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1500 questions
12
votes
1 answer
Separating NP from BQP relative to an oracle
I was looking at this lecture note where the author gives an oracle separation between $\mathsf{BQP}$ and $\mathsf{NP}$. He hints at how "standard diagonalisation techniques can be used to make this rigorous".
Can someone detail a diagonalisation…
BlackHat18
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12
votes
1 answer
Sampling random circuits vs Solovay-Kitaev compiler
Suppose I want to obtain a gate sequence representing a particular 1 qubit unitary matrix.
The gate set is represented by a discrete universal set, e.g. Clifford+T gates or $\{T,H\}$ gates.
A well known approach to solve the problem is to use…
Yaroslav Kharkov
- 141
- 4
12
votes
1 answer
Is there a general method of expressing optimization problem as a Hamiltonian?
Let's say, that we have an optimization problem in the form:
$$ \min_x f(x) \\ g_i(x) \leq 0, i = 1, ..., m \\ h_j(x) = 0, j = 1, ..., p,
$$
where $f(x)$ is an objective function, $g_i(x)$ are inequality constraints and $h_j(x)$ are equality…
brzepkowski
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12
votes
2 answers
How to calculate the distance of stabilizer code?
How to calculate the distance of the stabilizer code [[n,k,d]]? It's better if you can make a 3-qubit example. And what's the relationship between d and Pauli group?
Zeo
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12
votes
4 answers
How to quickly calculate the custom U3 gate parameters $\theta, \phi$ and $\lambda$ for any unitary?
In IBM Qiskit and Quantum Experience, the custom U3 gate is defined as
$$
U(\theta, \phi, \lambda) =
\begin{pmatrix}
\cos\left(\frac{\theta}{2}\right) & -e^{i\lambda} \sin\left(\frac{\theta}{2}\right) \\
e^{i\phi}…
Sanchayan Dutta
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12
votes
3 answers
Why do we have to uncompute rather than simply set registers to zero?
In implementing a quantum subroutine it is important to uncompute temporary registers after use, to ensure the output state of the subroutine is not entangled with them (which would affect its behaviour).
Why is it necessary to perform this through…
Sideshow Bob
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12
votes
5 answers
Advances on imperfect quantum copying
It is known by the no-cloning theorem that constructing a machine that is able to clone an arbitrary quantum state is impossible. However, if the copying is assumed not to be perfect, then universal quantum cloning machines can be generated, being…
Josu Etxezarreta Martinez
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12
votes
1 answer
Superconducting qubit researchers: Do your TLS's move?
I have a superconducting system with tens of qubits, each of which can be tuned using DC flux.
One of the main tasks for coherent manipulation of the qubits is to find good idling frequencies and operating points for entangling gates. This effort is…
psitae
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12
votes
1 answer
Is there an intuition built on ansatz in VQE algorithm or is it more a trial and error approach?
Variational Quantum Eigensolver is a popular algorithm in Quantum Computing. But the ansatz part is very tricky. I do not really understand if they are built on some intuition, according to hardware or something else; or if it was just a trial and…
cnada
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12
votes
1 answer
Significance of Clifford operations from quantum error correction perspective
In the literature on QECC, Clifford gates occupy an elevated status.
Consider the following examples which attest to this:
When you study stabilizer codes, you separately study how to perform encoded Clifford gates (even if these aren't applicable…
Tanmay Singal
- 160
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12
votes
1 answer
Advantage of simulating sparse Hamiltonians
In @DaftWullie's answer to this question he showed how to represent in terms of quantum gates the matrix used as example in this article. However, I believe it to be unlikely to have such well structured matrices in real life examples, therefore I…
FSic
- 859
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12
votes
1 answer
How are quantum algorithms devised?
This is a soft question, but I find it to be a very pertinent one...
Algorithms for Grover's search and Simon's problems seem to come completely out of the blue, and I find it very hard to understand what their thought process was when it came to…
Alan Whitteaker
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12
votes
1 answer
Prove that the trace distance is upper-bounded by the Hilbert-Schmidt distance
In (Haah et al. 2015), in the third page, second column, the authors use the following result: given a pair of states $\rho,\sigma$, we have
$$
\|\rho-\sigma\|_1 \le 2\sqrt{\min(\operatorname{rank}(\rho),\operatorname{rank}(\sigma))}…
glS
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12
votes
2 answers
Are all $[[n, k, d]]$ quantum codes equivalent to additive self-orthogonal $GF(4)^n$ classical codes?
Theorem 2 of [1] states:
Suppose $C$ is an additive self-orthogonal sub-code of $\textrm{GF}(4)^n$, containing $2^{n-k}$ vectors, such that there are no vectors of weight $
SLesslyTall
- 1,626
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12
votes
3 answers
What is the actual power of Quantum Phase Estimation?
I have some perplexity concerning the concept of phase estimation: by definition, given a unitary operator $U$ and an eigenvector $|u\rangle$ with related eigenvalue $\text{exp}(2\pi i \phi)$, the phase estimation allows to find the value of…
FSic
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