We present a general framework for modifying quantum approximate optimization algorithms (QAOA) to solve constrained network flow problems. By exploiting an analogy between flow constraints and Gauss's law for electromagnetism, we design lattice quantum electrodynamics (QED) inspired mixing Hamiltonians that preserve flow constraints throughout the QAOA process. This results in an exponential reduction in the size of the configuration space that needs to be explored, which we show through numerical simulations, yields higher quality approximate solutions compared to the original QAOA routine. We outline a specific implementation for edge-disjoint path (EDP) problems related to traffic congestion minimization, numerically analyze the effect of initial state choice, and explore trade-offs between circuit complexity and qubit resources via a particle-vortex duality mapping. Comparing the effect of initial states reveals that starting with an ergodic (unbiased) superposition of solutions yields better performance than beginning with the mixer ground-state, suggesting a departure from the "short-cut to adiabaticity" mechanism often used to motivate QAOA.
The Quantum Approximate Optimization Algorithm (QAOA) requires that circuit parameters are determined that allow one to sample from high-quality solutions to combinatorial optimization problems. Such parameters can be obtained using either costly outer-loop optimization procedures and repeated calls to a quantum computer or, alternatively, via analytical means. In this work we demonstrate that if one knows the probability density function describing how the objective function of a problem is distributed, that the calculation of the expectation of such a problem Hamiltonian under a Grover-drive…
Quantum technology provides a ground-breaking methodology to tackle challenging computational issues in power systems, especially for Distributed Energy Resources (DERs) dominant cyber-physical systems that have been widely developed to promote energy sustainability. The systems' maximum power or data sections are essential for monitoring, operation, and control, while high computational effort is required. Quantum Approximate Optimization Algorithm (QAOA) provides a promising means to search for these sections by leveraging quantum resources. However, its performance highly relies on the crit…
We study the entanglement dynamics of strongly driven atoms off-resonantly coupled with cavity fields. We consider conditions characterized not only by the atom-field coupling but also by the atom-field detuning. By studying two different models within the framework of cavity QED, we show that the so-called atomic entanglement sudden death (ESD) always occurs if the atom-field coupling lager than the atom-field detuning, and is independent of the type of initial atomic state.
In this paper, we propose a scheme for the controlled teleportation of an arbitrary two-atom entangled state $|ϕ>_{12}=a|gg>_{12}+b|ge>_{12}+c|eg>_{12}+d|ee>_{12}$ in driven cavity QED. An arbitrary two-atom entangled state can be teleported perfectly with the help of the cooperation of the third side by constructing a three-atom GHZ entangled state as the controlled channel. This scheme does not involve apparent (or direct) Bell-state measurement and is insensitive to the cavity decay and the thermal field. The probability of the success in our scheme is 1.0.
Combinatorial optimization is an important application targeted by quantum computing. However, near-term hardware constraints make quantum algorithms unlikely to be competitive when compared to high-performing classical heuristics on large practical problems. One option to achieve advantages with near-term devices is to use them in combination with classical heuristics. In particular, we propose using quantum methods to sample from classically intractable distributions -- which is the most probable approach to attain a true provable quantum separation in the near-term -- which are used to solv…
Photon blockade is a dynamical quantum-nonlinear effect that occurs in driven systems with an anharmonic excitation ladder. For a single atom strongly coupled to an optical cavity, we show that driving the atom gives a decisively larger optical nonlinearity than driving the cavity. This enhances single-photon blockade and allows for the implementation of two-photon blockade where the absorption of two photons suppresses the absorption of further photons. As a signature, we report on three-photon antibunching with simultaneous two-photon bunching observed in the light emitted from the cavity. O…
We propose a class of quantum simulators for antiferromagnetic spin systems, based on coupled photonic cavities in presence of two-photon driving and dissipation. By modeling the coupling between the different cavities through a hopping term with negative amplitude, we solve numerically the quantum master equation governing the dynamics of the open system and determine its non-equilibrium steady state. Under suitable conditions, the steady state can be described in terms of the degenerate ground states of an antiferromagnetic Ising model. When the geometry of the cavity array is incommensurate…
We use the scattering matrix formalism to analyze photon blockade in coherently-driven CQED systems with a weak drive. By approximating the weak coherent drive by an input single- and two-photon Fock state, we reduce the computational complexity of the transmission and the two-photon correlation function from exponential to polynomial in the number of emitters. This enables us to easily analyze cavity-based systems containing $\sim$50 quantum emitters with modest computational resources. Using this approach we study the coherence statistics of polaritonic photon blockade while increasing the n…
