Quantum Physics (quant-ph)

Abstract: The conventional McCartney model simplifies fog as a scattering medium with space-time invariance, as the time-variant nature of fog is a pure noise for classical optical imaging. In this letter, an opposite finding to traditional idea is reported. The time parameter is incorporated into the McCartney model to account for photon number fluctuation introduced by time-variant fog. We demonstrated that the randomness of ambient photons in the time domain results in the absence of a stable correlation, while the scattering photons are the opposite. This difference can be measured by photon number fluctuation correlation when two conditions are met. A defogging image is reconstructed from the target's information carried by scattering light. Thus, the noise introduced by time-variant fog is eliminated by itself. Distinguishable images can be obtained even when the target is indistinguishable by conventional cameras, providing a prerequisite for subsequent high-level computer vision tasks.

Abstract: Entanglement serves as the resource to empower quantum computing. Recent progress has highlighted its positive impact on learning quantum dynamics, wherein the integration of entanglement into quantum operations or measurements of quantum machine learning (QML) models leads to substantial reductions in training data size, surpassing a specified prediction error threshold. However, an analytical understanding of how the entanglement degree in data affects model performance remains elusive. In this study, we address this knowledge gap by establishing a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. Contrary to previous findings, we prove that the impact of entangled data on prediction error exhibits a dual effect, depending on the number of permitted measurements. With a sufficient number of measurements, increasing the entanglement of training data consistently reduces the prediction error or decreases the required size of the training data to achieve the same prediction error. Conversely, when few measurements are allowed, employing highly entangled data could lead to an increased prediction error. The achieved results provide critical guidance for designing advanced QML protocols, especially for those tailored for execution on early-stage quantum computers with limited access to quantum resources.

Abstract: Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a promising platform for quantum information processing. In DPQA, atomic qubits are selectively loaded into arrays of optical traps that can be reconfigured during the computation itself. Leveraging qubit transport and parallel, entangling quantum operations, different pairs of qubits, even those initially far away, can be entangled at different stages of the quantum program execution. Such reconfigurability and non-local connectivity present new challenges for compilation, especially in the layout synthesis step which places and routes the qubits and schedules the gates. In this paper, we consider a DPQA architecture that contains multiple arrays and supports 2D array movements, representing cutting-edge experimental platforms. Within this architecture, we discretize the state space and formulate layout synthesis as a satisfactory modulo theories problem, which can be solved by existing solvers optimally in terms of circuit depth. For a set of benchmark circuits generated by random graphs with complex connectivities, our compiler OLSQ-DPQA reduces the number of two-qubit entangling gates on small problem instances by 1.7x compared to optimal compilation results on a fixed planar architecture. To further improve scalability and practicality of the method, we introduce a greedy heuristic inspired by the iterative peeling approach in classical integrated circuit routing. Using a hybrid approach that combined the greedy and optimal methods, we demonstrate that our DPQA-based compiled circuits feature reduced scaling overhead compared to a grid fixed architecture, resulting in 5.1X less two-qubit gates for 90 qubit quantum circuits. These methods enable programmable, complex quantum circuits with neutral atom quantum computers, as well as informing both future compilers and future hardware choices.

Abstract: In the rapid development of cold atom qubit platform, the two-qubit Controlled-PHASE Rydberg blockade gate via off-resonant modulated driving has been making significant progress recently. In pursuit of higher fidelity, faster operation and better robustness, a major upgrade about suppression of high-frequency components in the modulation is called for, and a systematic method has been established here for this purpose. The quintessence of this newly constructed method can be interpreted as filtering out the relatively high frequency ingredients embedded in basis functions to generate the modulation waveforms and then analyzing whether they fulfill the requirement of gate condition. It turns out that appropriate waveforms of two-qubit entangling gate protocols can be successfully established via these frequency-adjusted basis functions, with the help of numerical optimization procedures. Moreover, this timely upgrade version can be further enhanced with adaptions to specific finite Rydberg blockade strength values and dual-pulse technique to overcome residual thermal motion of qubit atoms. Besides theoretical derivations, we also thoroughly investigate the representative modulation patterns, demonstrating the versatility of off-resonant modulated driving method in the design of two-qubit entangling Rydberg blockade gate.

