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1500 questions
6
votes
2 answers
How to implement Grover's diffusion operator when starting with a W state?
In the general form of Grover's algorithm, we start with the uniform superposition of n qubits. Now, suppose instead that we start with a generic state, for example the W state, and the oracle only inverts the phase of one of the basis.
To make it…
tigerjack
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6
votes
1 answer
Problem with the mathematical formulation of "qubitization"
In this research paper, the authors introduce a new algorithm to perform Hamiltonian simulation.
The beginning of their abstract is
Given a Hermitian operator $\hat{H} = \langle G\vert \hat{U} \vert G\rangle$ that is the projection of an oracle…
Adrien Suau
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6
votes
1 answer
Proof on approximating adiabatic evolution by quantum circuit
I am reading on how the adiabatic evolution can be approximated by a quantum circuit of size poly(nT) and I am trying to follow the derivation in the paper
W. van Dam, M. Mosca, and U. Vazirani, “How Powerful is Adiabatic
Quantum Computation?,”…
xi dai
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6
votes
2 answers
How many Kraus operators are required to characterise a channel with different start and end dimensions?
If we have a quantum channel mapping from a $d$-dimensional state to a $d$-dimensional state, it can be described by at most $d^2$ Kraus operators. Suppose our channel maps instead from a $d_1$-dimensional state to a $d_2$-dimensional state, with…
Jason
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6
votes
1 answer
Implementation of inverse QFT?
When implementing the inverse quantum Fourier transform, in addition to reversing the circuit, does one need to take the conjugate transpose of the phase shift gates in the circuit as well?
Jack Ceroni
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6
votes
1 answer
Why is this implementation of the order finding algorithm not working?
I asked a question about this earlier, but I am still coming across problems in my algorithm implementation.
I am trying to implement the order finding algorithm on Cirq finding the minimal positive $r$ for coprime $x$ and $N$ satisfying the…
Jack Ceroni
- 990
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- 16
6
votes
1 answer
Confusion on the definition of the phase-damping channel
I am reading about the phase damping channel, and I have seen that some of the different references talking about such channel give different definitions of the Kraus operators that define the action of such channel.
For example, Nielsen and Chuang…
Josu Etxezarreta Martinez
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6
votes
0 answers
Quantum channel Holevo information additivity: proof approach
I have an interesting idea for a proof approach that someone might find useful. Here it is.
Suppose we are given a quantum qubit channel $N$ (for example the amplitude damping channel) whose Holevo information we are trying to prove is additive…
user120404
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6
votes
2 answers
How to describe, or encode, the input vector x of Quantum Fourier Transform?
Firstly, I'd like to specify my goal: to know why QFT runs exponentially faster than classical FFT.
I have read many tutorials about QFT (Quantum Fourier Transform), and this tutorial somehow explains something important between classical and…
user3176354
- 175
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6
votes
1 answer
Does computing the quantum mutual information $I(\rho^{AB})$ require full tomographic information of $\rho^{AB}$?
In the discussions about quantum correlations, particularly beyond entanglement (discord, dissonance e.t.c), one can often meet two definitions of mutual information of a quantum system $\rho^{AB}$:
$$
I(\rho^{AB}) = S(\rho^A) + S(\rho^B) -…
Ilya
- 163
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6
votes
1 answer
What is the quantum bandwidth of a planar array of noisy qubits, assuming free classical communication?
A common task to perform during quantum computation on the surface code is moving qubits from one place to another. There are standard ways to do this within the surface code, but I was wondering what the actual fundamental limits are. If we forget…
Craig Gidney
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6
votes
2 answers
Measuring the Hamiltonian in the VQE
I am trying to implement VQE in pyQuil and am dumbfounded by how to measure the expectation value of a general Hamiltonian on $\mathbb{C}^{2^n}$ i.e. determine $\langle\psi , H \psi\rangle$ on a Quantum computer. As far as I understand on a real…
Jan Lukas Bosse
- 83
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6
votes
2 answers
Quantum counting in Q#
I cannot seem to get an estimate for the number of solutions using the quantum counting algorithm described in Nielsen and Chuang, i.e. phase estimation with the Grover iteration acting as $U$.
I try doing the following with control and target as…
nikojpapa
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6
votes
1 answer
Definition of locality in Bell experiments
Continuing from my previous question on Brunner et al.'s paper; so given a standard Bell experimental setup:
where independent inputs $x,y \in \{0, 1\}$ decide the measurement performed by Alice & Bob on quantum state $S$ with outcomes $a,b \in…
ahelwer
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6
votes
2 answers
In Bell nonlocality, why does $P(ab|xy)\neq P(a|x)P(b|y)$ mean the variables are not statistically independent?
I've been working through the paper Bell nonlocality by Brunner et al. after seeing it in user glS' answer here. Early on in the paper, the standard Bell experimental setup is defined:
Where $x, y \in \{0,1\}$, $a, b \in \{-1, 1\}$, and the two…
ahelwer
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