We describe an electrothermal model for the turn-on dynamics of superconducting nanowire single-photon detectors (SNSPDs). By extracting a scaling law from a well-known electrothermal model of SNSPDs, we show that the rise time of the readout signal encodes the photon number as well as the length of the nanowire with scaling $t_{\mathrm{rise}}\propto \sqrt{\ell /n}$. We show that these results hold regardless of the exact form of the thermal effects. This explains how SNSPDs have an inherent photon-number-resolving capability. We experimentally verify the photon-number dependence by collecting waveforms for different photon numbers, rescaling them according to our predicted relation, and performing statistical analysis that shows that there is no statistical significance between the rescaled curves. Additionally, we use our predicted dependence of the rise time on the detector length to provide further insight into previous theoretical work by other authors. By assuming a specific thermal model, we predict that rise time will scale with the bias current, $t_{\mathrm{rise}}\propto \sqrt{1/I_b}$. We fit this model to experimental data and find that $t_{\mathrm{rise}}\propto 1/(n^{0.52\pm 0.03}{I}_b^{0.63\pm 0.02})$, which suggests that further work is needed to better understand the bias-current dependence. This work gives insights into the nonequilibrium dynamics of thin superconducting films exposed to electromagnetic radiation.

Random numbers are a fundamental ingredient in fields such as simulation, modeling, and cryptography. Good random numbers should be independent and uniformly distributed. Moreover, for cryptographic applications, they should also be unpredictable. A fundamental feature of quantum theory is that certain measurement outcomes are intrinsically random and unpredictable. These can be harnessed to provide unconditionally secure random numbers. We demonstrate a real-time self-testing source-independent quantum random-number generator (SI QRNG) that uses squeezed light as a source. We generate secure random numbers by measuring the quadratures of the electromagnetic field without making any assumptions about the source other than an energy bound; only the detection device is trusted. We use homodyne detection to measure alternately the $\hat{Q}$ and $\hat{P}$ conjugate quadratures of our source. $\hat{P}$ measurements allow us to estimate a bound on any classical or quantum side information that a malicious eavesdropper may obtain. This bound gives the minimum number of secure bits we can extract from the $\hat{Q}$ measurement. We discuss the performance of different estimators for this bound. We operate this QRNG with a squeezed-state source and compare its performance with a thermal-state source. This is a demonstration of a QRNG using a squeezed state, as well as an implementation of real-time quadrature switching for a SI QRNG.

Nonreciprocal devices that allow unidirectional wave propagation are indispensable in many scientific fields, including, for example, optics, acoustics, electronics, and thermodynamics. Here, we propose to realize the nonreciprocal transmission of a microwave field in a two-cavity magnonics system consisting of two microwave cavities and a yttrium iron garnet (YIG) sphere, which is placed in one of them. We discover that magnon Kerr nonlinearity leads to the occurrence of magnon bistability and different magnonic responses for the forward and backward propagation of a microwave field. The different magnonic responses play a crucial role in the nonreciprocal transmission, which essentially breaks the space-reversal symmetry of transmission of the microwave field. More importantly, by adjusting the external bias magnetic field, which determines the frequency of the magnon, we can obtain a variable isolation of the microwave field or even its transmission in only one direction, which may be utilized to achieve light diodes. In addition, by increasing the strength of a microwave source applied to drive the magnon mode, stronger nonreciprocal transmission can be observed. These results may open a route to exploiting various nonreciprocal effects in cavity magnonics systems.

Quantum memories for light are important components for future long-distance quantum networks. We present on-chip quantum storage of telecommunication-band light at the single-photon level in an ensemble of erbium-167 ions in an yttrium orthosilicate photonic crystal nanobeam resonator. Storage times of up to $10\mu \mathrm{s}$ are demonstrated with an all-optical atomic-frequency-comb protocol in a dilution refrigerator under a magnetic field of 380 mT. We show this quantum-storage platform to have high bandwidth, high fidelity, and multimode capacity, and we outline a path toward an efficient erbium-167 quantum memory for light.

