All Questions
Tagged with vqe pauli-gates
8 questions
0
votes
1
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49
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Recovering phases in $2n$-bit binary representation of n-qubit Paulis
I am currently going through a paper discussing Pauli sampling strategies for VQE: https://arxiv.org/abs/1908.06942
I want to code and test their strategy.
They explain how to create a circuit ...
- 1
2
votes
1
answer
204
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How VQE is scalable if the dimension of the Pauli basis of the given Hamiltonian grows exponentially with the number of qubits?
For a given Hamiltonian operator $H$, It's possible to approximate its smallest eigenvalue using VQE. Any Hamiltonian is a Hermitian operator. Therefore, for a system with $n$ qubits, the set $S$ of ...
- 1,809
1
vote
2
answers
464
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Expectation value of Pauli strings for VQE
I am studying VQE and have boiled it down to a matter of determining the expectation value of Pauli strings:
$$\langle H \rangle = \sum_i \alpha_i \langle\psi|\hat{P_i}|\psi\rangle.$$
I have been ...
- 11
3
votes
1
answer
108
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Cliffords to Transform into Common Eigenbasis
Say I have the following Hamiltonian (given in terms of Pauli operators):
\begin{equation}
H=aX_1Z_2+bZ_1X_2.
\end{equation}
Both Pauli terms commute with each other. I want to make a measurement of $\...
- 474
2
votes
0
answers
36
views
Measurement on a specific basis and proof of circuit output
I am trying to understand a proof from Practical optimization for hybrid quantum-classical algorithms. In particular, I need clarifications on how do you perform the measurement on a different basis ...
- 493
2
votes
1
answer
250
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In Variational Quantum Eigensolvers, what does "grouping Pauli operators into tensor products requiring the same post-rotations" mean?
In this paper (nature version), the authors state
We group the Pauli operators into tensor product basis sets that require the same post-rotations.
As a result, they have the table S2 in the suppl. ...
- 975
1
vote
0
answers
286
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Changing the Basis
I am attempting to use a VQE algorithm to find the ground state of a deuterium nucleus by applying a constructed hamiltonian to an ansatz state with one parameter created by a circuit. While I am ...
3
votes
1
answer
445
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VQE: Can I build a non-hermitian Hamiltonian with just Pauli matrices?
From the VQE paper they claim that a Hamiltonian can be expressed as a polynomial series of pauli operators (equation 1).
While coding up VQE from scratch I made a function which would allow me to ...
- 656