Questions tagged [state-preparation]
a procedure that outputs repeated examples of the same quantum system - particle or multiparticle system - in the same quantum state
8
questions
2
votes
2answers
49 views
How to prove that EPR outcomes have equal probability no matter the basis?
Recently in class, we learned about the EPR state. I know that no matter what basis the first qubit is measured in, the two outcomes have an equal probability. However, how does one prove this? I ...
1
vote
0answers
40 views
When can we efficiently prepare a state corresponding to the *second-lowest* energy of a given Hamiltonian?
I'd like to know if there's anything that can be said about whether and when we can efficiently prepare a state corresponding to the second-lowest eigenvalue of a given Hamiltonian, or in any other ...
3
votes
1answer
67 views
How to prepare a random 1-qubit superposition for data encoding
Let's assume we have a normalized data vector $\vec{x}= [x_1,x_2]$. How can I prepare a state $$|\psi\rangle = x_1|0\rangle+x_2|1\rangle$$
for any $\vec{x}$. I know that this state is in general not ...
7
votes
0answers
114 views
Is there an efficient circuit implementing the unitary $U|x\rangle|0\rangle=|x\rangle\Big(\sqrt{1 - x/2^n}\,|0\rangle+\sqrt{x/2^n}|1\rangle\Big)?$
Given an $n$-qubit register $|x\rangle$, does there exist an efficient circuit implementing unitary operation $U$ such that
$$U |x\rangle|0\rangle = |x\rangle\Big(\sqrt{1 - x/2^n}\, |0\rangle + \sqrt{...
5
votes
2answers
78 views
How instantaneous is state preparation in a quantum register, if all possible superpositions are to be initialized equally?
Before the start of a quantum algorithm qubits need to be initialized into a quantum register. How fast can a quantum register of length $n$ be initialized in a way that all possible superpositions of ...
-3
votes
2answers
175 views
Have you ever seen the preparation of the state $a^{*}|0\rangle+b^*|1\rangle$ and $a|0\rangle+b|1\rangle$ from one initial state?
Have you ever seen the preparation of the state $a^{\star}|0\rangle+b^{\star}|1\rangle$ and $a|0\rangle+b|1\rangle$ from one initial state?
0
votes
1answer
63 views
Produce a quantum state with its density matrix an identity matrix up to an constant
For a n-qubit quantum state $|\psi\rangle=\displaystyle\sum_{i=0}^{2^N-1}|i\rangle$, by definition it's density matrix is $|\psi\rangle\langle\psi|=\displaystyle\sum_{i,j=0}^{2^N-1}|j\rangle\langle i|$...
1
vote
1answer
88 views
How can I find the fidelity of preparation?
I want to know the fidelity (or error rate) of the preparation of $|0\rangle$. How can I obtain it?
