This work proposes quantum circuit complexity—the minimal number of elementary operations needed to implement a quantum transformation—be established as a legitimate physical observable. We prove that circuit complexity satisfies all requirements for physical observables, including self-adjointness, gauge invariance, and a consistent measurement theory with well-defined uncertainty relations. We develop complete protocols for measuring complexity in quantum systems and demonstrate its connections to gauge theory and quantum gravity. Our results suggest that computational requirements may constitute physical laws as fundamental as energy conservation. This framework grants insights into the relationship between quantum information, gravity, and the emergence of spacetime geometry while offering practical methods for experimental verification. Our results indicate that the physical universe may be governed by both energetic and computational constraints, with profound implications for our understanding of fundamental physics.
Background:Taking actions to maintain a healthy lifestyle,including regular engagement in physical activity(PA)and reducing sedentary behavior(SB),may protect against the development of internalizing problems among healthy youth.However,it remains unclear whether such associations exist among youth with chronic pain who often report symptoms of depression and anxiety.To this end,we aimed to investigate the associations between independent and combined PA and/or SB patterns with indicators of internalizing problems in this vulnerable population.Methods:Data used in this cross-sectional study were retrieved from the U.S.National Survey of Children’s Health for the years 2021-2022.Specifically,caregiver proxy reports on sociodemgraphic factors and lifestyle behaviors of 4735 U.S.children and adolescents(referring to youth)aged 6-17 years were collected.We examined independent and combined patterns of PA and SB as exposures,with internalizing problems serving as outcomes of interest.Logistic regressions were used to examine the independent and combined associations of PA and/or SB patterns with anxiety and depression symptoms among youth with chronic pain while adjusting for covariates including age,sex,ethnicity,primary caregivers’education level,overweight status,and household federal poverty level.Results:Overall,our results indicated that PA was negatively associated with anxiety and depressive symptoms.Specifically,youth with chronic pain who engaged in at least 60-minute PA for 1-3 days,4-6 days,or every day reported significantly lower likelihood of experiencing symptoms of anxiety(OR=0.71,95%CI:0.60-0.84;OR=0.44,95%CI:0.36-0.53;OR=0.50,95%CI:0.40-0.63,respectively;all p-value<0.001)and depression(OR=0.63,95%CI:0.53-0.75;OR=0.38,95%CI:0.31-0.47;OR=0.46,95%CI:0.36-0.59,respectively;all p-value<0.001)symptoms compared to those with 0 days.Conversely,SB(operationalized via the proxy screen time)was positively associated with anxiety and depression symptoms.Youth with chronic pain who reported 4 or more hours
ingling YuYanxia ChenJinming LiAndréO.WerneckFabian HeroldAlyx TaylorBenjamin TariLiye Zou
