Gradients, parallelism, and variance of quantum estimates
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914273431650304 |
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| author | Preti, Francesco Schilling, Michael Bernád, József Zsolt Calarco, Tommaso Cárdenas-López, Francisco Motzoi, Felix |
| author_facet | Preti, Francesco Schilling, Michael Bernád, József Zsolt Calarco, Tommaso Cárdenas-López, Francisco Motzoi, Felix |
| contents | Computation of observables and their gradients on near-term quantum hardware is a central aspect of any quantum algorithm. In this work, we first review standard approaches to the estimation of observables with and without quantum amplitude estimation for both cost functions and gradients, discuss sampling problems, and analyze variance propagation on quantum circuits with and without Linear Combination of Unitaries (LCU). Afterwards, we systematically analyze the standard approaches to gradient computation with LCU circuits. Finally, we develop a LCU gradient framework for the most general gradients based on n-qubit gates and for time-dependent quantum control gradient, analyze the convergence behaviour of the circuit estimators, and provide detailed circuit representations of both for near-term and fault-tolerant hardware. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradients, parallelism, and variance of quantum estimates Preti, Francesco Schilling, Michael Bernád, József Zsolt Calarco, Tommaso Cárdenas-López, Francisco Motzoi, Felix Quantum Physics Computation of observables and their gradients on near-term quantum hardware is a central aspect of any quantum algorithm. In this work, we first review standard approaches to the estimation of observables with and without quantum amplitude estimation for both cost functions and gradients, discuss sampling problems, and analyze variance propagation on quantum circuits with and without Linear Combination of Unitaries (LCU). Afterwards, we systematically analyze the standard approaches to gradient computation with LCU circuits. Finally, we develop a LCU gradient framework for the most general gradients based on n-qubit gates and for time-dependent quantum control gradient, analyze the convergence behaviour of the circuit estimators, and provide detailed circuit representations of both for near-term and fault-tolerant hardware. |
| title | Gradients, parallelism, and variance of quantum estimates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.11214 |