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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Barren Plateau as a consequence of 2-desgin?

Initializing a parameterized quantum circuit with a unitary sampled from a uniform distribution (so sampling from the Haar distribution) or in a weaker form: a unitary which is a unitary 2-desgin, ...
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Expected Minimum Clique Coverage?

I'm curious if there is literature on this and, if there is, where to find it. Here I'm using ``clique" to mean a set of observables which all commute with each other. I also include the identity ...
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Performance metrics in QSVM

I have implemented QSVM on breast cancer dataset using link: "https://qiskit.org/documentation/stable/0.24/tutorials/machine_learning/01_qsvm_classification.html" but unable to compute other ...
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Expectation value of Pauli string for VQE

One approach to get the expectation value $\langle\psi|P\psi\rangle$ of a pauli string $P\in \{I, X, Y, X\}^{\otimes n}$ is the following. Let $(a_i, |\lambda_i\rangle)$ be eigenvalue-eigenvector ...
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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 on 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 is ...
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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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Find minimum eigenvalue of an Ising Hamiltonian combined with Error Mitigation

I am currently working on a variation of the Traveling Salesman Problem. For which I use the QUBO(Quadratic Unconstrained Binary Optimization). Within Qiskit there are potent functions to obtain the ...
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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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2 answers
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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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3 votes
1 answer
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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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Measurement of a Hamiltonian with Junk States

TL;DR: If I encode a Hermitian matrix in a non-Hermitian matrix, does that matter for VQE? Is the entire $H$ required to be Hermitian or just the parts corresponding to physical states? Say I have a ...
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1 answer
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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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Hardware efficient ansatz versus Alternating Layered Ansatz

I'm reading a paper Cost function dependent barren plateaus in shallow parametrized quantum circuits. There they introduce what is called Alternating Layered Ansatz (ALA). It is said that: The ...
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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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2 votes
1 answer
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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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2 votes
1 answer
101 views

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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2 votes
1 answer
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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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2 votes
1 answer
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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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4 votes
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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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2 votes
1 answer
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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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11 votes
1 answer
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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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2 votes
1 answer
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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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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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2 votes
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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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2 votes
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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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1 answer
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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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4 votes
3 answers
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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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2 votes
1 answer
104 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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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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2 votes
1 answer
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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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3 votes
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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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