The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantage. This motivated the development of various quantum error-mitigation protocols, each representing a method to extract useful computational output by combining measurement data from multiple samplings of the available imperfect quantum device. What are the ultimate performance limits universally imposed on such protocols? Here, we derive a fundamental bound on the sampling overhead that applies to a general class of error-mitigation protocols, assuming only the laws of quantum mechanics. We use it to show that (1) the sampling overhead to mitigate local depolarizing noise for layered circuits -such as the ones used for variational quantum algorithms -must scale exponentially with circuit depth, and (2) the optimality of probabilistic error cancellation method among all strategies in mitigating a certain class of noise. We discuss how our unified framework and general bounds can be employed to benchmark and compare various present methods of error mitigation and identify situations where present error-mitigation methods have the greatest potential for improvement.

The roles of free fatty acids (FFA), tumor necrosis factor-alpha (TNF-alpha), and adiponectin in the development of the insulin-resistant metabolic disorder in several subjects have been studied. A total of 70 Japanese male subjects were selected according to the following three sets of criteria: subjects in group A had, (1) a fasting plasma glucose (FPG)>or=110 to <140 mg/dl, (2) a triglyceride (TG) level>or=150 mg/dl, (3) a systolic blood pressure (SBP)>or=140 and/or diastolic blood pressure (DBP)>or=90 mmHg, and (4) a body mass index (BMI)>or=25 kg/m2 (age=53.4+/-8.5 years, BMI=27.0+/-1.3 kg/m2, n=16). Subjects in group B had, (1) FPG<110 mg/dl, (2) TG<150 mg/dl, (3) SBP<140 and DBP<90 mmHg, and (4) BMI>or=25 kg/m2 (age=47.2+/-10.3 years, BMI=26.6+/-1.31 kg/m2, n=38). Subjects in group C had, (1) FPG<110 mg/dl, (2) TG<150 mg/dl, (3) SBP<140 and DBP<90 mmHg, and (4) 20>or=BMI<22 kg/m2 (age=50.4+/-9.3 years, BMI=20.9+/-0.6 kg/m2, n=16). The homeostasis model assessment of insulin resistance in group A (2.7+/-1.4) was significantly higher (p<0.0001) than in groups B (1.6+/-0.7) and C (0.9+/-0.5). FFA in group A (1.17+/-0.57 mEq/l) was significantly higher than in groups B (0.62+/-0.23 mEq/l) and C (0.48+/-0.16 mEq/l) (p<0.0001). Serum TNF-alpha in group A (1.36+/-0.62 pg/ml) was significantly higher than in groups B (0.95+/-0.35 pg/ml; p=0.003) and C (0.76+/-0.09 pg/ml; p=0.0013). No significant differences in the serum level of adiponectin were observed between groups A and B or between groups B and C. The results suggest that FFA and possibly TNF-alpha levels are closely related to the development of insulin resistance in subjects with metabolic disorders.

The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantages, motivating the development of various quantum error-mitigation methods. Here, we derive fundamental bounds concerning how error-mitigation algorithms can reduce the computation error as a function of their sampling overhead. Our bounds place universal performance limits on a general error-mitigation protocol class. We use them to show (1) that the sampling overhead that ensures a certain computational accuracy for mitigating local depolarizing noise in layered circuits scales exponentially with the circuit depth for general error-mitigation protocols and (2) the optimality of probabilistic error cancellation among a wide class of strategies in mitigating the local dephasing noise on an arbitrary number of qubits. Our results provide a means to identify when a given quantum error-mitigation strategy is optimal and when there is potential room for improvement.

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