6

Quantum computers can run classical computations using exactly the same algorithms, and hence have the same running time in terms of scaling. For example, if you look at shor’s algorithm, a major component of that is modular exponentiation, but nobody ever draws the circuit because they just say “use the classical algorithm”. In terms of absolute running ...


6

Yes, since the trace norm is the sum of the absolute value of the singular values, and the singular values can be found for each of the $a$ blocks independently.


5

Your mistake is that you assume that $\rho$ and $\sigma$ are classical-quantum in the same classical basis on $X$. However, there is no need to do so -- all which is necessary is that there exists such a basis, which can however depend on the state. As soon as you choose a different classical basis for the two states, your argument breaks down.


2

You seem to be mixing two very different concepts here. Quantum cloning is talking about the absolute limits of what is theoretically possible in a perfect world. In this absolute theoretical limit, yes we can derive how well quantum cloning can work, and we also know that classical cloning is nominally perfect. There is then a separate question of how well ...


2

In quantum information theory, the standard way to obtain what it is called reduced density operator from a quantum system composed by several quantum states is to use the so-called partial trace operation. For the case where there are two quantum states, $\rho^{AB}$ can be reduced to $\rho^A$ and $\rho ^B$ in the following way: $\rho^A=tr_B(\rho^{AB})$ $\...


1

Classical registers are typically used for capturing measurement results, and may also be used for conditionally applying quantum operation. See: https://github.com/Qiskit/openqasm/blob/master/spec/qasm2.rst Given the problem you described, one approach would be to have a classical program that iteratively: 1) defines and executes a quantum circuit on a ...


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