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How to implement a while loop in a quantum computer?
How can a while loop be implemented in a quantum computer?
If quantum computing consists of :
preparing a state
applying a unitary operator
measuring,
then it seems like it's not possible to wait for an indefinite amount of time before…
Nichola
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7
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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
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
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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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How to decide which quantum device to use if a quantum algorithm is given?
I'm planning to write my master thesis in quantum computing. The subject of the thesis is to find out which attributes (properties, features) of quantum algorithms respectively their implementations (circuits) are important to decide which quantum…
krsp
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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
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Correct Formulation of N&C Exercise 4.11 and other textbooks misquoting
Inspired by the comments in this question How to approximate $Rx$, $Ry$ and $Rz$ gates?, there is the errata for question 4.11 pg 176 in N&C. The original form states that for any non parallel $m$ and $n$, then for an arbitrary $U$:
$U = …
Sam Palmer
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7
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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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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
- 13,891
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- 65
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
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3 answers
How many N-qubit stabilizer states are there?
An N-qubit stabilizer state is a state that can be produced by starting from the $|0\rangle^{\otimes N}$ state and applying only H, CNOT, and S gates. How many N-qubit stabilizer states are there?
Because every stabilizer state can be represented as…
Craig Gidney
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7
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1 answer
What did exactly Google do in simulating a random quantum circuit on a classical computer in supremacy experiment?
I've been working on Google quantum supremacy paper for quite some time now and I have a problem in understanding how exactly they simulate their actual random quantum circuit on a classical computer.
To be specific, in their quantum random circuit…
Ali s.k
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