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What is the motivation for Weyl matrices in quantum information theory?
Quantum Entanglement and Geometry — Andreas Gabriel (2010) — Sec: 2.3.4 ~p. 11
Another basis for $d\times d$-dimensional matrices that has proven to be quite useful in quantum information theory is the Weyl operator basis, which consists of $d^2$…
Sanchayan Dutta
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Simulating a 3-local Hamiltonian Term
This may be a fairly basic question, but in Nielsen & Chuang, the following circuit is given for simulating $\exp\left(-i\Delta t Z_1 \otimes Z_2 \otimes Z_3\right)$:
which uses an ancilla qubit initialized to $|0\rangle$. But from messing around…
Paradox
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Quantum fidelity simplified formula while both of the density matrices are single qubit states
I have a question while reading the quantum fidelity definition in Wikipedia Fidelity of quantum states, at the end of the Definition section of quantum fidelity formula, it says Explicit expression for qubits. If rho and sigma are both qubit…
tatakai
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Quantum Fourier Transform without SWAPs
The Quantum Fourier Transform from Nielsen and Chuang chapter 5 is pictured here:
In the textbook the author refers to "swap gates at the end of the circuit which reverse the order of the qubits".
My questions are:
Is it possible to transform the…
forky40
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What is the definition of Bell state on a n-qubit system?
Question 1: The bell state for a 2-qubit system has been defined in Neilsen and Chuang's book as the set of maximally entangled states spanned by $\{|00\rangle + |11\rangle, |00\rangle - |11\rangle, |01\rangle + |10\rangle, |01\rangle- |10\rangle…
John Jacob
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Grover algorithm for a database search: where is the quantum advantage?
I have been trying to understand what could be the advantage of using Grover algorithm for searching in an arbitrary unordered database D(key, value) with N values instead of a classical search.
I assumed that the oracle function is a function…
Foxhole
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How to interpret $-\rvert1\rangle \otimes \rvert1\rangle = -\rvert11\rangle$?
I'm having trouble accepting, intuitively, that $-\rvert1\rangle \otimes \rvert1\rangle = -\rvert11\rangle = \rvert1\rangle \otimes -\rvert1\rangle$.
It's my understanding that $ -\rvert1\rangle$ is just $\rvert1\rangle $ but time or space delayed…
Dragonsheep
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What are the main obstacles to overcome to build silicon-photonic quantum computers?
In superconducting quantum computers, we use mostly superconducting qubits or trapped ions. However, those systems are quite large because their environment either requires near absolute zero temperature (for superconducting to happen), or vacuum…
Aleksandar Kostovic
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What exactly makes quantum computers faster than classical computers?
What feature of a quantum algorithm makes it better than its classical counterpart? Are quantum computers faster than classical ones in all respects?
Tobias Fritzn
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How does measurement calibration work?
One of the possible ways to improve the results of an experiment on the IBM machine using the Qiskit language is to use the measurement calibration methods. This is the link to the documentation.
I understood that the calibration matrix is made…
Marco Ballarin
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Nielsen and Chuang's proof for 'approximating arbitrary unitary gates is generically hard'
The following statement is found on the page 199 of Nielsen and Chuang's book (10th Anniversary Edition) in the proof for the fact that 'approximating arbitrary unitary gates is generically hard':
Suppose we have $g$ different types of gates…
Nan
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Calculating the expectation value of a unitary operator on a quantum computer
What is the smartest way of calculating the expectation value of some unitary $U$ in some state $|\psi\rangle$?
There are two ways I know:
quantum phase estimation algorithm;
Hadamard test.
Are there more efficient techniques to do that?
Andrey Kardashin
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Homeomorphism or stereographic projection corresponding to the set of mixed states within the Bloch sphere
The Bloch sphere is homeomorphic to the Riemann sphere, and there exists a stereographic projection $\Bbb S^2\to \Bbb C_\infty$. But this only holds for pure states. To quote Wikipedia:
Quantum mechanics is mathematically formulated in Hilbert…
Sanchayan Dutta
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Which quantum computing programming language should I learn?
Which quantum computing programming language should I learn? What are the benefits of said language? As of Wikipedia, there's quite a bit to choose from.
I'm looking to develop end-user applications (when quantum computers become end-user ready).
AJ_4real
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Composing the CNOT gate as a tensor product of two level matrices
I don't understand, why is the control not gate used so often. As far as I understand it, if you apply two 2 level operations on two qubits then you get a 4 x 4 matrix by the tensor product. So how would you express the CNOT gate as a product of…
bilanush
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