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1500 questions
8
votes
1 answer
Does control and target matter in the CZ (Controlled-Z) Gate?
IBM Quantum Experience and other Algorithm Creators generally draw the CZ gates like this:
Does it not matter which qubit is the control and which is the target? If so why?
Jadon Erwin
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8
votes
1 answer
What's the role of mixer in QAOA?
In QAOA algorithm, two terms are being discussed; 1) clause or cost (C) Hamiltonian and 2) mixer consisting of pauli X gates.
What is the role of this mixer? Not clear why it comes after the C. Doesn't it cause the state to flip after evaluating…
John Parker
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- 11
8
votes
2 answers
What is the square root of the NOT gate?
I have encountered different matrix of operator "the Square Root of NOT gate".
For example, the matrix is specified here:
$\sqrt {NOT} = \frac{1}{2}\left( {\begin{array}{*{20}{c}}
{1 + i}&{1 - i}\\
{1 - i}&{1 + i}
\end{array}} \right)$
And here a…
alexhak
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8
votes
1 answer
What are examples of extremal non-projective POVMs?
Fix some finite-dimensional space $\mathcal X$. Define a POVM as a collection of positive operators summing to the identity: $\mu\equiv \{\mu(a):a\in\Sigma\}\subset{\rm Pos}(\mathcal X)$ such that $\sum_{a\in\Sigma}\mu(a)=I_{\mathcal X}$, where…
glS
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8
votes
1 answer
List of problems that can be reduced to finding the ground state of a Hamiltonian
I'm doing some reading into Variational Quantum Eigensolvers (VQEs), Quantum Approximate Optimization Algorithms (QAOAs), and other similar algorithms.
I know that the point is to find the ground state of a Hamiltonian. I'm interested in…
johndont
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- 1
8
votes
1 answer
How exactly does Simon's algorithm solve the Simon's problem?
Problem Statement: We are given a $2-1$ function $f:\{0,1\}^{n}\to\{0,1\}^{n}$ such that: there is a secret string $s\in\{0,1\}^{n}$ such that: $f(x)=f(x\oplus s)$. Challenge: find $s$.
Simon's algorithm says:
Set up a random superposition…
Sanchayan Dutta
- 17,497
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- 48
- 110
8
votes
0 answers
Definition of a NISQ device with respect to qubit counts and error rates
How do we define whether a device is a noisy intermediate-scale quantum (NISQ) device with respect to number of qubits and their error rates? Does it make sense to do this? I believe I once saw a definition of a NISQ device as one with on the order…
Greenstick
- 1,076
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8
votes
3 answers
In the adiabatic version of Grover's algorithm, how is the Hamiltonian constructed?
X-posted on physics.stackexchange
In quantum computation, there is a famous algorithm to search a marked item in an unstructured database called Grover's algorithm. It achieves a quadratic speedup over the best possible classical algorithm.
On the…
Hans-Ulrich Rudel
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8
votes
1 answer
Do global phases matter when a gate is converted into a controlled gate?
Let's say that we have a unitary matrix M such that:
$$
M = e^{i\pi/8}\begin{pmatrix}
1 & 0 \\
0 & e^{i\pi/12} \\
\end{pmatrix}
$$
If we were to apply this unitary matrix to the state $|1\rangle$, we would get:
$$
M|1\rangle\ =\…
user15116257
- 91
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8
votes
0 answers
Requirements for Achieving a Quantum Speedup
We usually talk about the power of a quantum computer by examining the separation between sets of gates that we know we can efficiently simulate on a classical computer (i.e. problems in the class BPP), and universal gate sets which, by definition,…
DaftWullie
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8
votes
4 answers
Computing $e^x$ on a quantum computer
Does anyone know how to make a quantum circuit to compute exponentials where the exponent can be a fraction? To be more precise, I'm looking for a fixed point quantum arithmetic circuit that does the following:
$$|\vec{x}\rangle|\vec{0}\rangle…
sheesymcdeezy
- 1,746
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8
votes
2 answers
What's the POVM corresponding to single-qubit state tomography?
Let $\rho$ be a single-qubit state.
A standard way to characterise $\rho$ is to measure the expectation values of the Pauli matrices, that is, to perform projective measurements in the three mutually unbiased bases corresponding to the Pauli…
glS
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8
votes
3 answers
Can I find the axis of rotation for any single-qubit gate?
Suppose I have an arbitrary qiskit $U_3$ gate: $U_3(\theta,\phi,\lambda)$. Is there a way I can find which axis the gate is rotating around? In other words, given any real numbers $\theta,\phi,\lambda$, can I find the vector $\hat n = (n_x,n_y,n_z)$…
ZR-
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8
votes
1 answer
Can quantum computer solve NP-complete problems?
As far as I know, quantum computers are able to solve only some of the NP-Problems in polynomial time, using the Grovers algorithm. I read that if one manages to create a reduction of Grovers algorithm on one of the NP-Complete algorithms, for…
nindo32
- 89
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8
votes
3 answers
If a Hamiltonian is quadratic in the ladder operator, why is its time evolution linear in the ladder operator?
How can one show that $\hat{U}^\dagger\hat{a}\hat{U}$ (with $\hat{U} =e^{-i\hat{H}t}$) involves only linear orders of the ladder operator, when $H$ is the general quadratic Hamiltonian $(\hat{H} = \alpha (\hat{a}^\dagger)^2+ \beta…
heromano
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