For questions about the Variational Quantum Eigensolver, a quantum/classical hybrid algorithm that can be used to find eigenvalues of a (often large) matrix H. When this algorithm is used in quantum simulations, H is typically the Hamiltonian of some system. In this hybrid algorithm, a quantum subroutine is run inside of a classical optimization loop.
Questions tagged [vqe]
244 questions
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What are the main differences between the "unitary coupled cluster" and the "hardware efficient" ansatzes in VQE?
There are two popular initial states, in general, for VQEs: the unitary coupled cluster ansatz and the hardware efficient ansatz (for details, see here: https://quantaggle.com/algorithms/ansatz/). Intuitively, what are the main differences between…
BlackHat18
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What is the expectation value for the ground state of $ H = \sum_i Z_i Z_{i+1} + \sum_i X_i $?
What is the expectation value for the ground state of $ H = \sum_i Z_i Z_{i+1} + \sum_i X_i $ ? In Eq. 15b this provides a solution in k space. The minimum would be reached for $E = -4$. But for example here the energy is calculated numerically as…
user18722294
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Generally, could VQE be used to prepare the highest energy state?
When I learned about the variational method in quantum mechanics and the variational quantum eigensolver (VQE), I was told that this method is used to prepare the ground state of a quantum system. I wonder if we could also use this method to…
ZR-
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The importance of the ansatz in VQE algorithm
Let's say I have a universal quantum computer that can perform anything.
In this case, any VQE algorithm can use any operation, so no ansatz is needed to implement it.
My question is, is the usage of the ansatz for the VQE algorithms because current…
Alex
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How does VQE work?
Here is the VQE overview from Peruzzo et al. 2013
I am trying to understand in detail how each step works, assuming at first one qubit and a Hamiltonian of the form:
\begin{equation}\tag{1}
H = \sum_{i}a_i H_i\;,\quad a_i\in\mathbb{R}
…
deb2014
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Barren Plateau as a consequence of 2-design?
Initializing a parameterized quantum circuit with a unitary sampled from a uniform distribution (so sampling from the Haar distribution) or in a weaker form: a unitary which is a unitary 2-design, brings the danger of starting in a barren…
nuemlouno
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Ground state returned by VQE is not an eigenstate?
With my VQE algorithm, I want to obtain both the ground state energy and its corresponding ground eigenstate. However, the state I reach using VQE is usually very different from the true ground eigenstate, though its energy is still typically nearly…
user22395
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Encoding a discrete functional in variational $n$-qubit states
So I have a discreet functional $f(x_{1},x_{2},...,x_{k})$ that I want to encode in a variational state: $|\psi(\lambda)>$. The number of variables in my functional takes values $k=9,18,30$.
I want the parameters $x_{1},x_{2}...x_{k}$ to be the…
C W
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In which situations is it hard to find an ansatz?
Looking at the single-qubit, toy example of VQE it's pretty much trivial that arbitrary X and Y rotations are sufficient to cover all of state space for our toy system.
Unfortunately, the toy example doesn't do enough to illustrate to me why it…
Alexander Soare
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