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4 votes

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
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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

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
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
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