Inference-Based Quantum Sensing.

In a standard quantum sensing (QS) task one aims at estimating an unknown parameter θ, encoded into an n-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response R(θ) (i.e., changes in the measurement outcomes). For simple cases the form of R(θ) is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. In this Letter, we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, R(θ) can be fully characterized by only measuring the system response at 2n+1 parameters. This allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than δ, if one measures the system response with a number of shots that scales only as Ω(log^{3}(n)/δ^{2}). Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations.

Noise-induced barren plateaus in variational quantum algorithms.

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

Quantum and Classical Ergotropy from Relative Entropies.

The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem.

Cost function dependent barren plateaus in shallow parametrized quantum circuits.

Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is [Formula: see text]. Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

Quantum Jarzynski Equality in Open Quantum Systems from the One-Time Measurement Scheme.

In open quantum systems, a clear distinction between work and heat is often challenging, and extending the quantum Jarzynski equality to systems evolving under general quantum channels beyond unitality remains an open problem in quantum thermodynamics. In this Letter, we introduce well-defined notions of guessed quantum heat and guessed quantum work, by exploiting the one-time measurement scheme, which only requires an initial energy measurement on the system alone. We derive a modified quantum Jarzynski equality and the principle of maximum work with respect to the guessed quantum work, which requires the knowledge of the system only. We further show the significance of guessed quantum heat and work by linking them to the problem of quantum hypothesis testing.

[Effect of tonometry on a glaucoma population study].

PURPOSE: The purpose of this study was to evaluate the influence of tonometry in detecting the occurrence of glaucoma. METHODS: The subjects, 845 out of 3,488 residents aged 40 years or older, were examined according to standard protocols, including tonometry, slit lamp examination, fundus photography, and automatic perimetry as a recall examination. The intraocular pressure in each subject was measured by both Goldmann applanation tonometer(GAT) and noncontact tonometer CT-70 (NCT). RESULTS: The mean +/- standard deviation intraocular pressure measured by GAT was 15.52 +/- 2.57 mmHg, and 15.03 +/- 2.90 mmHg by NCT. There was a statistically significant correlation(p < 0.0001). The difference between pairs of measurements by GAT and NCT was 0.50 +/- 1.93 mmHg. There was no influence of tonometry in detecting the incidence of glaucoma, which was 4.14%; primary open-angle glaucoma 0.59%, normal tension glaucoma 2.6%, primary angle-closure glaucoma 0.47%, and other types of glaucoma 0.48%. The detection of ocular hypertension was different, and was 2.13% with GAT and 2.72% with NCT. CONCLUSION: In our study, the influence of tonometry in detecting the incidence of glaucoma was very small. A noncontact tonometer is considered to be useful for glaucoma population study.