The sending-or-not-sending protocol of the twin-field quantum key distribution (TFQKD) has its advantage of unconditional security under any coherent attack and fault tolerance to a large misalignment error. Here, we consider the complete finite-key effects for the protocol and we calculate the secure key rate with a fixed security coefficient. The numerical simulation shows that the protocol with a typical finite number of pulses in practice can produce an unconditional secure final key under general attack, including all coherent attacks. It can exceed the secure distance of 500 km in a typical finite number of pulses in practice even with a large misalignment error.

Nuclear spins nearby nitrogen-vacancy (N-$V$) centers in diamond are excellent quantum memory for quantum computing and quantum sensing, but are difficult to initialize due to their weak interactions with the environment. Here, we propose and demonstrate a magnetic-field-independent, deterministic, and highly efficient polarization scheme by introducing chopped laser pulses into the double-resonance initialization method. With this method, we demonstrate the initialization of a single-nuclear-spin system approaching $98.1\mathrm{\%}$ and a ${}^{14}\mathrm{N}{–}^{13}\mathrm{C}$ double-nuclear-spin system approaching $96.8\mathrm{\%}$ at room temperature. The initialization is limited by a nuclear-spin depolarization effect due to chopped laser excitation. Our approach could be extended to N-$V$ systems with more nuclear spins and would be a useful tool in future applications such as nano-magnetic resonance imaging and single-cell NMR.

The information-theoretic security promised by quantum key distribution (QKD) holds as long as the assumptions in the theoretical model match the parameters in the physical implementation. The superlinear behavior of sensitive single-photon detectors represents one such mismatch and can pave the way to powerful attacks hindering the security of QKD systems, a prominent example being the after-gate attack. A long-standing tenet is that trapped carriers causing delayed detection can help mitigate this attack, but despite intensive scrutiny, it remains largely unproven. Here we approach this problem from a physical perspective and find evidence to support a detector’s secure response. We experimentally investigate two different carrier-trapping mechanisms causing delayed detection in fast-gated semiconductor avalanche photodiodes, one arising from the multiplication layer and the other arising from the heterojunction interface between absorption and charge layers. The release of trapped carriers increases the quantum bit error rate measured under the after-gate attack above the typical QKD security threshold, thus favoring the detector’s inherent security. This represents a significant step to avert quantum hacking of QKD systems.

Quantum key distribution (QKD) based on coherent states is well known for its implementation simplicity, but it suffers from loss-dependent attacks based on optimal unambiguous state discrimination. Crucially, previous research has suggested that coherent-state QKD is limited to short distances, typically below 100 km, assuming standard optical fiber loss and system parameters. In this work, we propose a six-coherent-state phase-encoding QKD protocol that is able to tolerate the total loss of up to 38 dB, assuming realistic system parameters, and up to 56 dB loss, assuming zero noise. The security of the protocol is calculated using a recently developed security proof technique based on semidefinite programming, which assumes only the inner-product information of the encoded coherent states, the expected statistics, and that the measurement is basis independent. Our results thus suggest that coherent-state QKD could be a promising candidate for high-speed provably secure QKD.

Magnetfree circulators are crucial devices to enable full-duplex communications with the goal of enhancing the spectral efficiency of wireless radios compared to currently deployed half-duplex systems. Nevertheless, implementations proposed to date at radio- and millimeter-wave frequencies have been based on spatiotemporally modulating a discrete number of nonlinear elements, such as varactors or switched capacitors, which, despite achieving strong nonreciprocity, suffer from spurious emission in adjacent channels and limited power handling. These problems jeopardize the practical use of these components in many applications, including wireless communications and quantum computing, and make them less attractive compared to harmonicfree magnetic devices. We address these problems by introducing N-way circulators, which consist of N spatiotemporally modulated angular-momentum (STM AM) biased units connected either in series or in parallel and modulated through a rotating phase pattern. We show that these circuits, for a sufficiently large N, effectively impart an overall linear and continuous angular-momentum bias, which significantly reduces spurious emission and increases the overall power handling. This, in turn, strengthens the argument of magnetless circulators compared to their magnetic counterparts, and opens exciting venues to address the realistic needs of practical systems.

To construct global quantum communication networks, reliable free-space quantum key distribution is essential, but there has appeared a bottleneck severely hindering practical implementation, i.e., background noise. Rather than questing for filters closer to the ultimate performance, we seek a preferable solution from continuous-variable techniques employing coherent detection. In this regard, we investigate the dependence of the performance of continuous-variable quantum key distribution on background noise; the background noise is quantified and experimentally verified. The results indicate effective resistance against background noise. This characteristic demonstrates the feasibility of all-day free-space quantum communication using coherent detection, thus offering an alternative candidate for building networks.