Abstract: The 2022 Tel Aviv conference on the Many Worlds interpretation of quantum mechanics highlighted many differences between theorists. A very significant dichotomy is between Everettian fission (splitting) and Saunders-Wallace-Wilson divergence. For fission, an observer may have multiple futures, whereas for divergence they always have a single future. Divergence was explicitly introduced to resolve the problem of pre-measurement uncertainty for Everettian theory, which is universally believed to be absent for fission. Here, I maintain that there is indeed uncertainty about future observations prior to fission, so long as objective probability is a property of Everettian branches. This is made possible if the universe is a set and branches are subsets with probability measure. A universe which is a set of universes which are macroscopically isomorphic and span all possible configurations of microscopic local be\"ables fulfils that role. If objective probability is a property of branches, a successful Deutsch-Wallace decision-theoretic argument would justify the Principal Principle and be part of probability theory rather than being specific to Many Worlds. Any macroscopic object in our environment becomes a set of isomorphs with different microscopic configurations, each in an elemental universe (elemental in the set-theoretic sense). This is similar to Many Interacting Worlds theory but the observer inhabits the set of worlds, not an individual world. An observer has many elemental bodies.

Abstract: Anyonic system not only has potential applications in the construction of topological quantum computer, but also presents a unique property known as topological entanglement entropy in quantum many-body systems. How to understand topological entanglement entropy is one of the most concerned problems for physicists. For an anyonic bipartite system, we define an operational measure of topological correlation based on the principle of maximal entropy, where the topological correlation is the information that cannot be accessed by local operations constrained by anyonic superselection rules and classical communication. This measure can be extended to measure non-local resources of other compound quantum systems in the presence of superselection rules. For a given anyonic bipartite state with maximal rank, we prove that its topological correlation is equal to its entropy of anyonic charge entanglement that has been shown in the literature to be able to derive topological entanglement entropy. This measure provides a more refined classification of correlations in a multipartite system with superselection rules and an illuminating approach to topological phase classification.

Abstract: We generalize the recent result that all analytic quantum dynamics can be represented exactly as the reduction of unitary dynamics generated by a time-dependent Hamiltonian. More precisely, we prove that the partial trace over analytic paths of unitaries can approximate any Lipschitz-continuous quantum dynamics arbitrarily well. We conclude by discussing potential improvements and generalizations of these results, their limitations, and the general challenges one has to overcome when trying to relate dynamics to quantities on the system-environment level.

Abstract: Gaussian boson sampling is a promising candidate for showing experimental quantum advantage. While there is evidence that noiseless Gaussian boson sampling is hard to efficiently simulate using a classical computer, the current Gaussian boson sampling experiments inevitably suffer from loss and other noise models. Despite a high photon loss rate and the presence of noise, they are currently claimed to be hard to classically simulate with the best-known classical algorithm. In this work, we present a classical tensor-network algorithm that simulates Gaussian boson sampling and whose complexity can be significantly reduced when the photon loss rate is high. By generalizing the existing thermal-state approximation algorithm of lossy Gaussian boson sampling, the proposed algorithm enables us to achieve increased accuracy as the running time of the algorithm scales, as opposed to the algorithm that samples from the thermal state, which can give only a fixed accuracy. The generalization allows us to assess the computational power of current lossy experiments even though their output state is not believed to be close to a thermal state. We then simulate the largest Gaussian boson sampling implemented in experiments so far. Much like the actual experiments, classically verifying this large-scale simulation is challenging. To do this, we first observe that in our smaller-scale simulations the total variation distance, cross-entropy, and two-point correlation benchmarks all coincide. Based on this observation, we demonstrate for large-scale experiments that our sampler matches the ground-truth two-point and higher-order correlation functions better than the experiment does, exhibiting evidence that our sampler can simulate the ground-truth distribution better than the experiment can.

Abstract: Universal robust quantum control is essential for performing complex quantum algorithms and efficient quantum error correction protocols. Geometric phase, as a key element with intrinsic fault-tolerant feature, can be well integrated into quantum control processes to enhance control robustness. However, the current geometric quantum control is still controversial in robust universality, which leads to the unsatisfactory result that cannot sufficiently enhance the robustness of arbitrary type of geometric gate. In this study, we find that the finite choice on geometric evolution trajectory is one of the main roots that constrain the control robustness of previous geometric schemes, as it is unable to optionally avoid some trajectory segments that are seriously affected by systematic errors. In view of this, we here propose a new scheme for universal robust geometric control based on geometric trajectory correction, where enough available evolution parameters are introduced to ensure that the effective correction against systematic errors can be executed. From the results of our numerical simulation, arbitrary type of geometric gate implemented by using the corrected geometric trajectory has absolute robustness advantages over conventional quantum one. In addition, we also verify the feasibility of the high-fidelity physical implementation of our scheme in superconducting quantum circuit, and finally discuss in detail the potential researches based on our scheme. Therefore, our theoretical work is expected to offer an attractive avenue for realizing practical fault-tolerant quantum computation in existing experimental platforms.

