Questions tagged [vqe]

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.

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Is VQE a class of algorithms or a specific algorithm?

Is VQE a class of algorithms or a specific algorithm? For example, is QAOA a VQE or is VQE an algorithm distinct from QAOA that solves the same class of problems? If VQE is a specific algorithm, what ...
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How to calculate an Expected Value of some operator acting on qubits?

I'm trying to implement the Variational Quantum Eigensolver in Qiskit. Suppose, I have an operator $A = \sigma_1^z\sigma_2^z$ acting on some two-qubit state $|\psi\rangle$. After a measurement I get ...
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Why exactly are variational algorithms considered promising?

There is obviously a great deal of work happening at the moment on variational quantum algorithms. However, I'm struggling to understand why exactly are they considered promising? Looking through some ...
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What does the paper "Training Variational Quantum Algorithms Is NP-Hard (Phys. Rev. Lett. 127, 120502)" mean?

I have seen the recent paper "Training Variational Quantum Algorithms Is NP-Hard (Phys. Rev. Lett. 127, 120502)" and the authors stated that training the classical optimization in ...
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848 views

What is the complexity of estimating the expectation value of an observable?

The average value of an operator $O$ in the state $\left.|\psi\right>$ is $$\overline{O}=\left<\psi|O|\psi\right>$$ Now for simplicity let $\left.|\psi\right>=\left.|0\right>^n$ and ...
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Decomposing Hamiltonian into qubit model representation

One of the main applications of VQE is its application to find the approximation to the ground state energy (smallest eigenvalue of the Hamiltonian) for a particular molecule through an iterative ...
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QUBO, Ising Hamiltonians and VQA

I understand that usually the combinatorial optimisation problems are turned into QUBO, which has a very simple mapping to Ising Hamiltonians. Ising Hamiltonians in turn have the desired properties of ...
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List of problems that can be reduced to finding the ground state of a Hamiltonian

I'm doing some reading into Variational Quantum Eigensolvers (VQEs), Quantum Approximate Optimization Algorithms (QAOAs), and other similar algorithms. I know that the point is to find the ground ...
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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 ...
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Creating a parameterized Operator in Qiskit

I'm trying to run a VQE for a specific custom Anzats. The Anzats is built up of an unitary matrix $U_H$, which I'm trying to created in this way: ...
568 views

Ansatz explanation for VQE

I have found quite a bit of information on the UCC ansatz, but I cannot really find basic explanations for the Ry and RyRz ansatzs... Are they just applying these gates to a circuit? If anyone has ...
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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 ...
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How to explain that I get a value lower than the smallest possible through minimization procedure in VQE?

As far as I know after minimization I have to obtain a value $E_{0}\le \frac{\langle \psi (\theta)|H|\psi (\theta)\rangle}{\langle \psi (\theta)|\psi (\theta)\rangle}$, where $E_{0}$ - eigenvalue of ...
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Is there a way I can create an ansatz such that the number of 1 is same in all the superposition states? [duplicate]

So I am working with a variational quantum algorithm and I realised that it would be very beneficial if I could create an ansatz where all the states in the superposition have same numbers of 1s. For ...
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What exactly makes VQE faster than classical optimization?

I have been trying to understand Variational Quantum Eigensolver (VQE), particularly from the non-linear binary programming perspective. But after reading a few resources I'm still confused about ...
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TypeError: 'NumPyMinimumEigensolver' object is not subscriptable

I'm trying to implement the same Jupyter notebook Jin-Sung Kim gave in his YouTube video The Variational Quantum Eigensolver — Programming on Quantum Computers — Coding with Qiskit S2E4; however, I'm ...
158 views

In which type of Hamiltonian does the ansatz need an entangler in VQE?

I would like to prepare an ansatz for VQE. I know UCC ansatz is one of the most useful ansatz, but I would like to reduce the number of CNOT. From the matrix of a given Hamiltonian, can we know the ...
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Variational Quantum Linear Solver (Hadamard test): circuit question

Trying to understand the circuit/algorithm for VQLS and I found this diagram to show the high-level idea of doing the Hadamard test in this tutorial. But I am not quite sure why we need the two ...
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Expected value in a VQE qiskit

I'm learning VQE(variational quantum eigensolver) of qiskit, but I have a question about how it measures the expected value of the energy ($\left \langle H \right \rangle$). I saw in other question ...
132 views

Resource recommendation on quantum simulations

I would like to know more about quantum simulations, so as to start on a few standard physical models (maybe particle in a box, harmonic oscillator, etc.) and then build up on more complex things. But ...
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How do I identify a VQE job run in real hardware?

I am running a VQEUCCFactory for H2 on a real hardware device. ...
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Variational Quantum Eigensolver (VQE) by scipy minimize in cirq does not work

I tried to make a cirq program calculating an eigenvalue of the observable by VQE. Inspired by the qulacs VQE tutorial, I defined a cost function from the expectation value of the observable with ...
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Ansatz for VQE demonstrating Quantum Advantage

What would be a possible ansatz quantum state in VQE (variational quantum eigensolver [1]) that would demonstrate the quantum advantage of VQE over classic computers? More specifically, I see that VQE ...
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Difference between Qiskit and Openfermion two body integrals

I am struggling with understanding the differences between OpenFermion and Qiskit libraries when it comes to Molecular Data, two body integrals. For example, I am working with the following ...
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Link to paper here. This algorithm seems neat but the unitary decomposition of the matrix M generally takes an exponential number of Pauli basis elements in the number of qubits $N$, therefore an ...