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 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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52 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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69 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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98 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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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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114 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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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 ...
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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
79 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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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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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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45 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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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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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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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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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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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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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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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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79 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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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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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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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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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 ...
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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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Calculating energy function with 1&2-RDM (reduced density matrix) in Qiskit

I am now working on designing quantum error mitigation with variational quantum eigensolvers (VQE). I need to get the 1&2-RDM from Qiskit, which has already been realized by Openchemist pakages ...
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3answers
104 views

error when running VQE in Qiskit

I am running the code, which gets the ground state energy with different atomic distances of LiH. However, I encountered this error. The code is as follow ...
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1answer
154 views

Simulation of a helium molecule using Qskit

I am trying to compute the ground state energy of He-He using VQE. For this purpose I have utilized Qskit and have written the following script: ...
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1answer
121 views

implement variational quantum eigensolver with openfermion

Can someone provide me with an example about how to implement VQE with OpenFermion, for example, use the UCCSD ansatz to get the ground state energy of LiH. I have checked some code, but none of them ...
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Qiskit: getting QAOA expectation

Suppose I run the Qiskit's QAOA algorithm. qaoa = QAOA(operator=qubit_operator, p=p, optimizer=optimizer) result = qaoa.run(quantum_instance) There is a built-in ...
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1answer
61 views

How to improve accuracy of ground energy values from a VQE

Using the Qiskit textbook I have been using a VQE to find the ground state energy of Hydrogen at different interatomic distances on a quantum machine. However, the average energy value I will always ...
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Implemented QAOA returns wrong result

I try to apply QAOA algorithm to find minimal energy state of the Hamiltonian: $H_A = \frac{1}{2}\sigma_z^1 + \frac{1}{2}\sigma_z^1\sigma_z^2$ It is expected that with p=2 my variational should ...
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Run VQE for parametrized quantum circuit with ancilla qubits

Let's say we have the following circuit (picture and code shown below), and now the $q_0$ is an ancilla qubit. If the system of interest has only two qubits, Is there a way to use only $q_{1,2}$ as my ...
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Applications of pauli operator grouping for simultaneous measurement in VQE

I have read some papers talking about Pauli operator grouping for simultaneous measurement in VQE. I was wondering can this "simultaneous measurement" approach be used in other variational ...
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1answer
64 views

Increase maximum shots on IBM Hardware when running Quantum Variational Algorithms

I am interested to know whether there is a quick and elegant way of increasing the number of shots (more than 8192 shots) on IBM hardware when running variational algorithms like VQE or QAOA. I know ...
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2answers
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Callback function in VQE do not return the intermediate values of the parameters

I tried to save all the intermediate values of the parameters when running the built-in VQE in qiskit. The callback function can save the mean values and counts, however it seems only save the very ...
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1answer
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Is it possible to measure “aux_operators” in built-in VQE with backend “qasm_simulator”

I am trying to measure the number operator, together with the ground state energy with the built-in VQE on Qiskit. However, if I pick the backend to be ...
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1answer
128 views

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 ...
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1answer
85 views

Decomposition of 2-qubit Hamiltonian into standard gate set for QAOA

I try to decompose ansatz into gate set in order to create a circuit in qiskit for QAOA algorithm. I don't understand how represent parametrized 2 qubit ansatz as circuit. $ H{_B} = \sum_{j=1}^{n} {\...
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1answer
183 views

Using Qiskit VQE for solving an eigenvalue problem

I am a new user of Qiskit and I believe there is a simple answer to my question but I have had a very hard time finding a straightforward answer. I am trying to transform a given $3 \times 3$ (...