When a signal is injected in a parametric oscillator close enough to its resonance, the oscillator frequency and phase are locked to those of the injected signal. Here we demonstrate two frequency-locking schemes using a Josephson mixer in the parametric down-conversion regime, pumped beyond the parametric oscillation threshold. The circuit then emits radiation out of two spectrally and spatially separated resonators at frequencies determined by the locking schemes that we choose. When we inject the signal close to a resonance, it locks the oscillator emission to the signal frequency by injection locking. When we inject the signal close to the difference of resonances, it locks the oscillator emission by parametric locking. We compare both schemes and investigate the dependence of the parametric locking range on the pump and the injected-signal power. Our results can be interpreted using Adler’s theory for lasers, which provides a link between laser physics and superconducting circuits that could enable better understanding of pumped circuits for quantum-information applications such as error correction, circulators, and photon-number detectors.

We investigate theoretically and experimentally the efficient control of the light spectrum in a fiber-loop circuit with two incorporated phase modulators (PMs). By varying the modulation phases in the PMs, photonic gauge potentials can be introduced in the loop, enabling full control of spectrum shift and band width. The spectrum evolution also depends rigorously on the resonant modulation condition, which suggests that the time delay of light in one circulation equals integer multiples of the modulation period such that the gauge potentials remain constant in distinct circulations. As the two PMs possess the same gauge potentials under resonant conditions, a 50-GHz frequency shift and three-fold band expansion are experimentally realized. For the out-of-phase modulation under resonant conditions, we also achieve the frequency analogue of perfect imaging for arbitrarily input spectra. As the resonant condition is broken, both the spectrum shift and band width are dramatically suppressed. This study may find potential applications in the spectrum management for both optical communications and signal processing.

High-fidelity quantum gates are essential for large-scale quantum computation, which can naturally be realized in a noise-resilient way. Geometric manipulation and decoherence-free subspace encoding are promising ways toward robust quantum computation. Here, by combining the advantages of both strategies, we propose and experimentally realize universal holonomic quantum gates in both a single-loop scheme and a composite scheme, based on nonadiabatic and non-Abelian geometric phases, in a decoherence-free subspace with nuclear magnetic resonance. Our experiment uses only two-body resonant spin-spin interactions and thus is experimental friendly. In particular, we also experimentally verify that the composite scheme is more robust against the pulse errors than the single-loop scheme. Therefore, our experiment provides a promising way toward faithful and robust geometric quantum manipulation.

Efficient generation of single photons on demand at a high repetition rate is a key to the practical realization of quantum-communication networks and optical quantum computations. Color centers in diamond and related wide-band-gap semiconductors are considered to be the most promising candidates for building such single-photon sources due to their outstanding emission properties at room temperature. However, efficient electrical excitation of color centers in most materials remains a challenge due to the inability to create a high density of free carriers. We predict a superinjection effect in diamond p-i-n diodes. By employing a comprehensive theoretical approach, we numerically demonstrate that one can overcome the doping problem in diamond and inject four orders of magnitude more electrons into the i region of the diamond p-i-n diode than the doping of the n region allows. This high density of free electrons can be efficiently used to boost the single-photon electroluminescence process and enhance the brightness of the diamond single-photon source by more than three orders of magnitude. Moreover, we show that such a high single-photon emission rate can be achieved at exceptionally low injection current densities of only $0.001\mathrm{A/m}{\mathrm{m}}^2$, which creates the backbone for the development of low-power and cost-efficient diamond quantum optoelectronic devices for quantum information technologies.

We demonstrate the structural imaging of magnetostatic spin-wave modes hosted in a millimeter-sized ferromagnetic sphere. Unlike for low-dimensional magnetic materials, there is no prior technique to image these modes in bulk magnetized solid of revolution. Based on resonant magnetic induction tomography in the microwave range, our approach ensures the robust identification of these nontrivial spin-wave modes by establishing their azimuthal and polar dependences, starting point of magnonic fundamental studies and hybrid systems with complex spin textures well beyond the uniform precession mode.

