Predicting properties of Scrooge ensembles with high accuracy and low sample complexity WF64CGYVK1

URI	`m2://res/WF64CGYVK1`
Kind	preprint
Creators	Yue Wu, Yuzhi Tong, Helen Propson, Yihui Quek, Liang Mao
Date	2026-09-30
Subjects	arxiv quant-ph, arxiv cond-mat.stat-mech, arxiv math-ph, arxiv math.MP
Scope	border

Expressions

e1: version, preprint

Date	2026-09-30
Ids	arXiv 2609.39992

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Median-of-means estimation of $p_{\mathrm{sym}}^{(k_i)} o_i$ with an approximate Schur transform	statement	lemma S19	arxiv
Block encoding	definition	definition S23	arxiv
Haar moment bounds	statement	lemma S1	arxiv
Bounds on the post-selection probability	statement	lemma S21	arxiv
Block encoding from a purification circuit, cf. Lemma 45 in Ref.	statement	lemma S24	arxiv
Complexity of the block encoding of each symmetric-sector term	statement	lemma S27	arxiv
Complexity of the block encoding of the Scrooge $k$-th moment; informal	statement	theorem 4	arxiv
Runtime of the Schur transform	statement	lemma S9	arxiv
Union bound for a sum of random variables	statement	lemma S20	arxiv
Efficient implementation of symmetric subspace projection; informal	statement	theorem 2	arxiv
Quantum algorithm for observable expectation evaluation for Scrooge moments; informal	statement	theorem 3	arxiv
EY3VYGPY61	statement	lemma S5	arxiv
Error induced by an approximate Schur transform	statement	lemma S15	arxiv
Sufficient $\lambda$ for a given relative error	statement	corollary S8	arxiv
Linear combination of block encodings, cf. Lemma 52 in Ref.	statement	lemma S26	arxiv
Additive and relative errors of the approximation method	statement	theorem 1	arxiv
State preparation pair	definition	definition S25	arxiv
Sufficient $\lambda$ for a given additive error	statement	corollary S4	arxiv
Sample and circuit complexities of operator expectation value estimation algorithm	statement	theorem S22	arxiv
NPFP6BKMR8	statement	corollary S13	arxiv
Median-of-means estimation of $p_{\mathrm{sym}}^{(k)}o$	statement	lemma S17	arxiv
Complexity of the block encoding of the Scrooge $k$-th moment	statement	theorem S28	arxiv
State-independent error bound	statement	lemma S11	arxiv
SV5Q139K15	statement	lemma S10	arxiv
Relative-error estimation of the post-selection probability	statement	lemma S14	arxiv
Additive error of polynomial approximation	statement	theorem S3	arxiv
Relative error of polynomial approximation	statement	theorem S7	arxiv
Median-of-means estimation of $p_{\mathrm{sym}}^{(k)}$ with an approximate Schur transform	statement	lemma S16	arxiv
WPFEZS1SP5	statement	lemma S6	arxiv
Y6DDSS4XMW	statement	lemma S2	arxiv
Efficient implementation of symmetric-subspace projection	statement	theorem S12	arxiv
Error induced by an approximate Schur transform	statement	lemma S18	arxiv

Catalogue records

arxiv: 2609.39992 (work)