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Deterministically achieving on-chip photon storage and retrieval is a fundamental challenge for integrated photonics. Moreover, this requirement is increasingly urgent as photon storage and retrieval is crucial to realize truly scalable room-temperature quantum computing. However, most of existing quantum memories integrated on chips must either work at cryogenic temperature or else are strongly coupled with the environment, which hugely reduces the efficiency. Here, we propose an on-chip room-temperature quantum memory comprising three coupled microcavities, which presents an ideal dark state decoupled by a waveguide, thereby allowing on-demand photon storage and retrieval with high efficiency and high fidelity simultaneously. Furthermore, we demonstrate that the single-photon temporal duration can be increased or decreased by a factor of 103, thereby enabling many crucial quantum applications. Our error-robust approach highlights the potential for a solid-state photonic molecule for use as on-chip quantum memory and for optical quantum computing.

We propose a scheme to generate spin cat states, i.e., superpositions of maximally separated quasiclassical states on a single high-dimensional nuclear spin in a solid-state device. We exploit a strong quadrupolar nonlinearity to drive the nucleus significantly faster than usual gate sequences, achieving collapses and revivals two orders of magnitude faster than the dephasing timescale. Furthermore, these states are engineered without entanglement with an ancilla, hence, are robust against error propagation. With our multitone control, we can realize arbitrary high-spin rotations within an experimentally feasible regime, as well as transform a spin coherent state to a spin cat state using only phase modulation, opening the possibility of storing and manipulating high-fidelity cat states.

Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate duration and gate error rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-ion chain by a quantum master equation (QME). The QME incorporates the single-ion two-photon effective Rabi frequency, Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing beams, and an imperfect initial motional ground state, with no fitting parameters, whereas state-of-the-art methods are oblivious to these effects in the gate design procedure. We employ global optimization to design pulse sequences for achieving a robust rapid two-qubit gate for a simulated chain of seven trapped ^{171}Yb^{+} ions by optimizing over numerically integrated QME solutions. Here, robust means resilient against slow drift of motional frequencies, and rapid means gate execution where the effective Rabi frequency is comparable to the detuning of the laser from the ion's bare electronic transition. Our robust quantum control delivers rapid high-quality two-qubit gates in long ion chains, enabling scalable quantum computing with trapped ions.

Efficient switching and routing of photons of different wavelengths is desirable for future quantum information applications. To this end the authors demonstrate interference in a multimode system between two optomechanically induced transparency processes in a diamond on-chip cavity.

Dynamic topological phenomena remain challenging to be probed experimentally. Here, Wang et al. theoretically characterize and experimentally detect dynamical skyrmions in parity‐time‐symmetric non‐unitary quench dynamics in single‐photon discrete‐time quantum walks.

Constructing all extreme instances of the set of completely positive trace-preserving (CPTP) maps, i.e., quantum channels, is a challenging and valuable open problem in quantum information theory. Here we introduce a systematic approach that, despite the lack of knowledge about the full parametrization of the set of CPTP maps on arbitrary Hilbert-spaced dimension, enables us to construct exactly those extreme channels that are covariant with respect to a finite discrete group or a compact connected Lie group. Innovative labeling of quantum channels by group representations enables us to identify the subset of group-covariant channels whose elements are group-covariant generalized-extreme channels. Furthermore, we exploit essentials of group representation theory to introduce equivalence classes for the labels and also partition the set of group-covariant channels. As a result, we show that it is enough to construct one representative of each partition. We construct Kraus operators for group-covariant generalized-extreme channels by solving systems of linear and quadratic equations for all candidates satisfying the necessary condition for being group-covariant generalized-extreme channels. Deciding whether these constructed instances are extreme or quasiextreme is accomplished by solving a system of linear equations. Proper labeling and partitioning the set of group-covariant channels leads to a novel systematic, algorithmic approach for constructing the entire subset of group-covariant extreme channels. We formalize the problem of constructing and classifying group-covariant generalized extreme channels, thereby yielding an algorithmic approach to solving, which we express as pseudocode. To illustrate the application and value of our method, we solve for explicit examples of group-covariant extreme channels. With unbounded computational resources to execute our algorithm, our method always delivers a description of an extreme channel for any finite-dimensional Hilbert space and furthermore guarantees a description of a group-covariant extreme channel for any dimension and for any finite-discrete or compact connected Lie group if such an extreme channel exists.

