9 votes
Accepted

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 ...
Mithrandir24601's user avatar
  • 3,686
8 votes
Accepted

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 ...
Ziofil's user avatar
  • 196
8 votes
Accepted

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 ...
user1271772 No more free time's user avatar
7 votes
Accepted

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 ...
Arthur Pesah's user avatar
6 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 ...
artha's user avatar
  • 388
5 votes
Accepted

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, ...
Mauricio's user avatar
  • 2,306
4 votes
Accepted

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, ...
iiooii's user avatar
  • 156
4 votes
Accepted

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 ...
Mithrandir24601's user avatar
  • 3,686
4 votes
Accepted

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,\...
Quantum Mechanic's user avatar
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 ...
JSdJ's user avatar
  • 5,449
4 votes
Accepted

What is an example of the need for complex numbers implied by the need of continuity of linear operators?

We are told that there is an operation $$ \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}\begin{bmatrix} \alpha \\ \beta \end{bmatrix}=\begin{bmatrix} \alpha \\ -\beta \end{bmatrix}. $$ We are ...
DaftWullie's user avatar
  • 57.9k
3 votes
Accepted

Truncated Qumode States and Support

Your guess is correct that this is not possible. A $d\times d$ matrix times an $d\times 1$ column vector gives you another $d\times 1$ column vector, so your truncated unitary cannot take the vector ...
Quantum Mechanic's user avatar
3 votes

How to translate between continuous variable model and discrete model?

Here is a partial answer. In general, the connection between continuous and discrete variables gets pretty complicated... However, if you restrict yourself to Gaussian unitaries on the CV side, and ...
Cole Comfort's user avatar
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{...
keisuke.akira's user avatar
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 ...
Rammus's user avatar
  • 5,743
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 ...
Quantum Mechanic's user avatar
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's user avatar
  • 24.8k
2 votes

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 ...
Mark Spinelli's user avatar
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? ...
artha's user avatar
  • 388
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 $...
Juan Miguel Arrazola's user avatar
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 ...
Troncho Col's user avatar
1 vote

What are the postulates of Continuous Variable Quantum Computing?

There is quite a bit to unpack here, so I provide a brief overview of things with links to relevant wikis and papers wherever necessary. Qumode States vs Qubits To start with, it is important we first ...
Song of Physics's user avatar
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 ...
Rammus's user avatar
  • 5,743
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 ...
MonteNero's user avatar
  • 2,481
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 ...
Song of Physics's user avatar
1 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 ...
Mithrandir24601's user avatar
  • 3,686
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) ...
user1271772 No more free time's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible