Preprint

FZJ-2026-01398

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Gradients, parallelism, and variance of quantum estimates

Preti, F. (Corresponding author)FZJ* ; Schilling, M. ; Bernád, J. Z.FZJ* ; Calarco, T.FZJ* ; Cárdenas-López, F.FZJ* ; Motzoi, F.FZJ*

2026
arXiv

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Please use a persistent id in citations: doi:10.48550/arXiv.2509.11214  doi:10.34734/FZJ-2026-01398

Report No.: arXiv:2509.11214

Abstract: 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.

Keyword(s): Quantum Physics (quant-ph) ; FOS: Physical sciences

Note: 36 pages, 11 figures

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)
2. Quantum Control (PGI-8)

Research Program(s):

1. 5214 - Quantum State Preparation and Control (POF4-521) (POF4-521)
2. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)
3. 5221 - Advanced Solid-State Qubits and Qubit Systems (POF4-522) (POF4-522)
4. HAICU (E5430311) (E5430311)
5. AIDAS - Joint Virtual Laboratory for AI, Data Analytics and Scalable Simulation (aidas_20200731) (aidas_20200731)
6. BMBF 13N16149 - QSolid - Quantencomputer im Festkörper (BMBF-13N16149) (BMBF-13N16149)
7. EXC 2004:  Matter and Light for Quantum Computing (ML4Q) (390534769) (390534769)
8. QCFD - Quantum Computational Fluid Dynamics (101080085) (101080085)
9. OpenSuperQ - An Open Superconducting Quantum Computer (820363) (820363)
10. OpenSuperQPlus100 - Open Superconducting Quantum Computers (OpenSuperQPlus) (101113946) (101113946)

Appears in the scientific report 2026

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