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1500 questions
6
votes
3 answers
Classical complexity for Simon's problem
Simon's problem is that you are given a function $f : \{0,1\}^n \to \{0,1\}^n$ such that $f(x)=f(y)$ if and only if $x \bigoplus y$ is either $0^n$ or some unknown $s$. The problem is to find $s$. If $s=0^n$, then $f$ is 1 to 1 otherwise 2 to…
Tech Solver
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6
votes
2 answers
Ways in which $\frac{1}{\sqrt 2} (|00\rangle + |11\rangle)$ can be expressed as $\frac{1}{\sqrt 2} (|uu\rangle + |vv\rangle)$
I want to find out what values $|u\rangle$ and $|v\rangle$ can take if I want to write $\frac{1}{\sqrt 2} (|00\rangle + |11\rangle)$ as $\frac{1}{\sqrt 2} (|uu\rangle + |vv\rangle).$ Say $|u\rangle = a|0\rangle + b|1\rangle$ and $|v\rangle =…
Mahathi Vempati
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6
votes
4 answers
Measuring qubits in QuTiP
How can you measure qubits in QuTiP?
As far as I have seen you can define a Hamiltonian and let it evolve in time. It is also possible to define a quantum circuit, however, measuring and running it is not possible.
Does anyone know how to do this?…
nippon
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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
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
- 101
- 3
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
- 61
- 2
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
- 1,000
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6
votes
1 answer
How to show there is a channel $\tilde\Lambda$ such that $\tilde\Lambda\circ\Lambda=\Lambda'$ with $\Lambda,\Lambda'$ dephasing channels?
I'm taking a quantum information course and one of my exercises says to find $p,p'$ for which there is a channel $\tilde\Lambda(\Lambda(\rho))=\Lambda'(\rho)$, where $\Lambda$ and $\Lambda'$ are dephasing channels with…
M.B.
- 161
- 1
6
votes
1 answer
What's the notion of input size for Quantum Verification?
I've been looking into $\mathsf{QPIP}_\tau$ as a complexity class. The following will be a summary of definition 3.12 in Classical Verification of Quantum Computations by Urmila Mahadev.
A language $L$ is said to have a Quantum Prover Interactive…
Mark Schultz-Wu
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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
- 1,000
- 7
- 17
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
- 4,136
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6
votes
1 answer
Determining whether $P(ab|xy)$ factorizes in Bell experiments
Continuing from my previous (1, 2) questions on Brunner et al.'s paper (arXiv) on Bell nonlocality.
Again, we have the following standard Bell experiment setup:
where independent inputs $x,y \in \{0, 1\}$ decide the measurement performed by Alice &…
ahelwer
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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
- 4
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
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