Abstract: An all-photonic repeater scheme based on a type of graph state called a repeater graph state (RGS) promises tolerance to photon losses as well as operational errors, and offers a fast Bell pair generation rate, limited only by the RGS creation time (rather than enforced round-trip waits). Prior research on the topic has focused on the RGS generation and analyzing the secret key sharing rate, but there is a need to extend to use cases such as distributed computation or teleportation as will be used in a general-purpose Quantum Internet. Here, we propose a protocol and architecture that consider how end nodes participate in the connection; the capabilities and responsibilities of each node; the classical communications between nodes; and the Pauli frame correction information per end-to-end Bell pair. We give graphical reasoning on the correctness of the protocol via graph state manipulation rules. We then show that the RGS scheme is well suited to use in a link architecture connecting memory-based repeaters and end nodes for applications beyond secret sharing. Finally, we discuss the practicality of implementing our proposed protocol on quantum network simulators and how it can be integrated into an existing proposed quantum network architecture.

Abstract: Graph states are useful computational resources in quantum computing, particularly in measurement-based quantum computing models. However, compiling arbitrary graph states into executable form for fault-tolerant surface code execution and accurately estimating the compilation cost and the run-time resource cost remains an open problem. We introduce the Substrate Scheduler, a compiler module designed for fault-tolerant graph state compilation. The Substrate Scheduler aims to minimize the space-time volume cost of generating graph states. We show that Substrate Scheduler can efficiently compile graph states with thousands of vertices for "A Game of Surface Codes"-style patch-based surface code systems. Our results show that our module generates graph states with the lowest execution time complexity to date, achieving graph state generation time complexity that is at or below linear in the number of vertices and demonstrating specific types of graphs to have constant generation time complexity. Moreover, it provides a solid foundation for developing compilers that can handle a larger number of vertices, up to the millions or billions needed to accommodate a wide range of post-classical quantum computing applications.

Abstract: Dynamics of double Jaynes-Cummings models are studied in the presence of Markovian noise and cavity disorders with specific attention to entanglement sudden death and revivals. The study is focused on the glassy disorders, which remain unchanged during the observations. The field is initially assumed to be in a vacuum state, while the atoms are considered to be in a specific two-qubit superposition state. Specifically, the study has revealed that the presence of noise, or a nonlinear pump results in interesting behaviors in the entanglement dynamics. Further, entanglement sudden death is observed in the presence of Markovian noise and nonlinear pump. The presence of entanglement sudden deaths and revivals have also been observed in cases where they were absent initially for the chosen states. The effect of noise on the dynamics of the system is to decay the characteristics, while that of the disorder is to wash them out. On the other hand, the introduction of nonlinearity is found to cause the dynamics of the system to speed up.

Abstract: We adopt an open quantum system approach to study the effects of the back-reaction from a quantum field onto the dynamics of a moving mirror. We describe the coupling between the mirror and the field by using a microscopic model from which the dielectric response of the mirror is obtained from first principles. Using second-order perturbation theory, we derive the master equation governing the mechanical motion of the mirror. Our analysis reveals that the mirror experiences coloured noise and non-local dissipation, which originate from the emission of particle pairs via the dynamical Casimir effect. We show that the noise and dissipation kernels, that enter in the definition of the time-dependent coefficients of the master equation, are related by fluctuation-dissipation relations.

Abstract: Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. The classical de Finetti's theorem provides a representation of infinitely exchangeable sequences of random variables as mixtures of independent and identically distributed variables. The quantum de Finetti theorem extends this result to symmetric quantum states on tensor product Hilbert spaces. However, both theorems do not hold for finitely exchangeable sequences. The aim of this work is to investigate two lesser-known representation theorems. Developed in classical probability theory, they extend de Finetti's theorem to finitely exchangeable sequences by using quasi-probabilities and quasi-expectations. With the aid of these theorems, we illustrate how a de Finetti-like representation theorem for finitely exchangeable sequences requires a mathematical representation which is formally equivalent to quantum theory (with boson-symmetric density matrices).

Abstract: We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes. Our work is inspired by a recent experimental demonstration of large-scale quantum registers, where tightly localized fermion pairs are used to encode qubits exhibiting long coherence time and robustness against laser intensity noise. We describe how to engineer the SWAP gate and high-fidelity controlled-phase gates by adjusting the fermion hopping as well as Feshbach interaction strengths. Combined with previously demonstrated single-qubit rotations, these gates establish the computational universality of the system. Furthermore, we show that 2D quantum Ising Hamiltonians with tunable transverse and longitudinal fields can be efficient simulated by modulating Feshbach interaction strengths. We present a sample-efficient protocol to characterize engineered gates and Hamiltonian dynamics based on an improved classical shadow process tomography that requires minimal experimental controls. Our work opens up new opportunities to harness existing ultracold quantum gases for quantum information sciences.