All clocks, in some form or another, use the evolution of nature towards higher entropy states to quantify the passage of time. Due to the statistical nature of the second law and corresponding entropy flows, fluctuations fundamentally limit the performance of any clock. This suggests a deep relation between the increase in entropy and the quality of clock ticks. Indeed, minimal models for autonomous clocks in the quantum realm revealed that a linear relation can be derived, where for a limited regime every bit of entropy linearly increases the accuracy of quantum clocks. But can such a linear relation persist as we move towards a more classical system? We answer this in the affirmative by presenting the first experimental investigation of this thermodynamic relation in a nanoscale clock. We stochastically drive a nanometer-thick membrane and read out its displacement with a radio-frequency cavity, allowing us to identify the ticks of a clock. We show theoretically that the maximum possible accuracy for this classical clock is proportional to the entropy created per tick, similar to the known limit for a weakly coupled quantum clock but with a different proportionality constant. We measure both the accuracy and the entropy. Once non-thermal noise is accounted for, we find that there is a linear relation between accuracy and entropy and that the clock operates within an order of magnitude of the theoretical bound.

On-chip actuation and readout of mechanical motion is key to characterize mechanical resonators and exploit them for new applications. We capacitively couple a silicon nitride membrane to an off resonant radio-frequency cavity formed by a lumped element circuit. Despite a low cavity quality factor (QE ≈ 7.4) and off resonant, room temperature operation, we are able to parametrize several mechanical modes and estimate their optomechanical coupling strengths. This enables a fast characterization of a device without requiring a superconducting cavity, thereby eliminating the need for cryogenic cooling. Finally, we observe optomechanically induced transparency and absorption, crucial for a number of applications including sensitive metrology, ground state cooling of mechanical motion and slowing of light.Cavity optomechanics boasts a number of tools for investigating the interaction between radiation and mechanical motion and enables the characterization and development of highly sensitive devices [1]. Silicon nitride membranes have been fabricated to exhibit very high tensile stress, resulting in high quality factors, and have been used for a number of applications including measurement of radiation pressure shot noise [2], optical squeezing [3], bidirectional conversion between microwave and optical light [4], optical detection of radio waves [5, 6], microkelvin cooling [7] and cooling to the quantum ground state of motion [8][9][10].Radio-frequency (rf) cavities allow for sensitive mechanical readout on-chip [5,11,12]. Here, we use an off-resonant rf cavity to actuate and characterize a silicon nitride membrane at room temperature. We detect several modes and extract the quality factor and cavity coupling strength for each of them. Furthermore, we observe optomechanically induced transparency (OMIT) and optomechanically induced absorption (OMIA) deep in the unresolved sideband regime. OMIT and OMIA are an unambiguous signature of the optomechanical interaction [13] and they can be used to slow or advance light [14]. OMIT has also been proposed as a means to achieve ground state cooling of mechanical motion in the unresolved sideband regime [15,16].Our device consists of a high-stress silicon nitride membrane which is 50 nm thick, has an area of 1.5 mm×1.5 mm and 90% of this area is metalized with 20 nm of Al. We suspend this membrane over two Cr/Au electrodes patterned on a silicon chip. For actuation, a dc voltage V dc = 15 V is applied to electrode 1, with electrode 2 grounded. Measurements were performed at room temperature and at approximately 10 −6 mbar. For optomechanical readout and control, electrode 1 is connected to an effective rf cavity. The cavity is realised using an on-chip inductor L and capacitors C D and C M mounted on the sample holder [17], in addition to the capacitance formed by the membrane C C . The cir-cuit behaves as an LC resonator with total capacitance C T = C C + C P , where C P accounts for the capacitance between the two sides of the antenna and other parasitic capacitances. This ca...

Quantum mechanics has recently indicated that, at the fundamental level, temporal order is not fixed. This phenomenon, termed Indefinite Causal Order, is yet to receive metaphysical or theological engagement. We examine Indefinite Causal Order, particularly as it emerges in a 2018 photonic experiment. In this experiment, two operations A and B were shown to be in a superposition with regard to their causal order. Essentially, time, intuitively understood as fixed, flowing, and fundamental, becomes fuzzy. We argue that if Indefinite Causal Order is true, this is good evidence in favor of a B‐theory of time, though such a B‐theory requires modification. We then turn to theology, suggesting that a B‐theoretic temporal ontology invites serious reconsideration of the doctrine of salvation. This paper concludes that the best explanation for salvation given a B‐theory is mind‐dependent salvific becoming, a type of psychological soteriological change that occurs through downward causation.

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Quantum Natural Language Processing (QNLP) deals with the design and implementation of NLP models intended to be run on quantum hardware. In this paper, we present results on the first NLP experiments conducted on Noisy Intermediate-Scale Quantum (NISQ) computers for datasets of size greater than 100 sentences. Exploiting the formal similarity of the compositional model of meaning by Coecke, Sadrzadeh, and Clark (2010) with quantum theory, we create representations for sentences that have a natural mapping to quantum circuits. We use these representations to implement and successfully train NLP models that solve simple sentence classification tasks on quantum hardware. We conduct quantum simulations that compare the syntax-sensitive model of Coecke et al. with two baselines that use less or no syntax; specifically, we implement the quantum analogues of a “bag-of-words” model, where syntax is not taken into account at all, and of a word-sequence model, where only word order is respected. We demonstrate that all models converge smoothly both in simulations and when run on quantum hardware, and that the results are the expected ones based on the nature of the tasks and the datasets used. Another important goal of this paper is to describe in a way accessible to AI and NLP researchers the main principles, process and challenges of experiments on quantum hardware. Our aim in doing this is to take the first small steps in this unexplored research territory and pave the way for practical Quantum Natural Language Processing.