We theoretically study the quantum interference induced photon blockade phenomenon in atom cavity QED system, where the destructive interference between two different transition pathways prohibits the two-photon excitation. Here, we first explore the single atom cavity QED system via an atom or cavity drive. We show that the cavity-driven case will lead to the quantum interference induced photon blockade under a specific condition, but the atom driven case can't result in such interference induced photon blockade. Then, we investigate the two atoms case, and find that an additional transition …
We perform Floquet spectroscopy in a GaAs double quantum dot system coupled to a high-impedance superconducting resonator. By applying microwave induced consecutive passages under a double resonance condition, we observe novel Landau-Zener-Stückelberg-Majorana interference patterns that stem from a cavity-assisted interference pattern modified by the depletion of the ground state. Our experimental results reveal the stationary state behavior of a strongly driven two-level system, and are consistent with the simulations based on our theoretical model. This study provides an excellent platform f…
We consider a superconducting charge qubit coupled to distinct orthogonal electromagnetic field modes belonging to a coplanar wave guide and a microstrip transmission line resonators. This architecture allows the simultaneous implementation of a Jaynes-Cummings and anti-Jaynes-Cummings dynamics, a resonant method for generating mesoscopic qubit-field superpositions and for field-state reconstruction. Furthermore, we utilize this setup to propose a field measurement technique that is, in principle, robust to qubit dephasing and field relaxation due to a fast pre-measurement.
We propose a realizable circuit QED architecture for engineering states of a superconducting resonator off-resonantly coupled to an ancillary superconducting qubit. The qubit-resonator dispersive interaction together with a microwave drive applied to the qubit gives rise to a Kerr resonator with two-photon driving that enables us to efficiently engineer the quantum state of the resonator such as generation of the Schrodinger cat states for resonator-based universal quantum computation. Moreover, the presented architecture is easily scalable for solving optimization problem mapped into the Isin…
Strongly driven cavity quantum electrodynamical-optomechanical hybrid system
Laboratory of Photonics and Quantum Measurements (LPQM), Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院光子与量子测量实验室）；Center for Quantum Science and Engineering, EPFL（洛桑联邦理工学院量子科学与工程中心）
We introduce a circuit-QED architecture combining fixed-frequency qubits and microwave-driven couplers. In the appropriate frame, the drive parameters appear as tunable knobs enabling selective two-qubit coupling and coherent-error suppression. We moreover introduce a set of controlled-phase gates based on drive-amplitude and drive-frequency modulation. We develop a theoretical framework based on Floquet theory to model microwave-activated interactions with time-dependent drive parameters, which we also use for pulse shaping. We perform numerical simulations of the gate fidelity for realistic …
Photon Anomalous Blockade in Waveguide Cavity QED with Atomic Mirrors
School of integrated circuits, Tsinghua University（清华大学集成电路学院）；Beijing Automation Control Equipment Institute（北京自动化控制设备研究所）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）
By driving a dispersively coupled qubit-resonator system, we realize an "impedance-matched" $Λ$ system that has two identical radiative decay rates from the top level and interacts with a semi-infinite waveguide. It has been predicted that a photon input from the waveguide deterministically induces a Raman transition in the system and switches its electronic state. We confirm this through microwave response to a continuous probe field, observing near-perfect ($99.7\%$) extinction of the reflection and highly efficient ($74\%$) frequency down-conversion. These proof-of-principle results lead to…
We study an interferometric method for the measurement of the statistics of work performed on a driven quantum system, which has been put forward recently [Dorner et al., Phys. Rev. Lett. 110 230601 (2013), Mazzola et al., Phys. Rev. Lett. 110 230602 (2013)]. The method allows replacing two projective measurements of the energy of the driven system with qubit tomography of an ancilla that is appropriately coupled to it. We highlight that this method could be employed to obtain the work statistics of closed as well as open driven system, even in the strongly dissipative regime. We then illustra…
Scaling law for optimal excitation storage and superradiant release in waveguide QED systems
National Taiwan University（台湾大学）；Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）；Center for Quantum Science and Engineering, National Taiwan University（台湾大学量子科学与工程中心）；Trapped-Ion Quantum Computing Laboratory, Hon Hai Research Institute（鸿海研究院会离子阱量子计算实验室）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）；Department of Physics, National Central University（中央大学物理系）
A common experimental setup in cavity quantum electrodynamics (QED) consists of a single two-level atom interacting with a single mode of the electromagnetic field inside an optical cavity. The cavity is externally driven and the output is continuously monitored via homodyne measurements. We derive formulas for the optimal rates at which these measurements provide information about (i) the quantum state of the system composed of atom and electromagnetic field, and (ii) the coupling strength between atom and field. We find that the two information rates are anticorrelated.
