# 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 there any physical meaning of this formula?

I am reading a review about the variational quantum algorithm. And there is a definition of the cost function: $C(\theta)=\sum_k f_k (Tr[O_k U(\theta)\rho_kU^\dagger(\theta)])$ Where $U(\theta)$ is a ...
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### Error when running a VQE circuit in IBMQ backends

I want to run a VQE circuit of 4 qubits for a simple Hamiltonian with Qiskit. The circuit run smoothly in simulators. However, when I try to implement it on real IBM' quantum computers it gives me the ...
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### What is the input for the interpret of Quantum Variational Regressors?

I'm trying to implement my first variational regressor using qiskit. I would like to understand how the interpret of a CircuitQNN works. I need to define an interpret that works on the amplitudes of a ...
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### Save output, wavefunction file and orbital information in Qiskit

I am going through LiH ground state energy calculation. I would like to know how to save the output file in Qiskit as one would do in classical computing using software like Gaussian or Psi4. Also, ...
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### How to know state coresponding to -1 or 1 for multi qubits VQE?

Can help to explain how to get -1 and 1 for 2 qubits VQE with $\langle XY\rangle$ since we have 4 states $|00\rangle,|01\rangle,|10\rangle,|11\rangle$? For the case of 1 qubit, it is straight forward ...
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### Do VQE and QAOA use the same Hamiltonian?

In this paper, it talks about the 2-local Hamiltonian in the form: $H = \sum_{(u,v)\in E} H_{uv} + \sum_{k \in v} H_k$ It also says the Ising model, Heisenberg model, XY model and QAOA are in the ...
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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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### What's the importance of a relationship with Gibbs state in the context of VarQITE or variational algorithms?

Trying to figure out VarQITE or variational algorithm, I ran into the Gibbs state. What's the importance of a relationship with Gibbs state in this context. Why can we just use the arbitrary state ...
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### From general Hamiltonian to Ising Hamiltonian

I would like to convert my qubit hamiltonian fom the HeH+ system that I have obtained using Qiskit to an Ising or QUBO model. I have seen multiples examples from QUBO to Qubit Hamiltonian but on the ...
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### Active space chosen for VQE in qiskit

I encountered a problem when learning from the qiskit tutorial about solving electronic structure problem with VQE. Under the "Running VQE on a Statevector Simulator" part, the code provided ...
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### Trouble when implement a self designed gradient in qiskit

everyone! I have trouble when implement a self-designed gradient to the VQE algorithm. The following code will pop the 'ListOp' object is not callable exception to the last line of the code when ...
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### If a hybrid classical+quantum algorithm can achieve quantum advantage, does this mean that the quantum part alone can?

Take for example a variational algorithm which has a classical optimization part and a quantum sampling part. In principle, the quantum part can be simulated by another classical computer given ...
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### Why the last IBMQ job of my VQE have just one circuit?

I am running a VQE over the H2 molecule on ibmq_quito and I set a callback function to save all jobs id's of all iterations. When I check the penultimate job (and the previous ones), I have 2 circuits ...
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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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### How does Qiskit's VQE encode binary digits into a solution from a given Hamiltonian?

So far I have been working with the VQE on different Hamiltonians that happened to have degeneracies, that is there were always at least two different global minima, because the Hamiltonians I was ...
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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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### Is VQE or one of its variations enough to help with medicine development?

One of the reasons quantum computing is often hyped in media is because of how it'll help with vaccine and medicine development. For example, this article in Financial Express and this other in ...
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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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### How to find the expectation value of several circuits using Qiskit aqua operator logic?

I am using the method from this SE answer to calculate the expectation value using qiskit aqua operator logic which works well for a single circuit. Here is a simplified code snippet to demonstrate ...
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### Are inconsistent results between different VQE runs justified?

I made this post a while ago, where I learned I could use qiskit's VQE to calculate (or approximate) the Transverse Field Ising Hamiltonian and other similar Hamiltonians. After working with my code ...
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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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### How does the performance of QAOA and VQE compare to Grover's?

I believe finding the optimal solution is guaranteed for Grover's Algorithm along with quadratic speed-up according to Nielsen and Chuang's book. I wonder if there is any statement regarding QAOA and ...
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### Use one_body_integrals to know which orbitals to freeze in ElectronicStructureProblem

In exercise 5 of the this year's IBM Quantum Challenge, you need to use the FreezeCoreTransformer (along two_qubit_reduction and ...
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### Quantum annealing - studies showing empirical evidence for better performance in comparison with classical computers

Currently, it is not known wheter quantum anneling or algorithms like VQE and QAOA for general purpose quantum computers bring about any increase in computational power. However, there are some ...
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### Reducing an ansatz to a shallower circuit

Given a very general hardware efficient ansatz as in Figure: and say that you already know all the rotation parameter for the gates in the red box, is there any way to build a gate sequence that ...
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### What explains my anomalously scaled up VQE?

I am trying to implement VQE from the Qiskit to obtain the ground state of a very specific Hamiltonian that has been generated via a docplex minimized quadratic ...
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### 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 ...
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### Role of entanglement in a VQE ansatz for combinatorial problems

Variational Quantum Eigensolver is used in quantum chemistry and combinatorial optimization (CO). I'm interested in the latter. In the CO setting a Hamiltonian is a diagonal matrix with real entries ...
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### Set the bounds for ansatz parameters in VQE

How can I make intervals for free parameters when I use VQE function? (https://qiskit.org/documentation/stubs/qiskit.algorithms.VQE.html) I have built a parametrized ($\theta_1,...,\theta_n$) circuit ...
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### Qiskit Portfolio Optimization : Does the resulting matrix show the stock combination to select?

The IBM Qiskit Portfolio Optimization sample finally provides an array similar to [1,0,1,1] representing the 4 digits as the stocks. So does the ...
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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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### What does it mean to have a negative cost (aka loss) function?

In the Variational Quantum Linear Solver (VQLS) paper they define four cost functions (2 global and 2 local) and state in Appendix B that "all four cost functions are non-negative." However, ...
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### Source code for Hamiltonian measurement in qiskit [duplicate]

In variational quantum eigensolver, it is common to transform the Hamiltonian to a qubit form by Jordan-Wigner transformation, for example. After that, the algorithm needs to measure the qubit ...