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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How is this Variational Quantum Singular Value Decomposition paper efficient in any way?
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 ...
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What is the original paper introducing the Variational Quantum Eigensolver?
My question is very simple. I am looking for original paper where Variational Quantum Eigensolver (VQE) has been introduced. After some Googling I was able to find many applications of VQE and its ...
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Expectation value of Pauli strings for VQE
I am studying VQE and have boiled it down to a matter of determining the expectation value of Pauli strings:
$$\langle H \rangle = \sum_i \alpha_i \langle\psi|\hat{P_i}|\psi\rangle.$$
I have been ...
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Hamiltonian & QubitMappingType cannot be imported from qiskit.chemistry.core
I'm trying to implement the same Jupyter notebook in The Variational Quantum Eigensolver — Programming on Quantum Computers — Coding with Qiskit S2E4;however,I found a problem:
Error:
...
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Convexity of cost function in quantum machine learning
I have a small confusion regarding convexity of the most typical cost function considered in many QML papers: $\text{Tr}(\rho O)$, where $O$ is a Hermitian operator and $\rho$ is a quantum state. This ...
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Qiskit: QAOAnsatz circuit with custom Hamiltonian
I am trying to implement the Quantum Approximate Optimization Ansatz by creating a parametrized subcircuit
$$V (α) = e^{−iH_M α_1} e^{−iH_D b_1} ... e^{−iH_M α_n} e^{−iH_D b_n}$$
with the custom ...
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Why does VQE with pennylane and scikit-optimize gp_minimize give 'func must be scalar' error?
I am trying to replace the SPSA optimizer in the VQE tutorial of pennylane by the bayesian optimizer of scikit-opimize.
When running the code below I get the error "func should return a scalar&...
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How can I get the counts, as well as the solution bitstring from Qiskit VQE?
I just set up a Qiskit VQE algorithm and calculated the eigenstates. However, I'm searching now, how to show up the final, most likely solution-bit-string. And/or to print the counts. I actually ...
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VQE Execution error: The ansatz must be parameterized, but has 0 free parameters
I am experiencing some problems with qiskit implementation of VQE. First of all, in initialize an ansatz in one of the following ways:
...
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Understanding QAOA from Basics/scratch
Recently after working on QAOA with finance and graph coloring problems. I have started exploring the QAOA from scratch. I would like to understand the QAOA derivation mathematically and have started ...
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What are the important parameters when it comes to VQE algorithms in qiskit?
So I wrote an algorithm for a quadratic problem (qubo) and try to solve it. My question is why I don't get the correct results when running my algorithm on a quantum computer like IBM_manila. In the ...
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Why am I able to simulate such high qubit numbers on my laptop?
Recently I've been working on a VQE-related project, for which I'm using Qiskit's TwoLocal variational form (qiskit version 0.34.2). I noticed that I was able to simulate this circuit up to ...
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Mathematical Context of MPT formula in qiskit VQE
In the video at timestamp: 43:34, We input the mean-variance parameters.
https://www.youtube.com/watch?v=UtMVoGXlz04&t=3327s
Based on the formula as mentioned here in section Formulation
https://...
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Qiskit best programming practices - how to speed up qiskit code?
I am currently doing some experiments using Variational Quantum Eigensolver in molecular dynamics using qiskit, and noticed that the time for execution on real backend is significantly higher than the ...
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QVA with local Hadamard Overlap
I am trying to implement in Qiskit the quantum variational linear solver given here (https://arxiv.org/pdf/1909.05820.pdf) with a local Hadamard overlap test and failing substantially. The cost is not ...
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Question about performing VQE with an embedded Hamiltonian
Say I have a physical Hamiltonian $\mathcal{H}$ which is $D$-dimensional and I encode it into a larger matrix $M$ which is $\Delta$-dimensional. In the cases I care about $\Delta$ is strictly greater ...
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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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How to implement the VQE in qiskit using UCCSD?
I am new to VQE and want to see the whole circuit of UCCSD in VQE implementation. I saw the code post here Visualize full UCC circuit in qiskit I tried to import all packages but have no idea with one/...
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What are "unbounded loss functions" and "unbounded operators"?
I am reading this paper: Quantum Generative Training Using Rényi Divergences. In it, the authors mention the following multiple times:
"...an unbounded loss function can circumvent the existing ...
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How to optimise QAOA
I have a similarly naive question about the classical part of the optimisation in the Quantum Approximate Optimization Algorithm. Specifically, the cost function is given prescribed as
\begin{align}
...
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Variational quantum eigensolver in qiskit
I have implemented a hybrid quantum NN on a dataset to perform classification. Now I want to apply quantum PCA to my dataset to find the eigenvalues. After going through a few qiskit tutorials, I ...
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VQE from scratch, what have I got wrong?
I've been working on a code to run VQE with a grouped measurement. For some reason, my expectation values are slightly off from those computed by pennylane, the software I decided to use for this ...
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Qiskit - Simpler way to create a Hamiltonian
I am looking for an efficient way to create a Hamiltonian in Qiskit.
Following are my desired input and outputs
input: 'ZZI'
output: Z^Z^I, where Z and I are operators.
Here is how I am doing it ...
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Cliffords to Transform into Common Eigenbasis
Say I have the following Hamiltonian (given in terms of Pauli operators):
\begin{equation}
H=aX_1Z_2+bZ_1X_2.
\end{equation}
Both Pauli terms commute with each other. I want to make a measurement of $\...
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Ground state compute issue by qiskit
I use the following code to calculate the ground state for the LiH molecule in an active space. I come across two problems. The first is I found that the Hartree Fock state gave energy that is far ...
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Confusion about the objective function of VQEs and QAOAs
I am a bit puzzled on how the objective function of the VQEs and QAOAs. Of course, the parametrised state is constructed differently in these two algorithms but they do share a common objective to be ...
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How can I run a VQE on one of IBMQ's Quantum Computers
I have implemented a VQE based on Qiskit's VQE function and want to run that on an actual quantum computer. My understanding was, that an IBMQ backend can be passed into the function as a Quantum ...
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How to show mathematically the equivalency between Ising Model and QUBO?
It is said that the Ising Model using spin variables $s ∈ \{−1, 1\}$
$$H(s)=\sum_{i}h_is_i+\sum_{i<j}J_{ij}s_is_j,$$
and a Quadratic Unconstrained Binary Optimization (QUBO) problem with binary ...
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How to express real matrices as linear combinations of unitaries?
I am working on using Variational Quantum Linear Solver (VQLS) for some tasks. Here, we need to represent matrix A as a linear combination of unitaries.
$$ {\bf A} = \Sigma^n_{i=1} c_iA_i $$
My ...
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Why the partial derivative of cost function is written in this form?
I am reading a paper about QCNN and BP problem. And in the paper there is a part illustrating the relation between the trainability and variance of the cost. The cost function is written as,
$C(\theta)...
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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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Does the formula $\sum_k f_k{\rm Tr}(O_k U\rho_k U^\dagger)$ have any physical meaning, in the context of variational quantum algorithms?
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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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.
Can ...
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How to know state corresponding to -1 or 1 for multi qubits VQE?
I was hoping someone can explain to me how to get -1 and 1 for a 2-qubit 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 ...
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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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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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