The system of linear equations problem (SLEP) is specified by a complex invertible matrix A, the condition number κ of A, a vector b, a Hermitian matrix M, and an accuracy ε, and the task is to estimate x^{†}Mx, where x is the solution vector to the equation Ax=b. We aim to establish a lower bound on the complexity of the end-to-end quantum algorithms for SLEP with respect to ε, and devise a quantum algorithm that saturates this bound. To make lower bounds attainable, we consider query complexity in the setting in which a block encoding of M is given, i.e., a unitary black box U_{M} that contains M/α as a block for some α∈R^{+}. We show, by constructing a quantum algorithm and deriving a lower bound, that the quantum query complexity for SLEP in this setting is Θ(α/ε). Our lower bound is established by reducing the problem of estimating the mean of a black box function to SLEP. Our Θ(α/ε) result tightens and proves the common assertion of polynomial accuracy dependence [poly(1/ε)] for SLEP without making any complexity-theoretic assumptions, and shows that improvement beyond linear dependence on accuracy is not possible if M is provided via block encoding.

We devise a quasilinear quantum algorithm for generating an approximation for the ground state of a quantum field theory (QFT). Our quantum algorithm delivers a superquadratic speedup over the state-of-the-art quantum algorithm for ground-state generation, overcomes the ground-state-generation bottleneck of the prior approach and is optimal up to a polylogarithmic factor. Specifically, we establish two quantum algorithms—Fourier-based and wavelet-based—to generate the ground state of a free massive scalar bosonic QFT with gate complexity quasilinear in the number of discretized QFT modes. The Fourier-based algorithm is limited to translationally invariant QFTs. Numerical simulations show that the wavelet-based algorithm successfully yields the ground state for a QFT with broken translational invariance. Furthermore, the cost of preparing particle excitations in the wavelet approach is independent of the energy scale. Our algorithms require a routine for generating one-dimensional Gaussian (1DG) states. We replace the standard method for 1DG-state generation, which requires the quantum computer to perform lots of costly arithmetic, with a novel method based on inequality testing that significantly reduces the need for arithmetic. Our method for 1DG-state generation is generic and could be extended to preparing states whose amplitudes can be computed on the fly by a quantum computer.

A multiphoton collective phase is a multiphoton-scattering feature that cannot be reduced to a sequence of two-photon scattering events, and the three-photon “triad phase” is the smallest nontrivial example. Observing a higher-order collective phase is experimentally challenging, and only triad and four-photon tetrad collective phases have been observed. We introduce a scheme to make higher-order multiphoton collective-phase observations feasible by designing a sparse interferometer, which significantly reduces complexity compared with the current best scheme for observing a multiphoton collective phase. Specifically, our scheme reduces the optical depth from logarithmic to constant and reduces the number of beam splitters from O(nlogn) to linear scaling with respect to the collective-phase order n. As constant depth reduces loss and dispersion to a fixed rate regardless of collective-phase order, a major obstacle to observing large-scale collective phases is removed.

Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. Compared to qubit, qudit provides a larger state space to store and process information, and thus can provide reduction of the circuit complexity, simplification of the experimental setup and enhancement of the algorithm efficiency. This review provides an overview of qudit-based quantum computing covering a variety of topics ranging from circuit building, algorithm design, to experimental methods. We first discuss the qudit gate universality and a variety of qudit gates including the pi/8 gate, the SWAP gate, and the multi-level controlled-gate. We then present the qudit version of several representative quantum algorithms including the Deutsch-Jozsa algorithm, the quantum Fourier transform, and the phase estimation algorithm. Finally we discuss various physical realizations for qudit computation such as the photonic platform, iron trap, and nuclear magnetic resonance.

Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of particles. In an experiment with n particles the expressions we derive contain a term for each partition of the integer n; Gamas's theorem is used to determine which of these terms are automatically zero based on the pairwise level of distinguishability between particles. Most sampling schemes (such as “boson sampling”) are limited to completely indistinguishable particles; our paper aids in the understanding of systems where an arbitrary level of distinguishability is permitted. As an application of our paper we introduce a sampling scheme with partially-distinguishable fermions, which we call “generalized fermion sampling”.

Quantum teleportation is a primitive in several important applications, including quantum communication, quantum computation, error correction, and quantum networks. In this paper, we propose an optimal test for the performance of continuous-variable (CV) quantum teleportation in terms of the energy-constrained channel fidelity between ideal CV teleportation and its experimental implementation. Work prior to ours considered suboptimal tests of the performance of CV teleportation, focusing instead on its performance for particular states, such as ensembles of coherent states, squeezed states, cat states, etc. Here, we prove that the optimal state for testing CV teleportation is an entangled superposition of twin Fock states. We establish this result by reducing the problem of estimating the energy-constrained channel fidelity between ideal CV teleportation and its experimental approximation to a quadratic program and solving it. As an additional result, we obtain an analytical solution to the energy-constrained diamond distance between a photodetector and its experimental approximation. These results are relevant for experiments that make use of CV teleportation and photodetectors.

