlackHat18
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7
votes
2 answers
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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2 answers
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
votes
1 answer
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 S
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7
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1 answer
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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1 answer
$T_2>2T_1$ qubits on the ibm_washington quantum processor
I have been checking out the parameters of the new ibm_washington processor and I have the following doubt about the calibration data provided by them. Checking out the relaxation and dephasing times I found out that some of their qubits are said to…
Josu Etxezarreta Martinez
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7
votes
1 answer
Does conjugation by a Clifford send each non-identity Pauli to every other non-identity Pauli with equal frequency?
I see here in Olivia DeMatteo's notes, she states:
When we consider the action of the entire Clifford group on a single non-identity Pauli, it
maps that Pauli to each of the $d^2 − 1$ other possible Paulis an equal number of times. Since we
have…
Quantum Guy 123
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2 answers
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
votes
1 answer
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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7
votes
3 answers
Why isn't $Ry(\pi/2)$ gate equivalent to Hadamard gate?
I've been experimenting with quantum circuits and can't quite fathom how the difference between states comes together.
Speaking in terms of simulations using qiskit, the following code yelds the same results:
circuit =…
Ricardo
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7
votes
1 answer
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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7
votes
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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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7
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3 answers
References examining Bell inequality violations at large distances
Could anyone point to some references examining Bell inequality violations at large distances please?
I see many times, in pop science articles and research literature alike, that the quantum information of the entangled state is transmitted…
psitae
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7
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Are SIC-POVMs optimal for quantum state reconstruction?
Mutually unbiased bases (MUBs) are pairs of orthonormal bases $\{u_j\}_j,\{v_j\}_j\in\mathbb C^N$ such that
$$|\langle u_j,v_k\rangle|= \frac{1}{\sqrt N},$$
for all $j,k=1,...,N$.
These are useful for a variety of reasons, e.g. because they provide…
glS
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