We present a novel method to realize a multi-target-qubit controlled phase gate with one microwave photonic qubit simultaneously controlling $n-1$ target microwave photonic qubits. This gate is implemented with $n$ microwave cavities coupled to a superconducting flux qutrit. Each cavity hosts a microwave photonic qubit, whose two logic states are represented by the vacuum state and the single photon state of a single cavity mode, respectively. During the gate operation, the qutrit remains in the ground state and thus decoherence from the qutrit is greatly suppressed. This proposal requires only a single-step operation and thus the gate implementation is quite simple. The gate operation time is independent of the number of the qubits. In addition, this proposal does not need applying classical pulse or any measurement. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one microwave photonic qubit simultaneously controlling two target microwave photonic qubits is feasible with current circuit QED technology. The proposal is quite general and can be applied to implement the proposed gate in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a natural or artificial $\Lambda$-type three-level atom.

Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses.

The initial nonlinear wave equation for the electromagnetic vector potential is solved perturbatively about the known exact plane wave solution in both the free vacuum case, as well as when a constant magnetic field is applied. A nonlinear wave equation with nonzero convective part for the (relatively) slowly varying amplitude of the first-order perturbation has been derived. This equation governs the propagation of electromagnetic waves with a reduced speed of light, where the reduction is roughly proportional to the intensity of the initial pumping plane wave. A system of coupled nonlinear wave equations for the two slowly varying amplitudes of the first-order perturbation, which describe the two polarization states, has been obtained for the case of constant magnetic field background.

Further, the slowly varying wave amplitude behavior is shown to be similar to that of a cnoidal wave, known to describe surface gravity waves in shallow water. It has been demonstrated that the two wave modes describing the two polarization states are independent, and they propagate at different wave frequencies. This effect is usually called nonlinear birefringence.

A misunderstanding of entangled states has spawned decades of concern about quantum measurements and a plethora of quantum interpretations. The "measurement state" or "Schrodinger's cat state" of a superposed quantum system and its detector is nonlocally entangled, suggesting that we turn to nonlocality experiments for insight into measurements. By studying the full range of superposition phases, these experiments show precisely what the measurement state does and does not superpose. These experiments reveal that the measurement state is not, as had been supposed, a paradoxical superposition of detector states. It is instead a nonparadoxical superposition of two correlations between detector states and system states. In this way, the experimental results resolve the problem of definite outcomes ("Schrodinger's cat"), leading to a resolution of the measurement problem. However, this argument does not yet resolve the measurement problem because it is based on the results of experiments, while measurement is a theoretical problem: How can standard quantum theory explain the definite outcomes seen experimentally? Thus, we summarize the nonlocality experiments' supporting theory, which rigorously predicts the experimental results directly from optical paths. Several previous theoretical analyses of the measurement problem have relied on the reduced density operators derived from the measurement state, but these solutions have been rejected due to criticism of reduced density operators. Because it avoids reduced density operators, the optical-path analysis is immune to such criticism.

The paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L 2 (R + ). Using the isomorphism of this space with the space of square-integrable functionals of the Poisson process, the equations can be represented as classical stochastic differential equations, driven by Poisson processes. This leads to a discontinuous dynamical state reduction which we compare to the Ghirardi-Rimini-Weber model. A purely quantum object is found which plays the role of an observer, encoding all events occuring in the system space. An algorithm introduced by Dalibard et al. to numerically solve quantum master equations is interpreted in the context of unravellings and the trajectories of expected values of system observables are calculated.

Two main mechanisms dictate the tunneling process in a double quantum dot: overlap of excited wave functions, effectively described as a tunneling rate, and phonon-assisted tunneling. In this paper, we study different regimes of tunneling that arise from the competition between these two mechanisms in a double quantum dot molecule immersed in a unimodal optical cavity. We show how such regimes affect the mean number of excitations in each quantum dot and in the cavity, the spectroscopic resolution and emission peaks of the photoluminescence spectrum, and the second-order coherence function which is an indicator of the quantumness of emitted light from the cavity.