Practical implementation of quantum key distributions (QKD) requires efficient, real-time feedback control to maintain system stability when facing disturbance from either external environment or imperfect internal components. Usually, a “scanning-and-transmitting” program is adopted to compensate physical parameter variations of devices, which can provide accurate compensation but may cost plenty of time in stopping and calibrating processes, resulting in reduced efficiency in key transmissions. Here, we propose to employ a well-known machine learning model, i.e., the long short-term memory network (LSTM), to predict those physical parameter variations in advance and actively perform real-time control on corresponding QKD devices. Experimentally, we take the phase-coding scheme as an example and run the LSTM-model-based QKD system for more than 10 days. Experimental results show that we can keep the same level of quantum-bit error rate as the traditional scanning-and-transmitting program by employing our machine learning method, but dramatically reducing the scanning time and resulting in significantly enhanced key transmission efficiency. Furthermore, our current machine learning model should also be applicable to other QKD systems using any coding scheme or QKD protocols and thus seems a very promising candidate in large-scale application of quantum communication networks in the near future.

A striking characteristic of superconducting circuits is that their eigenspectra and intermode coupling strengths are well predicted by simple Hamiltonians representing combinations of quantum-circuit elements. Of particular interest is the Cooper-pair-box Hamiltonian used to describe the eigenspectra of transmon qubits, which can depend strongly on the offset-charge difference across the Josephson element. Notably, this offset-charge dependence can also be observed in the dispersive coupling between an ancillary readout mode and a transmon fabricated in the offset-charge-sensitive (OCS) regime. We utilize this effect to achieve direct high-fidelity dispersive readout of the joint plasmon and charge-parity state of an OCS transmon, which enables efficient detection of charge fluctuations and nonequilibrium-quasiparticle dynamics. Specifically, we show that additional high-frequency filtering can extend the charge-parity lifetime of our device by 2 orders of magnitude, resulting in a significantly improved energy relaxation time $T_1\sim 200\mu \mathrm{s}$.

Obtaining the density matrix that fully describes a quantum system is central to quantum science. Recently, the technique of “direct measurement” has been proposed to characterize a quantum state in situ; however, all the existing schemes require sequential weak and strong measurements, which strongly limits their practical application. Here, we present an efficient scheme for directly measuring arbitrary quantum matrix elements with only one strong measurement or weak measurement on each qudit. Our scheme is experimentally feasible for the direct measurement of arbitrary quantum states; in particular, multiparticle quantum entangled states. This scheme has applications in the characterization of large-scale quantum systems.

The hardware overhead associated with microwave control is a major obstacle to the scale-up of superconducting quantum computing. An alternative approach involves irradiation of the qubits with trains of single-flux-quantum (SFQ) pulses, pulses of voltage whose time integral is precisely equal to the superconducting flux quantum. Here, we describe the derivation and numerical validation of compact SFQ pulse sequences in which classical bits are clocked to the qubit at a frequency that is roughly a factor 5 higher than the qubit oscillation frequency, allowing for variable pulse-to-pulse timing. The control sequences are constructed by repeated streaming of short subsequence registers that are designed to suppress leakage out of the computational manifold. With a single global clock, high-fidelity ($>99.99$%) control of qubits resonating at over 20 distinct frequencies is possible. SFQ pulses can be stored locally and delivered to the qubits via a proximal classical Josephson digital circuit, offering the possibility of a streamlined, low-footprint classical coprocessor for monitoring errors and feeding back to the qubit array.

In this work, we introduce machine-learning (ML) methods to implement fast and high-fidelity readout of a trapped-ion qubit on a hardware module, which is based on field-programmable gate arrays (FPGAs) and an ARM (Advanced RISC Machines) processor. An average readout fidelity of 99.5% (with ${10}^5$ magnitude trials) within $171\mu \mathrm{s}$ is achieved in experiments. Different ML architectures including convolutional neural networks and fully connected neural networks are implemented to compare with traditional methods, demonstrating higher fidelity and more robust readout results in a relatively short time with the proposed methods. Our hardware implementation of the proposed ML methods with FPGAs improves the readout efficiency to a higher level, through reducing the communication time between the trapped-ion system and central processing units (CPUs) in general personal computer (PCs) and the hardware can be devolved to a functional module, which is compatible with the real-time readout and feedback control of qubit states.