Quantum interferometry and quantum information processing have been proposed for Bose-Einstein condensates (BECs), but BECs are described in complicated ways such as using quantum field theory or using a nonlinear differential equation. Nonlinear quantum mechanics does not mesh well with the superposition principle at the heart of interferometry and quantum information processing but could be compatible. Thus, we develop a rigorous foundation for quantum gates, obtained by solving the equation for evolution, and then we employ this foundation, combined with quantum-control techniques and appropriate state-sampling techniques, to devise feasible nonlinear Hadamard gates and thereby feasible, i.e., high-contrast, nonlinear Ramsey interferometry. Our approach to BEC interferometry and quantum logic shifts the paradigm by enlarging to the case of nonlinear quantum mechanics, which we apply to the cases of BEC interferometry and quantum information processing.

In quantum mechanics, physical states are represented by rays in Hilbert space H, which is a vector space imbued by an inner product 〈|〉, whose physical meaning arises as the overlap 〈ϕ|ψ〉 for |ψ〉 a pure state (description of preparation) and 〈ϕ| a projective measurement. However, current quantum theory does not formally address the consequences of a changing inner product during the interval between preparation and measurement. We establish a theoretical framework for such a changing inner product, which we show is consistent with standard quantum mechanics. Furthermore, we show that this change is described by a quantum operation, which is tomographically observable, and we elucidate how our result is strongly related to the exploding topic of PT-symmetric quantum mechanics. We explain how to realize experimentally a changing inner product for a qubit in terms of a qutrit protocol with a unitary channel.

Abstract We experimentally demonstrate coherent amplification of probe field in a tripod-type atoms driven by strong coupling, signal and weak probe fields. We suppress linear and nonlinear atomic absorptions for resonant and near resonant probe via double electromagnetically induced transparency (DEIT). Combining these advantages of suppressed absorption along with temperature- or atomic-density-controlled transfer of population(ToP) between hyperfine ground states, we can induce near-resonant amplification of probe through stimulated Raman scattering(SRS) pumped by low-intensity signal field. The increased population difference of initial and final states of SRS due to increased ToP rate, together with reduced absorption at the second EIT window in an optically thick Cesium vapor, gives rise to highly effective coherent amplification.

Discord, originally notable as a signature of bipartite quantum correlation, in fact can be nonzero classically, i.e. arising from noisy measurements by one of the two parties. Here we redefine classical discord to quantify channel distortion, in contrast to the previous restriction of classical discord to a state, and we then show a monotonic relationship between classical (channel) discord and channel distortion. We show that classical discord is equivalent to (doubly stochastic) channel distortion by numerically discovering a monotonic relation between discord and total-variation distance for a bipartite protocol with one party having a noiseless channel and the other party having a noisy channel. Our numerical method includes randomly generating doubly stochastic matrices for noisy channels and averaging over a uniform measure of input messages. Connecting discord with distortion establishes discord as a signature of classical, not quantum, channel distortion.

A fully homomorphic encryption system hides data from unauthorized parties while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more powerful server without revealing their inputs, a fully homomorphic cryptosystem can be used as a building block in the construction of a number of cryptographic functionalities. Designing such a scheme remained an open problem until 2009, decades after the idea was first conceived, and the past few years have seen the generalization of this functionality to the world of quantum machines. Quantum schemes prior to the one implemented here were able to replicate some features in particular use cases often associated with homomorphic encryption but lacked other crucial properties, for example, relying on continual interaction to perform a computation or leaking information about the encrypted data. We present the first experimental realization of a quantum fully homomorphic encryption scheme. To demonstrate the versatility of a a quantum fully homomorphic encryption scheme, we further present a toy two-party secure computation task enabled by our scheme.

Nonclassical interference of photons lies at the heart of optical quantum information processing. Here, we exploit tunable distinguishability to reveal the full spectrum of multiphoton nonclassical interference. We investigate this in theory and experiment by controlling the delay times of three photons injected into an integrated interferometric network. We derive the entire coincidence landscape and identify transition matrix immanants as ideally suited functions to describe the generalized case of input photons with arbitrary distinguishability. We introduce a compact description by utilizing a natural basis that decouples the input state from the interferometric network, thereby providing a useful tool for even larger photon numbers.