We show that a nontrivial topologies of the spatial section of Minkowski space-time allow for motion of a charged particle under quantum vacuum fluctuation of the electromagnetic field. This is a potentially observable effect of the quantum vacuum fluctuations of the electromagnetic field. We derive mean squared velocity dispersion when the charged particle lies in Minkowski space-time with compact spatial sections in one, two and/or three directions. We concretely examine the details of these stochastic motions when the spatial section is endowed with different globally homogeneous and inhomogeneous topologies. We also show that compactification in just one direction of the spatial section of Minkowski space-time is sufficient to give rise to velocity dispersion components in the compact and noncompact directions. The question as to whether these stochastic motions under vacuum fluctuations can locally be used to unveil global (topological) homogeneity and inhomogeneity is discussed. In globally homogeneous space topologically induced velocity dispersion of a charged particle is the same regardless of the particle's position, whereas in globally inhomogeneous the time-evolution of the velocity depends on the particle's position. Finally, by using the Minkowskian topological limit of globally homogeneous spaces we show that the greater is the value of the compact topological length the longer is the time interval within the velocity dispersion of a charged is negligible. This means that no motion of a charged particle under electromagnetic quantum fluctuations is allowed when Minkowski space-time is endowed with the simply-connected spatial topology. The ultimate ground for such stochastic motion of charged particle under electromagnetic quantum vacuum fluctuations is a nontrivial space topology.

Quantum coherence is a fundamental resource that quantum technologies exploit to achieve performance beyond that of classical devices. A necessary prerequisite to achieve this advantage is the ability of measurement devices to detect coherence from the measurement statistics. Based on a recently developed resource theory of quantum operations, here we quantify experimentally the ability of a typical quantum-optical detector, the weak-field homodyne detector, to detect coherence. We derive an improved algorithm for quantum detector tomography and apply it to reconstruct the positive-operator-valued measures (POVMs) of the detector in different configurations. The reconstructed POVMs are then employed to evaluate how well the detector can detect coherence using two computable measures. These results shed new light on the experimental investigation of quantum detectors from a resource theoretic point of view.

We give an explicit simple method to build quantum neural networks (QNNs) to solve classification problems. Besides the input (state preparation) and output (amplitude estimation), it has one hidden layer which uses a tensor product of $\log M$ two-dimensional rotations to introduce $\log M$ weights. Here $M$ is the number of training samples. We also have an efficient method to prepare the quantum states of the training samples. By the quantum-classical hybrid method or the variational method, the training algorithm of this QNN is easy to accomplish in a quantum computer. The idea is inspired by the kernel methods and the radial basis function (RBF) networks. In turn, the construction of QNN provides new findings in the design of RBF networks. As an application, we introduce a quantum-inspired RBF network, in which the number of weight parameters is $\log M$. Numerical tests indicate that the performance of this neural network in solving classification problems improves when $M$ increases. Since using exponentially fewer parameters, more advanced optimization methods (e.g. Newton's method) can be used to train this network. Finally, about the convex optimization problem to train support vector machines, we use a similar idea to reduce the number of variables, which equals $M$, to $\log M$.

Quantum metrology enables a measurement sensitivity below the standard quantum limit (SQL), as demonstrated in the Laser Interferometer Gravitational-wave Observatory (LIGO). As a unique quantum resource, entanglement has been utilized to enhance the performance of, e.g., microscopy, target detection, and phase estimation. To date, almost all existing entanglement-enhanced sensing demonstrations are restricted to improving the performance of probing optical parameters at a single sensor, but a multitude of applications rely on an array of sensors that work collectively to undertake sensing tasks in the radiofrequency (RF) and microwave spectral ranges. Here, we propose and experimentally demonstrate a reconfigurable RF-photonic sensor network comprised of three entangled sensor nodes. We show that the entanglement shared by the sensors can be tailored to substantially increase the precision of parameter estimation in networked sensing tasks, such as estimating the angle of arrival (AoA) of an RF field. Our work would open a new avenue toward utilizing quantum metrology for ultrasensitive positioning, navigation, and timing.