We present exact numerical solutions of the damped-driven Jaynes--Cummings model adapted to describe absorptive optical bistability in the limit of a few atoms strongly coupled to a high-finesse resonator. We show that the simplifying semiclassical result for many physical quantities of interest is well reproduced by the quantum model including even with only a few atoms in the strongly coupled system. Nontrivial atom-field quantum cross-correlations show up in the strong-driving limit.
We investigate steady state entanglement in an open quantum system, specifically a single atom in a driven optical cavity with cavity loss and spontaneous emission. The system reaches a steady pure state when driven very weakly. Under these conditions, there is an optimal value for atom-field coupling to maximize entanglement, as larger coupling favors a loss port due to the cavity enhanced spontaneous emission. We address ways to implement measurements of entanglement witnesses and find that normalized cross-correlation functions are indicators of the entanglement in the system. The magnitude…
We study the properties of an array of QED-cavities coupled by nonlinear elements in the presence of photon leakage and driven by a coherent source. The main effect of the nonlinear couplings is to provide an effective cross-Kerr interaction between nearest-neighbor cavities. Additionally, correlated photon hopping between neighboring cavities arises. We provide a detailed mean-field analysis of the steady-state phase diagram as a function of the system parameters, the leakage, and the external driving, and show the emergence of a number of different quantum phases. A photon crystal associated…
We present a method to engineer the unitary charge conjugation operator, as given by quantum field theory, in the highly controlled context of quantum optics, thus allowing one to simulate the creation of charged particles with well-defined momenta simultaneously with their respective antiparticles. Our method relies on trapped ions driven by a laser field and interacting with a single mode of a light field in a high Q cavity.
It is shown how to implement quantum feedback and probabilistic error correction in an open quantum system consisting of a single atom, with ground- and excited-state Zeeman structure, in a driven two-mode optical cavity. The ground state superposition is manipulated and controlled through conditional measurements and external fields, which shield the coherence and correct quantum errors. Modeling of an experimentally realistic situation demonstrates the robustness of the proposal for realization in the laboratory.
We measure the quantum speed of the state evolution of the field in a weakly-driven optical cavity QED system. To this end, the mode of the electromagnetic field is considered as a quantum system of interest with a preferential coupling to a tunable environment: the atoms. By controlling the environment, i.e., changing the number of atoms coupled to the optical cavity mode, an environment assisted speed-up is realized: the quantum speed of the state re-population in the optical cavity increases with the coupling strength between the optical cavity mode and this non-Markovian environment (the n…
We investigate the quantum fluctuations of a single atom in a weakly driven cavity, where the center of mass motion of the atom is quantized in one dimension. We present analytic results for the second order intensity correlation function $g^{(2)}(τ)$ and the intensity-field correlation function $h_θ(τ)$, for both transmitted and fluorescent light for weak driving fields. We find that the coupling of the center of mass motion to the intracavity field mode can be deleterious to nonclassical effects in photon statistics; less so for the intensity-field correlations.
