# Questions tagged [state-preparation]

a procedure that outputs repeated examples of the same quantum system - particle or multiparticle system - in the same quantum state

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### Qiskit general amplitude embedding leads to long circuits

I am trying to use Qiskit to simulate many-body systems. Hence I calculate the ground state of Hamiltonians a lot. There are 2 ways I do them. 1: Calculate the ground state classically, then do state ...
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### Can we use inverse transform sampling in probability loading process of quantum computing?

Recently, I read some papers about Quantum Monte Carlo (QMC), which can speed up the classical Monte Carlo quadratically. However, the efficiency of QMC largely depends on the probability loading ...
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### Is $\rho = \sum_{j} p_j|n_j\rangle\langle n_j|$ a valid construction for any mixed state?

I have a mixed state $\rho$ and its hamiltonian $H$. Firstly, I find the eigenvalues $\{p_j\}$ of $\rho$, and orthonormal basis of $H$. I write $\rho$ in terms of $H$'s eigenstates and $\rho$'s ...
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### Quantum Information Retrieval from Bipartite Mixed States under LOCC: Maximizing Individual State Knowledge

In the context of Local Operations and Classical Communication (LOCC), given a bipartite mixed state represented as $\rho=\frac{1}{n}\sum_{i=1}^n|\psi_i\rangle\langle\psi_i|$, where $|\psi_i\rangle$ ...
126 views

### Can we create a W state of n qubits with constant circuit depth using mid circuit measurements?

I saw this post where the GHZ state with many qubits (here 6) can be made by performing some mid circuit measurements in constant circuit depth: Depth circuit optimization for 6-qubits GHZ state I was ...
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### Is the CNOT in the standard three-qubit circuit for the GHZ state necessary?

This is a very basic question about the GHZ state. I know the standard construction: A Hadamard on one qubit, and then CNOT gates with targets on all the other ones. However, why can't I just have $n$...
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### How can a density matrix be prepared on a quantum register?

I am currently trying to implement the VQSE algorithm. There the biggest eigenvalues and their corresponding eigenvectors of a density matrix $\rho$ are computed. In contrast to VQE, the matrix $\rho$ ...
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359 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 ...
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### If we can prepare a ground state efficiently, when can we prepare the second-lowest energy eigenstate?

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 ...
• 12.8k
183 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 ...
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