Single-photon sources based on semiconductor quantum dots have emerged as an excellent platform for high efficiency quantum light generation. However, scalability remains a challenge since quantum dots generally present inhomogeneous characteristics. Here we benchmark the performance of fifteen deterministically fabricated single-photon sources. They display an average indistinguishability of 90.6 +/- 2.8 % with a single-photon purity of 95.4 +/- 1.5 % and high homogeneity in operation wavelength and temporal profile. Each source also has state-of-the-art brightness with an average first lens brightness value of 13.6 +/- 4.4 %. Whilst the highest brightness is obtained with a charged quantum dot, the highest quantum purity is obtained with neutral ones. We also introduce various techniques to identify the nature of the emitting state. Our study sets the groundwork for large-scale fabrication of identical sources by identifying the remaining challenges and outlining solutions.

An important topic in quantum information is the theory of error correction codes. Practical situations often involve quantum systems with states in an infinite dimensional Hilbert space, for example coherent states. Motivated by these practical needs, we apply the theory of non-commutative graphs, which is a tool to analyze error correction codes, to infinite dimensional Hilbert spaces. As an explicit example, a family of non-commutative graphs associated with the Schr\"odinger equation describing the dynamics of a two-mode quantum oscillator is constructed and maximal quantum anticliques for these graphs are found.

Local Hamiltonians with topological quantum order exhibit highly entangled ground states that cannot be prepared by shallow quantum circuits. Here, we show that this property may extend to all low-energy states in the presence of an on-site $\mathbb{Z}_2$ symmetry. This proves a version of the No Low-Energy Trivial States (NLTS) conjecture for a family of local Hamiltonians with symmetry protected topological order. A surprising consequence of this result is that the Goemans-Williamson algorithm outperforms the Quantum Approximate Optimization Algorithm (QAOA) for certain instances of MaxCut, at any constant level. We argue that the locality and symmetry of QAOA severely limits its performance. To overcome these limitations, we propose a non-local version of QAOA, and give numerical evidence that it significantly outperforms standard QAOA for frustrated Ising models on random 3-regular graphs.

In this article we present a full description of the quantum Kerr Ising model---a linear optical network of parametrically pumped Kerr non-linearities. We consider the non-dissapative Kerr Ising model and, using variational techniques, show that the energy spectrum is primarily determined by the adjacency matrix in the Ising model and exhibits highly non-classical cat like eigenstates. We then introduce dissipation to give a quantum mechanical treatment of the measurement process based on homodyne detection via the conditional stochastic Schrodinger equation. Finally we identify a quantum advantage in comparison to the classical analogue for the example of two anti-ferromagnetic cavities.

We investigate the structure of the gravity-induced Generalized Uncertainty Principle in three dimensions. The subtleties of lower dimensional gravity, and its important differences with respect to four and higher dimensions, are duly taken into account, by considering different possible candidates for the gravitational radius, $R_g$, that is the minimal length/maximal resolution of the quantum mechanical localization process. We find that the event horizon of the $M \neq 0$ Ba\~{n}ados-Teitelboim-Zanelli micro black hole furnishes the most consistent $R_g$. This allows us to obtain a suitable formula for the Generalized Uncertainty Principle in three dimensions, and also to estimate the corrections induced by the latter on the Hawking temperature and Bekenstein entropy. We also point to the extremal $M=0$ case, and its natural unit of length introduced by the cosmological constant, $\ell = 1 / \sqrt{-\Lambda}$, as a possible alternative to $R_g$, and present a condensed matter analog realization of this scenario.

In this paper, we present a quasi-polynomial time classical algorithm that estimates the partition function of quantum many-body systems at temperatures above the thermal phase transition point. It is known that in the worst case, the same problem is NP-hard below this point. Together with our work, this shows that the transition in the phase of a quantum system is also accompanied by a transition in the hardness of approximation. We also show that in a system of n particles above the phase transition point, the correlation between two observables whose distance is at least log(n) decays exponentially. We can improve the factor of log(n) to a constant when the Hamiltonian has commuting terms or is on a 1D chain. The key to our results is a characterization of the phase transition and the critical behavior of the system in terms of the complex zeros of the partition function. Our work extends a seminal work of Dobrushin and Shlosman on the equivalence between the decay of correlations and the analyticity of the free energy in classical spin models. On the algorithmic side, our result extends the scope of a recent approach due to Barvinok for solving classical counting problems to quantum many-body systems.