Chip-based cavity quantum electrodynamics (QED) devices consisting of a self-assembled InAs quantum dot (QD) coupled to a high quality factor GaAs microdisk cavity are coherently probed through their optical channel using a fiber taper waveguide. We highlight one particularly important aspect of this all-fiber measurement setup, which is the accuracy to which the optical coupling level and optical losses are known relative to typical free-space excitation techniques. This allows for precise knowledge of the intracavity photon number and measurement of absolute transmitted and reflected signals…
We utilize high-bandwidth phase quadrature homodyne measurement of the light transmitted through a Fabry-Perot cavity, driven strongly and on resonance, to detect excess phase noise induced by a single intracavity atom. We analyze the correlation properties and driving-strength dependence of the atom-induced phase noise to establish that it corresponds to the long-predicted phenomenon of spontaneous dressed-state polarization. Our experiment thus provides a demonstration of cavity quantum electrodynamics in the strong driving regime, in which one atom interacts strongly with a many-photon cavi…
We present a numerical study comparing semiclassical and quantum models of a damped, strongly interacting cavity QED system composed of a single two-level atom interacting with a single quantized cavity mode driven externally by a tunable monochromatic field. We compute the steady state transmission spectrum of the coupled system under each model and show that in the strong coupling regime, the two models yield starkly different results. The fully quantum mechanical model of the system correctly yields the expected multiphoton transmission spectra while the semiclassical approach results in a …
Motivated by recent "circuit QED" experiments we investigate the noise properties of coherently driven nonlinear resonators. By using Josephson junctions in superconducting circuits, strong nonlinearities can be engineered, which lead to the appearance of pronounced effects already for a low number of photons in the resonator. Based on a master equation approach we determine the emission spectrum and observe for typical circuit QED parameters, in addition to the primary Raman-type peaks, second-order peaks. These peaks describe higher harmonics in the slow noise-induced fluctuations of the osc…
Optical cavity QED provides a platform with which to explore quantum many-body physics in driven-dissipative systems. Single-mode cavities provide strong, infinite-range photon-mediated interactions among intracavity atoms. However, these global all-to-all couplings are limiting from the perspective of exploring quantum many-body physics beyond the mean-field approximation. The present work demonstrates that local couplings can be created using multimode cavity QED. This is established through measurements of the threshold of a superradiant, self-organization phase transition versus atomic pos…
Geometric phases are well known in classical electromagnetism and quantum mechanics since the early works of Pantcharatnam and Berry. Their origin relies on the geometric nature of state spaces and has been studied in many different systems such as spins, polarized light and atomic physics. Recent works have explored their application in interferometry and quantum computation. Earlier works suggest how to observe these phases in single quantum systems adiabatically driven by external classical devices or sources, where, by classical, we mean any system whose state does not change considerably …
Generation of quasi-particle--hole pairs in gapped graphene monolayers in the combined field of two counterpropagating light waves is studied. The process represents an analogue of electron-positron pair production from the QED vacuum by the Breit-Wheeler effect. We show, however, that the two-dimensional structure of graphene causes some striking differences between both scenarios. In particular, contrary to the QED case, it allows for non-zero pair production rates at the energy threshold when the Breit-Wheeler reaction proceeds nonlinearly with absorption of three photons.
Multi-qubit parity measurements are essential to quantum error correction. Current realizations of these measurements often rely on ancilla qubits, a method that is sensitive to faulty two-qubit gates and which requires significant experimental overhead. We propose a hardware-efficient multi-qubit parity measurement exploiting the bifurcation dynamics of a parametrically driven nonlinear oscillator. This approach takes advantage of the resonator's parametric oscillation threshold which is a function of the joint parity of dispersively coupled qubits, leading to high-amplitude oscillations for …
We examine the entanglement between two qubits, supposed to be remotely located and driven by independent quantized optical fields. No interaction is allowed between the qubits, but their degree of entanglement changes as a function of time. We report a collapse and revival of entanglement that is similar to the collapse and revival of single-atom properties in cavity QED.
Evaluating the Impact of Urban Road Topology on Quantum Approximate Optimization: A Comparative Study of Planned and Organic Networks in Islamabad and Karachi(Pakistan)
A single three-level atom driven by a longitudinal mode of a high-Q cavity is used to implement two-qubit quantum phase gates for the intracavity field. The two qubits are associated to the zero-and one-photon Fock states of each of the two opposite circular polarization states of the field. The three-level atom yields the conditional phase gate provided the two polarization states and the atom interact in a $V$-type configuration and the two photon resonance condition is fulfilled. Microwave and optical implementations are discussed with gate fidelities being evaluated against several decoher…
The driven-damped Jaynes-Cummings model in the regime of strong coupling is found to exhibit a coexistence between the quantum photon blockaded state and a quasi-coherent bright state. We characterize the slow time scales and the basin of attraction of these metastable states using full quantum simulations. This form of bistability can be useful for implementing a qubit readout scheme that does not require additional circuit elements. We propose a coherent control sequence that makes use of a simple linear chirp of drive amplitude and frequency as well as qubit frequency. By optimizing the par…
