updating spin-chain-vqe tutorial to use SPSA

[nathanearnestnoble]

Work done by Aryaman Manish Kolhe (@Chasmiccoder) and Ritajit Majumdar (@ritajitmajumdar1). Would like to update tutorial with this SPSA implementation.

Fixes #3632

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[qiskit-bot]

One or more of the following people are relevant to this code:

• @MeltemTolunay
• @miamico

[nathanearnestnoble]

Resolves issue 3632 (#3632)

[kaelynj]

Looks like this needs the title and metadata tags at the very top of the file. You should be able to replace this cell with the following:

---
title: Ground-state energy estimation of the Heisenberg chain with VQE
description: Build, deploy, and run a Qiskit pattern for simulating a Heisenberg chain and estimating its ground state energy.
---  

*Usage estimate: 37 minutes on a Heron processor (NOTE: This is an estimate only. Your runtime might vary.)*

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[kaelynj]

Suggested change

"description": "Build, deploy, and run a Qiskit pattern for simulating a Heisenberg chain and estimating its ground state energy.",

[kaelynj]

The title and metadata tags now need to go at the top of the file (though I'm not totally sure when that changed 😅 )

[kaelynj]

Suggested change

"title": "Ground state energy estimation of the Heisenberg chain with VQE"

[abbycross]

@kaelynj @nathanearnestnoble I fixed the metadata but am getting an error regarding an unused variable session, stemming from

    # Evaluate the problem using a QPU via Qiskit IBM Runtime
    with Session(backend=backend) as session:
        estimator = EstimatorV2()
        estimator.skip_transpilation = True
        x_opt = spsa(
            cost_func,
            x0=x0,
            args=(isa_ansatz, isa_observable, estimator, cost_history_dict),
            maxiter=maxiter,
        )

can you help clear the error? I can then clear the rest of the checks, like converting the output to images.

[Chasmiccoder]

Hi @abbycross and everyone. Thank you for helping merge this work.

I believe from the code snippet you have shared, the error can be fixed as follows:

with Session(backend=backend) as _:

The problem might be that if you write

with Session(backend=backend) as session:

then the variable session is being created but not used in the code block, which is being flagged by the compiler.

[ritajitmajumdar1]

Rather just do

estimator = EstimatorV2(mode=session)

This ensures the entire block runs as a single session. Unless the Estimator is initiated with session, I presume it would run in a job mode.

[abbycross]

Are there any suggestions to add here, for what to read or other tutorials to explore after doing this tutorial? If not, we can remove this whole cell.

[ritajitmajumdar1]

Not sure if there are any tutorials as follow up. Since this is variational, the only variational algorithm in the current tutorials is QAOA. But it is not an extension of this tutorial.