The recent development of hybrid systems based on superconducting circuits has opened up the possibility of engineering sensors of quanta of different degrees of freedom. Quantum magnonics, which aims to control and read out quanta of collective spin excitations in magnetically-ordered systems, furthermore provides unique opportunities for advances in both the study of magnetism and the development of quantum technologies. Using a superconducting qubit as a quantum sensor, we report the detection of a single magnon in a millimeter-sized ferromagnetic crystal with a quantum efficiency of up to~$0.71$. The detection is based on the entanglement between a magnetostatic mode and the qubit, followed by a single-shot measurement of the qubit state. This proof-of-principle experiment establishes the single-photon detector counterpart for magnonics.

Field-orthogonal temporal mode analysis of optical fields is recently developed for a new framework of quantum information science. But so far, the exact profiles of the temporal modes are not known, which makes it difficult to achieve mode selection and de-multiplexing. Here, we report a novel method that measures directly the exact form of the temporal modes. This in turn enables us to make mode-orthogonal homodyne detection with mode-matched local oscillators. We apply the method to a pulse-pumped, specially engineered fiber parametric amplifier and demonstrate temporally multiplexed multi-dimensional quantum entanglement of continuous variables in telecom wavelength. The temporal mode characterization technique can be generalized to other pulse-excited systems to find their eigen modes for multiplexing in temporal domain.

It is of theoretical and experimental interest to engineer topological phases with very large topological invariants via periodic driving. As advocated by this work, such Floquet engineering can be elegantly achieved by the particle swarm optimization (PSO) technique from the swarm intelligence family. With the recognition that conventional gradient-based optimization approaches are not suitable for directly optimizing topological invariants as integers, the highly effective PSO route yields new promises in the search for exotic topological phases, requiring limited physical resource. Our results are especially timely in view of two important insights from literature: low-frequency driving may be beneficial in creating large topological invariants, but an open-ended low-frequency driving often leads to drastic fluctuations in the obtained topological invariants. Indeed, using a simple continuously driven Harper model with three quasi-energy bands, we show that the Floquet-band Chern numbers can enjoy many-fold increase compared with that using a simple harmonic driving of the same period, without demanding more energy cost of the driving field. It is also found that the resulting Floquet insulator bands are still well-gapped, with the maximized topological invariants in agreement with physical observations from Thouless pumping. The emergence of many edge modes under the open boundary condition is also consistent with the bulk-edge correspondence. Our results are expected to be highly useful towards the optimization of many different types of topological invariants in Floquet topological matter.

We propose an algorithm which combines the beneficial aspects of two different methods for studying finite-temperature quantum systems with tensor networks. One approach is the ancilla method, which gives high-precision results but scales poorly at low temperatures. The other method is the minimally entangled typical thermal state (METTS) sampling algorithm which scales better than the ancilla method at low temperatures and can be parallelized, but requires many samples to converge to a precise result. Our proposed hybrid of these two methods purifies physical sites in a small central spatial region with partner ancilla sites, sampling the remaining sites using the METTS algorithm. Observables measured within the purified cluster have much lower sample variance than in the METTS approach, while sampling the sites outside the cluster reduces their entanglement and the computational cost of the algorithm. The sampling steps of the algorithm remain straightforwardly parallelizable. The hybrid approach also solves an important technical issue with METTS that makes it difficult to benefit from quantum number conservation. By studying S=1 Heisenberg ladder systems, we find the hybrid method converges more quickly than both the ancilla and METTS algorithms at intermediate temperatures and for systems with higher entanglement.

Arrays of neutral-atom qubits in optical tweezers are a promising platform for quantum computation. Despite experimental progress, a major roadblock for realizing neutral atom quantum computation is the qubit initialization. Here we propose that supersymmetry---a theoretical framework developed in particle physics---can be used for ultra-high fidelity initialization of neutral-atom qubits. We show that a single atom can be deterministically prepared in the vibrational ground state of an optical tweezer by adiabatically extracting all excited atoms to a supersymmetric auxiliary tweezer with the post-selection measurement of its atomic number. The scheme works for both bosonic and fermionic atom qubits trapped in realistic Gaussian optical tweezers and may pave the way for realizing large scale quantum computation, simulation and information processing with neutral atoms.