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1500 questions
7
votes
2 answers
Symmetry of tensor product w.r.t. Vazirani 2-qubit video
Quantum Computing (QC) pioneer Vazirani has graciously long provided some nice videos on an intro to QC. E.g. in "2 qubit gates + tensor product" (2014) he introduces the tensor product w.r.t. QC gates. I was generally able to follow this video but…
vzn
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7
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3 answers
Does entanglement allow enhanced communication efficiency?
From what I gather, communication is not possible with quantum mechanics. With the experiment on teleportation, entanglement is referred to as coordination and not communication. However, my belief is that communication is taking place. For example,…
Jose
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7
votes
1 answer
Understanding Hardy's proof of "nonlocality without inequalities"
I'm reading the proof of "nonlocality without inequality" presented in (Hardy 1992).
In this protocol, we consider two particles (say, an electron and a positron) evolving almost independently: they both pass through one of two beamsplitters…
glS
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7
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2 answers
Why does one need a non-commuting Hamiltonian for an algorithm to exhibit "quantumness"
In two places so far, I've heard statements of the sort "... and we need the Hamiltonian to be non-commuting. If not, the algorithm is classical, and we get no benefit from using a quantum computer."
For reference, here are two timestamped youtube…
Alexander Soare
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7
votes
2 answers
How to do quantum circuit arithmetic?
I'm looking at a circuit from this paper on quantum machine learning.
So to introduce my own notation:
we start with $|\psi_0⟩ = |0,a,b⟩ = a_0b_0|000⟩ + a_0b_1|001⟩ + a_1b_0|010⟩ + a_1b_1|011⟩$
after the first $H$-gate we have $|\psi_1⟩$
after the…
Alexander Soare
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7
votes
1 answer
Product of block-encoded matrices
I am trying to understand just the first step of the proof fo Lemma 53 of this paper, with scarce success.
Before starting, let me state this definition:
Definition: Block encoding of operator A.
Let $A$ be a $s$-qubit operator, and $\alpha,…
asdf
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7
votes
2 answers
Projective vs general measurements - a missing piece
This may be a very basic and common question (also discussed a lot), but strikingly enough I couldn't find the answer in the books or elsewhere.
The projective measurement is given by the PVM on the space $H$:
$$\sum P_i = I,$$
where $P_i$ are…
Danylo Y
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7
votes
2 answers
What is the usefulness of the Suzuki-Trotter formula?
I can't seem to wrap my head around the Trotter-Suzuki formula. I have seen this answer but I am still confused of the applicability of the formula. Let me explain:
As I understand it Trotterization lets us use directly the Schrodinger equation…
Bidon
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7
votes
1 answer
What's the point of VQE if classical computers can solve for eigenvalues easily?
From a few VQE tutorials online I see that they normally start with something like:
VQE is a way of getting a good estimate for the upper bound of the ground state of a quantum system's Hamiltonian. The Hamiltonian is known.
Then they proceed to…
Alexander Soare
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7
votes
0 answers
If we could only get two-qubit tomography as an output, what algorithms are possible
According to the circuit model, the output for a quantum computation on $n$ qubits is an $n$-bit string. But what if we instead got a full two qubit tomography for all $n(n-1)$ pairs of qubits?
This would need to be calculated over many shots. If we…
James Wootton
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7
votes
1 answer
Why is a different convention used for the $Rz$ implementation on IBM Q?
A $z$ rotation gate is defined as
$$
Rz(\theta)=\mathrm{e}^{-i\frac{\theta}{2}Z}=
\begin{pmatrix}
\mathrm{e}^{-i\frac{\theta}{2}} & 0 \\
0 & \mathrm{e}^{i\frac{\theta}{2}}
\end{pmatrix},
$$
however, when one uses $Rz$ gate on IBM Q, the results are…
Martin Vesely
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7
votes
1 answer
What are the differences between the Toffoli and Fredkin gates (historical, practical, etc.)
I'm trying to understand the historical ordering and the practical differences between the Toffoli Gate and the Fredkin Gate.
Toffoli's February 1980 tech report MIT/LCS/TM-151 states:
Where reference [7] is:
Conservative Logic is then published…
vy32
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7
votes
1 answer
Why is phase gate a member of universal gate set?
According to Solovay-Kitaev theorem it is possible to approximate any unitary quantum gate by sequence of gates from small set of another gates. The approximation can be done with an arbitrary accuracy $\epsilon$.
One of such set of gates is…
Martin Vesely
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7
votes
1 answer
Question Regarding Quantum Period-Finding Fourier Transform Approximation
I am following the 5.4.1 Period-Finding Algorithm in Nielsen and Chuang as shown below:
My confusion lies with the second expression of point 3 in the procedure. Why is the second expression an approximation as opposed to just being equal to the…
Rehaan Ahmad
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7
votes
2 answers
Prove that for one-qubit unitaries $\|U-V\|_1=2\max_\psi\|(U-V)|\psi\rangle\|$
Given two 1-qubit rotations $U=R_n (\theta)$ and $V=R_m(\phi)$ with $n$ and $m$ vectors defining a rotation and $\theta, \phi$ angles, define $D(U,V)={\rm tr}(|U-V|)=:\|U-V\|_1$ where $|U-V|=\sqrt{(U-V)^\dagger (U-V)}$, $\|U-V\|_1$ is the trace norm…
Apo
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