9
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How are gates implemented in a continuous-variable quantum computer?
Taking an $n$-mode simple harmonic oscillator (SHO) in a (Fock) space $\mathcal F = \bigotimes_k\mathcal H_k$, where $\mathcal H_k$ is the Hilbert space of a SHO on mode $k$.
This gives the usual ...
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8
votes
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How are two photons entangled in the Xanadu computer?
QML researcher at Xanadu here.
Our X-series chip produce entangled states by squeezing light and then combining it at beam splitters: those 'cables' are waveguides in a chip, which when they are close ...
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8
votes
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Does a Wigner function uniquely determine a quantum state?
For any quantum state, we have a unique density matrix $\rho$.
For any $\rho$, we can do the Wigner transformation to get a unique Wigner function $P(x,p)$.
For any Wigner function $P(x,p)$, we can ...
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7
votes
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What types of quantum systems use infinite values?
You are right, photonic systems are described by an infinite (separable) Hilbert space---the bosonic Fock space---and their formalism makes extensive use of infinite values, both countable and ...
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votes
Is "probabilitistic,universal, fault tolerant quantum computation" possible with continuous values?
To start off, I would really suggest you to read this review on "Quantum information with continuous variables(cv)". It covers most of your questions with cv architecture. Since it is a very big ...
- 388
5
votes
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What is the relation between a Fock state and a qudit?
I would say it is not exactly the same.
A qudit of size $d$ has a finite number of states. A Fock state can have discretely infinite number of states in principle.
The goal of having multiple qudits, ...
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4
votes
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Are qubits preferred over qumode, and if so, why?
Both models have their potential advantages and disadvantages. The CV model doesn't require energy intensive cooling systems. CV will also work better for continuous-valued problems. Nevertheless, ...
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4
votes
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Matrix representation of continuous-variable gates
Background
Often, in quantum optics, the Heisenberg picture is used, where instead of considering equations of motion of states, equations of motions of operators are looked at instead. When ...
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4
votes
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Why is a state Gaussian if and only if its covariance matrix satisfies $\boldsymbol\sigma+i\boldsymbol\Omega\ge0$?
From the definition of the covariance matrix,
$${\sigma}_{ij}=\left\langle \frac{x_i x_j+ x_j x_i}{2}\right\rangle -\langle x_i\rangle\langle x_j\rangle,$$ where we define
$$\boldsymbol{x}=(q_1,p_1,\...
- 3,494
4
votes
Accepted
What is meant with "reconciliation" in CV QKD?
I assume the paper you are reading is referring to information reconciliation.
Information reconciliation is a vital part of post-processing in QKD, to limit (or erase in the best-case scenario) the ...
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3
votes
Accepted
Relation between Wigner quasi-probability distribution and statistical second-moment
You mean something like
$$W_{G}(\mathbf{r}) =\frac{2^{n}}{\pi^{n} \sqrt{\operatorname{Det} \sigma}} \mathrm{e}^{-(\mathbf{r}-\overline{\mathbf{r}})^{\top} \boldsymbol{\sigma}^{-1}(\mathbf{r}-\overline{...
- 1,803
3
votes
Accepted
What is the difference between CV QKD and DV QKD?
It's the dimension of the Hilbert spaces. In DV-QKD you have a finite dimensional Hilbert space (like a qubit). Thus your measurement outcomes come from a finite set. On the other hand a CV-QKD ...
- 5,201
2
votes
Accepted
How to write the covariance matrix of a quantum gaussian state as a function of photon numbers?
Recall that $a=(q+ip)/\sqrt{2}$ in some dimensionless units (Weedbrook might change the units because I think they like $\hbar=2$; I'm using $[q,p]=i$ and $[a,a^\dagger]=1$). We can thus find the ...
- 3,494
2
votes
Accepted
What is infinite squeezing?
The idea of squeezing arises when discussing the state of a quantum harmonic oscillator (e.g. a bosonic system). Such systems differ from simpler qudit systems in that, even when only a single mode is ...
glS♦
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2
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Is Gaussian boson sampling (used for showing quantum advantage) a subcategory of the continuous variable approach?
@gIS's comment effectively answers the question, but to provide a bit more detail Aaronson at shtetl-optimized has a nice blog post on the Gaussian Boson Sampling approach of USTC, contrasting it with ...
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2
votes
What is continuous quantum register and how it relates to qubits?
direct definition is a quantum register that stores a real number defined by an observable with a spectrum consisting of ℝ
Yes, qubits can be used to discretize a continuous quantum system.
How?
...
- 388
2
votes
What is the difference between CV QKD and DV QKD?
One example to understand it, if someone finds it useful, is the following:
Most QKD is done by sending light through a channel. In DV-QKD we send single photons through the channel, one at a time. We ...
- 31
2
votes
Accepted
Quantum teleportation over continuous variables?
Here's a schematic description of quantum teleportation for general systems:
Alice and Bob share a maximally entangled state.
To teleport $|\psi\rangle$ to Bob, Alice performs a joint measurement of $...
1
vote
What are necessary and sufficient conditions for the output of a parametrized unitary $U(\theta)$ to be smooth?
I'm still not sure I fully understand what you're asking but here's my take.
Let $\rho$ be the input to my circuit, at the end of the circuit I receive an output $\rho_U = U \rho U^\dagger$. Now ...
- 5,201
1
vote
Accepted
Variational Algorithms - Is there a way to avoid discontinuities in optimal variational parameters?
Let $C(\theta)$ be an arbitrary quantum circuit parametrized by $\theta \in \mathbb{R}^n$. And let $L(C(\theta))$ be a continuous non-convex objective function we would like to optimize. Given that ...
- 2,339
1
vote
Accepted
Implementing a simple 3 mode gate using Strawberry Fields
Let the 3-mode operator be $\mathcal{O}_{123}(s)$. Dropping the tensor products and hat symbols here for convenience, one can apply the Fourier gate on the $2^{nd}$ and $3^{rd}$ mode, which I denote ...
- 148
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vote
What is the mean value of displacement operator for the coherent state?
So you want to calculate $\left<\beta |D\left(\alpha\right)|\beta\right>$ where $\left|\beta\right>$ is a coherent state and $D\left(\alpha\right)$ is the displacement operator.
The easiest ...
- 3,647
1
vote
Matrix representation of continuous-variable gates
The link you gave says:
The CV model is a natural fit for simulating bosonic systems (electromagnetic fields, harmonic oscillators, phonons, Bose-Einstein condensates, or optomechanical resonators) ...
- 13.4k
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