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1500 questions
10
votes
1 answer
Quantum algorithm for QR and SVD matrix decomposition?
I would like to know if exist a quantum algorithm tailored to compute the QR decomposition and SVD of a matrix? Pointers to relevant papers will be very appreciated.
user3116936
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10
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2 answers
Why is Deutsch's gate universal?
(This is related to Exercise 4.44 in Nielsen and Chuang)
Deutsch quantum gate is basically a $iR_x(\alpha \pi)$ gate with two control qubits. The constant $\alpha$ is an irrational number that allows to perform any rotation $R_x (\theta)$ by sending…
MBolin
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9
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1 answer
How to interpret a 4 qubit quantum circuit as a matrix?
This is part of Simon Algorithm (Initial state + some Oracle function)
There is a post that explains how to interpret circuits (How to interpret a quantum circuit as a matrix?), but I'm not sure how to apply to the following circuit.
The first…
Felipe Rojo Amadeo
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9
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2 answers
How to implement controlled multiqubit gates in qiskit?
To implement a stabilizer code I need to measure stabilizer generators, as shown in Fig. 10.16 in Nielsen & Chuang. Is there a way for controlled multiqubit gates in qiskit?
Jacey Li
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9
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1 answer
Can a Toffoli gate be implemented using Fredkin gates?
Even though this seems to be a much asked basic question, I couldn't find a reputed answer to this:
Implement a 3-qubit Toffoli gate using 3-qubit Fredkin gates.
The best I could do was using 4 gates to give
Can we use less than 4 gates?
In the…
lineage
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9
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1 answer
Is quantum teleportation a natural phenomenon?
Quantum teleportation is a reasonably well-defined physical process, whereby a quantum state is transferred between two separated entities that already share an entangled state. It's been demonstrated experimentally, and applications have been…
Alec Edgington
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9
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1 answer
Why is the probability vector of a uniformly random state $\sum_i\alpha_i|i\rangle$ uniformly random only if $\alpha_i\in\mathbb C$?
In these lecture notes by Scott Aaronson, the author states the following (towards the end of the document, just before the Linearity section):
There's actually another phenomenon with the same "Goldilocks" flavor, which was observed by Bill…
glS
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9
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1 answer
How to selectively apply noise in Qiskit simulations?
In Qiskit it is possible to specify noise models to apply to simulations. This allows noise to be defined for certain operations, like measurement or each type of gate.
Is it also possible to change the noise for different parts of the circuit. Such…
James Wootton
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9
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4 answers
How do I prove that the Hadamard satisfies $H\equiv e^{i\pi H/2}$?
I am trying to solve this exercise from Qiskit's textbook, problem set 2 "Basic Synthesis of Single-Qubit Gates":
Show that the Hadamard gate can be written in the following two forms
\begin{equation}
H = \frac{X + Z}{\sqrt{2}} \equiv \exp\left(i…
walid
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9
votes
2 answers
How to decompose a unitary transform into two-level unitary matrices?
I'm struggling to understand the process of how to decompose a unitary transform into two-level unitary matrices. I've been trying to understand the process as detailed in arXiv:1210.7366, but I don't get where those 2x2 matrices in the individual…
Yuerno
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9
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2 answers
Could the Hadamard gate have been constructed differently with similar characteristics?
Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it $H^1$.
$$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}$$
$$H^1 = \begin{bmatrix}-1&1\\1&1\end{bmatrix}$$
From my maths it's a unitary matrix, so it's a…
Nate Lowry
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9
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1 answer
Do pure qudit states lie on a hypersphere in the Bloch representation?
It is known that every state $\rho$ of a $d$-level system (or if you prefer, qudits living in a $d$-dimensional Hilbert space) can be mapped into elements of $\mathbb R^{d^2-1}$ through the mapping provided by the Bloch representation, by writing it…
glS
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9
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1 answer
Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 2): simplifiable and intractable tilings
In Google's 54 qubit Sycamore processor, they created a 53 qubit quantum circuit using a random selection of gates from the set $\{\sqrt{X}, \sqrt{Y}, \sqrt{W}\}$ in the following pattern:
FIG 3. Control operations for the quantum supremacy…
Sanchayan Dutta
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9
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3 answers
Access results from an experiment without having to run the script again
I have ran an experiment in one of the IBM processors and the work has finished. However, I can not obtain the data as histograms or counts in the qiskit notebook because the experiment was concluded while I was logged off and therefore now I would…
Henao
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9
votes
2 answers
Distance calculation between two vectors
In Quantum Machine Learning for data scientists, Page 34 gives an algorithm to calculate the distance between two classifical vectors. As mentioned in this question, it is not clear how the SwapTest is done and used to derive the distance. One…
czwang
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