# Tag Info

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 ...
• 59.3k

### 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 ...
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 ...
• 4,344
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 ...
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 ...
• 5,968

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