notesum.ai

Published at November 26

Mixed-State Quantum Denoising Diffusion Probabilistic Model

quant-ph

cs.AI

cs.LG

Released Date: November 26, 2024

Authors: Gino Kwun¹, Bingzhi Zhang², Quntao Zhuang³

Aff.: ¹Thomas Lord Department of Computer Science, University of Southern California; ²Department of Physics and Astronomy, University of Southern California; ³Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California

Arxiv: http://arxiv.org/abs/2411.17608v1

Task	$n$	$n_{a}$	$n_{\rm train}$	$T$	$L$	Cost function	Forward schedule	Ancilla type	Performance
Clustered states (Fig. 1 and Fig. 6 a2)	1	2	100	6	4	Wasserstein	Cosine	Haar ( $\|\phi_{\rm Haar}\rangle\otimes\|0\rangle$ )	$\overline{F}_{\text{data},0}=0.9853\pm 0.0001$
Clustered states (Fig. 1 and Fig. 6 a2)	1	2	100	6	4	Wasserstein	Cosine	Haar ( $\|\phi_{\rm Haar}\rangle\otimes\|0\rangle$ )	$\overline{F}_{\text{gen},0}=0.9873\pm 10^{-5}$
Clustered states (Fig. 6 a3)	1	2	100	6	4	Wasserstein	Cosine	zero ( $\|00\rangle$ )	$\overline{F}_{\text{data},0}=0.9852\pm 0.0001$
Clustered states (Fig. 6 a3)	1	2	100	6	4	Wasserstein	Cosine	zero ( $\|00\rangle$ )	$\overline{F}_{\text{gen},0}=0.9888\pm 10^{-5}$
Circular states (Fig. 2 and Fig. 6 b3)	1	2	200	6	8	Wasserstein	Cosine square	zero ( $\|00\rangle$ )	${\rm Wass}_{\rm data}=0.0063$
Circular states (Fig. 2 and Fig. 6 b3)	1	2	200	6	8	Wasserstein	Cosine square	zero ( $\|00\rangle$ )	${\rm Wass}_{\text{gen}}=0.0151$
Circular states (Fig. 6 b2)	1	2	200	4	8	Wasserstein	Cosine square	Haar ( $\|\phi_{\rm Haar}\rangle\otimes\|0\rangle$ )	${\rm Wass}_{\rm data}=0.0068$
Circular states (Fig. 6 b2)	1	2	200	4	8	Wasserstein	Cosine square	Haar ( $\|\phi_{\rm Haar}\rangle\otimes\|0\rangle$ )	${\rm Wass}_{\text{gen}}=0.0163$
Many-body phase (Fig. 3 and Fig. 5)	4	2	100	6	12	MMD	Cosine square	zero ( $\|00\rangle$ )	$\overline{M}_{x,\text{data}}=0.951\pm 3\times 10^{-5}$
Many-body phase (Fig. 3 and Fig. 5)	4	2	100	6	12	MMD	Cosine square	zero ( $\|00\rangle$ )	$\overline{M}_{x,\text{gen}}=0.940\pm 0.0005$
Many-body phase (Fig. 5)	4	2	100	6	12	MMD	Linear	zero ( $\|00\rangle$ )	$\overline{M}_{x,\text{data}}=0.952\pm 3\times 10^{-5}$
Many-body phase (Fig. 5)	4	2	100	6	12	MMD	Linear	zero ( $\|00\rangle$ )	$\overline{M}_{x,\text{gen}}=0.427\pm 0.0343$
Many-body phase (Fig. 5)	4	2	100	6	12	MMD	Cosine	zero ( $\|00\rangle$ )	$\overline{M}_{x,\text{data}}=0.952\pm 3\times 10^{-5}$
Many-body phase (Fig. 5)	4	2	100	6	12	MMD	Cosine	zero ( $\|00\rangle$ )	$\overline{M}_{x,\text{gen}}=0.679\pm 0.0232$