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Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat
Quantum Physics · Submitted 3 Dec 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find our algorithm converges faster and achieves higher fidelities than state of the art, both in terms of measurement settings, as well as in terms of noise tolerance, in the cases of depolarizing and Gaussian noise models.
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The abstract, sentence by sentence
We propose a non-convex optimization algorithm, based on the Burer-Monteiro (BM) factorization, for the quantum process tomography problem, in order to estimate a low-rank process matrix $\chi$ for near-unitary quantum gates. In this work, we compare our approach against state of the art convex optimization approaches based on gradient descent. We use a reduced set of initial states and measurement operators that require $2 \cdot 8^n$ circuit settings, as well as $\mathcal{O}(4^n)$ measurements for an underdetermined setting. We find our algorithm converges faster and achieves higher fidelities than state of the art, both in terms of measurement settings, as well as in terms of noise tolerance, in the cases of depolarizing and Gaussian noise models.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose a non-convex optimization algorithm, based on the Burer-Monteiro (BM) factorization, for the quantum process tomography problem, in order to estimate a low-rank process matrix $\chi$ for near-unitary quantum gates. | contribution 0.88 | 0.88 | 0.06 | asserted 0.97 |
| s1 | In this work, we compare our approach against state of the art convex optimization approaches based on gradient descent. | method 0.55 | 0.76 | 0.04 | asserted 0.57 |
| s2 | We use a reduced set of initial states and measurement operators that require $2 \cdot 8^n$ circuit settings, as well as $\mathcal{O}(4^n)$ measurements for an underdetermined setting. | method 0.99 | 0.84 | 0.03 | asserted 0.98 |
| s3 | We find our algorithm converges faster and achieves higher fidelities than state of the art, both in terms of measurement settings, as well as in terms of noise tolerance, in the cases of depolarizing and Gaussian noise models. | result 1.00 | 0.96 | 0.88 | asserted 1.00 |
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Original abstract
We propose a non-convex optimization algorithm, based on the Burer-Monteiro (BM) factorization, for the quantum process tomography problem, in order to estimate a low-rank process matrix $\chi$ for near-unitary quantum gates. In this work, we compare our approach against state of the art convex optimization approaches based on gradient descent. We use a reduced set of initial states and measurement operators that require $2 \cdot 8^n$ circuit settings, as well as $\mathcal{O}(4^n)$ measurements for an underdetermined setting. We find our algorithm converges faster and achieves higher fidelities than state of the art, both in terms of measurement settings, as well as in terms of noise tolerance, in the cases of depolarizing and Gaussian noise models.
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What it cites · 18 sentences without a confident label
Cites as background 18 papers
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Since then, other procedures for QPT that focus on optimization objectives are proposed, such as the projected least-squares on the process matrix representation [ref] and the gradient-descent on the Kraus representation [ref] versions of QPT; for more information, please refer to the Related Works section of this paper.
Projected Least-Squares Quantum Process Tomography · Introduction · 0.94
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Since then, other procedures for QPT that focus on optimization objectives are proposed, such as the projected least-squares on the process matrix representation [ref] and the gradient-descent on the Kraus representation [ref] versions of QPT; for more information, please refer to the Related Works section of this paper.
Gradient-descent quantum process tomography by learning Kraus operators · Introduction · 0.94
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The work done in [ref] reflects a non-convex approach of performing QST.
Provable quantum state tomography via non-convex methods · for QST · 0.81
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