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Dual-comb interferometry harnesses the interference of two laser frequency combs to provide unprecedented capability in spectroscopy applications. In the past decade, the state-of-the-art systems have reached a point where the signal-to-noise ratio per unit acquisition time is fundamentally limited by shot noise from vacuum fluctuations. To address the issue, we propose an entanglement-enhanced dual-comb spectroscopy protocol that leverages quantum resources to significantly improve the signal-to-noise ratio performance. To analyze the performance of real systems, we develop a quantum model of dual-comb spectroscopy that takes practical noises into consideration. Based on this model, we propose quantum combs with side-band entanglement around each comb lines to suppress the shot noise in heterodyne detection. Our results show significant quantum advantages in the uW to mW power range, making this technique particularly attractive for biological and chemical sensing applications. Furthermore, the quantum comb can be engineered using nonlinear optics and promises near-term experimentation.

 

Squeezed light has long been used to enhance the precision of a single optomechanical sensor. An emerging set of proposals seeks to use arrays of optomechanical sensors to detect weak distributed forces, for applications ranging from gravity-based subterranean imaging to dark matter searches; however, a detailed investigation into the quantum-enhancement of this approach remains outstanding. Here, we propose an array of entanglement-enhanced optomechanical sensors to improve the broadband sensitivity of distributed force sensing. By coherently operating the optomechanical sensor array and distributing squeezing to entangle the optical fields, the array of sensors has a scaling advantage over independent sensors (i.e.,$$\sqrt{M}\to M$$$\sqrt{M}\to M$, whereMis the number of sensors) due to coherence as well as joint noise suppression due to multi-partite entanglement. As an illustration, we consider entanglement-enhancement of an optomechanical accelerometer array to search for dark matter, and elucidate the challenge of realizing a quantum advantage in this context.

 

Entanglement has been known to boost target detection, despite it being destroyed by lossy-noisy propagation. Recently, Zhuang and Shapiro (2022Phys. Rev. Lett.128010501) proposed a quantum pulse-compression radar to extend entanglement’s benefit to target range estimation. In a radar application, many other aspects of the target are of interest, including angle, velocity and cross section. In this study, we propose a dual-receiver radar scheme that employs a high time-bandwidth product microwave pulse entangled with a pre-shared reference signal available at the receiver, to investigate the direction of a distant object and show that the direction-resolving capability is significantly improved by entanglement, compared to its classical counterpart under the same parameter settings. We identify the applicable scenario of this quantum radar to be short-range and high-frequency, which enables entanglement’s benefit in a reasonable integration time.

 

The nature of dark matter is unknown and calls for a systematical search. For axion dark matter, such a search relies on finding feeble random noise arising from the weak coupling between dark matter and microwave haloscopes. We model such process as a quantum channel and derive the fundamental precision limit of noise sensing. An entanglement-assisted strategy based on two-mode squeezed vacuum is thereby demonstrated optimal, while the optimality of a single-mode squeezed vacuum is found limited to the lossless case. We propose a “nulling” measurement (squeezing and photon counting) to achieve the optimal performances. In terms of the scan rate, even with 20-decibel of strength, single-mode squeezing still underperforms the vacuum limit which is achieved by photon counting on vacuum input; while the two-mode squeezed vacuum provides large and close-to-optimum advantage over the vacuum limit, thus more exotic quantum resources are no longer required. Our results highlight the necessity of entanglement assistance and microwave photon counting in dark matter search.

 

Quantum Approximate Optimization algorithm (QAOA) aims to search for approximate solutions to discrete optimization problems with near-term quantum computers. As there are no algorithmic guarantee possible for QAOA to outperform classical computers, without a proof that bounded-error quantum polynomial time (BQP) ≠ nondeterministic polynomial time (NP), it is necessary to investigate the empirical advantages of QAOA. We identify a computational phase transition of QAOA when solving hard problems such as SAT—random instances are most difficult to train at a critical problem density. We connect the transition to the controllability and the complexity of QAOA circuits. Moreover, we find that the critical problem density in general deviates from the SAT-UNSAT phase transition, where the hardest instances for classical algorithms lies. Then, we show that the high problem density region, which limits QAOA’s performance in hard optimization problems (reachability deficits), is actually a good place to utilize QAOA: its approximation ratio has a much slower decay with the problem density, compared to classical approximate algorithms. Indeed, it is exactly in this region that quantum advantages of QAOA over classical approximate algorithms can be identified.

 

Bosonic encoding of quantum information into harmonic oscillators is a hardware efficient approach to battle noise. In this regard, oscillator-to-oscillator codes not only provide an additional opportunity in bosonic encoding, but also extend the applicability of error correction to continuous-variable states ubiquitous in quantum sensing and communication. In this work, we derive the optimal oscillator-to-oscillator codes among the general family of Gottesman-Kitaev-Preskill (GKP)-stablizer codes for homogeneous noise. We prove that an arbitrary GKP-stabilizer code can be reduced to a generalized GKP two-mode-squeezing (TMS) code. The optimal encoding to minimize the geometric mean error can be constructed from GKP-TMS codes with an optimized GKP lattice and TMS gains. For single-mode data and ancilla, this optimal code design problem can be efficiently solved, and we further provide numerical evidence that a hexagonal GKP lattice is optimal and strictly better than the previously adopted square lattice. For the multimode case, general GKP lattice optimization is challenging. In the two-mode data and ancilla case, we identify the D4 lattice—a 4-dimensional dense-packing lattice—to be superior to a product of lower dimensional lattices. As a by-product, the code reduction allows us to prove a universal no-threshold-theorem for arbitrary oscillators-to-oscillators codes based on Gaussian encoding, even when the ancilla are not GKP states.

 

Optomechanical systems have been exploited in ultrasensitive measurements of force, acceleration and magnetic fields. The fundamental limits for optomechanical sensing have been extensively studied and now well understood—the intrinsic uncertainties of the bosonic optical and mechanical modes, together with backaction noise arising from interactions between the two, dictate the standard quantum limit. Advanced techniques based on non-classical probes, in situ ponderomotive squeezed light and backaction-evading measurements have been developed to overcome the standard quantum limit for individual optomechanical sensors. An alternative, conceptually simpler approach to enhance optomechanical sensing rests on joint measurements taken by multiple sensors. In this configuration, a pathway to overcome the fundamental limits in joint measurements has not been explored. Here we demonstrate that joint force measurements taken with entangled probes on multiple optomechanical sensors can improve the bandwidth in the thermal-noise-dominant regime or the sensitivity in the shot-noise-dominant regime. Moreover, we quantify the overall performance of entangled probes with the sensitivity–bandwidth product and observe a 25% increase compared with that of classical probes. The demonstrated entanglement-enhanced optomechanical sensors would enable new capabilities for inertial navigation, acoustic imaging and searches for new physics.