Stratified Sampling for Quasi-Probability Decompositions

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Dai, Joshua W., Koczor, Bálint
Natura: Preprint
Pubblicazione: 2026
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866914323959382016
author Dai, Joshua W.
Koczor, Bálint
author_facet Dai, Joshua W.
Koczor, Bálint
contents Quasi-probability decompositions (QPDs) have proven essential in many quantum algorithms and protocols -- one replaces a ``difficult'' quantum circuit with an ensemble of ``easier'' circuit variants whose weighted outcomes reproduce any target observable. This, however, inevitably yields an increased configuration variance beyond Born-rule shot noise. We develop a broad framework for accounting for and reducing this variance and prove that stratified sampling -- under ideal proportional allocation -- results in an unbiased estimator with a variance that is never worse than naïve sampling (with equality only in degenerate cases). Furthermore, we provide a classical dynamic programme to enable stratification on arbitrary product-form QPDs. Numerical simulations of typical QPDs, such as Probabilistic Error Cancellation (PEC) and Probabilistic Angle Interpolation (PAI), demonstrate constant-factor reductions in overall variance (up to $\sim 60$--$80\%$ in an oracle model) and robust $\sim 10\%$ savings in the pessimistic single-shot regime. Our results can be applied immediately to reduce the net sampling cost of practically relevant QPDs that are commonly used in near term and early fault-tolerant algorithms without requiring additional quantum resources.
format Preprint
id arxiv_https___arxiv_org_abs_2602_11245
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Stratified Sampling for Quasi-Probability Decompositions
Dai, Joshua W.
Koczor, Bálint
Quantum Physics
Quasi-probability decompositions (QPDs) have proven essential in many quantum algorithms and protocols -- one replaces a ``difficult'' quantum circuit with an ensemble of ``easier'' circuit variants whose weighted outcomes reproduce any target observable. This, however, inevitably yields an increased configuration variance beyond Born-rule shot noise. We develop a broad framework for accounting for and reducing this variance and prove that stratified sampling -- under ideal proportional allocation -- results in an unbiased estimator with a variance that is never worse than naïve sampling (with equality only in degenerate cases). Furthermore, we provide a classical dynamic programme to enable stratification on arbitrary product-form QPDs. Numerical simulations of typical QPDs, such as Probabilistic Error Cancellation (PEC) and Probabilistic Angle Interpolation (PAI), demonstrate constant-factor reductions in overall variance (up to $\sim 60$--$80\%$ in an oracle model) and robust $\sim 10\%$ savings in the pessimistic single-shot regime. Our results can be applied immediately to reduce the net sampling cost of practically relevant QPDs that are commonly used in near term and early fault-tolerant algorithms without requiring additional quantum resources.
title Stratified Sampling for Quasi-Probability Decompositions
topic Quantum Physics
url https://arxiv.org/abs/2602.11245