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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30 views

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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62 views

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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23 views

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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31 views

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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63 views

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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1answer
65 views

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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139 views

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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30 views

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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1answer
67 views

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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38 views

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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1answer
50 views

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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46 views

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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186 views

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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33 views

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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1answer
139 views

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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96 views

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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87 views

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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1answer
88 views

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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60 views

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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120 views

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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1answer
108 views

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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1answer
114 views

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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34 views

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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1answer
108 views

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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15 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 ...
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2answers
134 views

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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1answer
78 views

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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1answer
51 views

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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93 views

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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62 views

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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27 views

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 ...
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2answers
128 views

How to measure a qubit Hamiltonian in qiskit

I am using qiskit to get some measurement results of observables similar to the Hamiltonian. Can someone provide the way how qiskit measures the Hamiltonian (Jordan-Wigner transformed) when using VQE? ...
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1answer
123 views

Compute measurement values of observables by Qiskit

Is there a way to get certain measurement results by variational quantum eigensolver in qiskit? More specifically, I want to get measurement results for certain operators, like $\langle a^\dagger_ia_j\...
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1answer
58 views

How does this expression from the VQLS paper result in a CZ-gate?

I am reading the VQLS paper and equation C2 on page 10 they have: $ \delta_{ll'}^j = \beta_{ll'} + \langle0|V^\dagger A_{l'}^\dagger U(Z_j \otimes I_\bar{j}) U^\dagger A_lV|0\rangle $ Here they define ...
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1answer
72 views

Unable to use iSWAP in Qiskit TwoLocal entangling_block

I would like to use a general entangler in the entanglement_block of the TwoLocal function. The function seems to work with 'cz', 'cx', 'swap' gates, but it fails for 'iswap' gate. Below is the error ...
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1answer
61 views

What is the largest reported number of qubits used in a VQE simulation?

Numerous studies have investigated the simulation of an X-qubit circuit, demonstrating the 'classical simulation supremacy' on supercomputers. X is less than 50. However, useful VQE circuits are often ...
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1answer
52 views

Getting the current variational parameters in Qiskit

I am right now using variational quantum eigensolver (VQE) to calculate the ground state of some molecules, like H2, by qiskit. The quesiton is that how to get the current parameters of the varaional ...
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1answer
77 views

What is the physical unit of the energy calculated using VQE on Qiskit?

Suppose there is any arbitrary ansatz producing variational energy for any arbitrary Hamiltonian. What is the physical unit corresponding to the energy? Since numerical algorithms only output a ...
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1answer
128 views

What is the main advantage of using the Variational Quantum Eigensolver over a classical algorithm?

What is the main advantage of using the Variational Quantum Eigensolver (quantum computing) over a classical algorithm? I know a key fact is the speed-up, but how is this speed-up quantised.
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269 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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1answer
188 views

VQE - How to get from expectation value to eigenvalue?

In VQE, for a single-qubit Hamiltonian, I can use a standard ansatz to make a state $\psi$ and use two products to compute the expectation value $\langle\psi|{\cal H}|\psi\rangle$. As I vary the ...
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0answers
58 views

How to calculate $\operatorname{Var}[H]$ in the context of VQEs?

Given a Hermitian operator $H$, I can calculate the variance of the Hamiltonian $Var[H]$ as $$ Var[H] = \langle H^2 \rangle -\langle H \rangle^2 $$ Now, $H$ can be decomposed as $$ H = \sum_i \alpha_i ...
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0answers
50 views

Is there a general proof of convergence of variational quantum eigensolvers (VQEs) to the minimum eigenvalue?

For QAOA it is known that in the large $p$ limit, the algorithm finds the minimum/maximum (see article A Quantum Approximate Optimization Algorithm). Is there in general a proof for VQE starting ...
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1answer
93 views

Need some help with simulating molecules with VQE

I have studied the example of the simulation of LiH molecule in Learning Quantum Computation using Qiskit. It is available on this link: https://qiskit.org/textbook/ch-applications/vqe-molecules.html#...
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1answer
104 views

Why does the Qiskit tutorial for the Variational Quantum Linear Solver not work properly?

I am following this very nice qiskit tutorial on how to implement a simple variational quantum linear solver (VQLS). There are 3 examples implemented in the tutorial all of which are solving the $Ax=b$...
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36 views

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 ...
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1answer
48 views

In VQE, what ansatz would be best used for a maximally entangled $n$-qubit $H$?

What ansatz would be best used for a maximally entangled n qubit H? I came across this question in the Qiskit textbook and I really don't know how I would answer it.
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75 views

What does the identity operator represent when computing $\langle\varphi|I\otimes Z|\varphi\rangle$?

Consider a single qubit state $|\varphi\rangle$ and a hamiltonian $H = Z$. Evaluating $\langle \varphi | H | \varphi \rangle$ corresponds to a measurement of $|\varphi\rangle$ in the computational ...