We introduce an exactly solvable model of interacting Majorana fermions realizing $Z_2$ topological order with a $Z_2$ fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid-state systems, including topological insulators, nanowires, or two-dimensional electron gases, proximitized by $s$-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.

By coupling a macroscopic mechanical oscillator to two microwave cavities, we simultaneously prepare and monitor a nonclassical steady state of mechanical motion. In each cavity, correlated radiation pressure forces induced by two coherent drives engineer the coupling between the quadratures of light and motion. We, first, demonstrate the ability to perform a continuous quantum nondemolition measurement of a single mechanical quadrature at a rate that exceeds the mechanical decoherence rate, while avoiding measurement backaction by more than 13 dB. Second, we apply this measurement technique to independently verify the preparation of a squeezed state in the mechanical oscillator, resolving quadrature fluctuations 20% below the quantum noise.

Circulators and directional amplifiers are crucial nonreciprocal signal routing and processing components involved in microwave read-out chains for a variety of applications. They are particularly important in the field of superconducting quantum information, where the devices also need to have minimal photon losses to preserve the quantum coherence of signals. Conventional commercial implementations of each device suffer from losses and are built from very different physical principles, which has led to separate strategies for the construction of their quantum-limited versions. However, as recently theoretically, by establishing simultaneous pairwise conversion and/or gain processes between three modes of a Josephson-junction-based superconducting microwave circuit, it is possible to endow the circuit with the functions of either a phase-preserving directional amplifier or a circulator. Here, we experimentally demonstrate these two modes of operation of the same circuit. Furthermore, in the directional amplifier mode, we show that the noise performance is comparable to standard nondirectional superconducting amplifiers, while in the circulator mode, we show that the sense of circulation is fully reversible. Our device is far simpler in both modes of operation than previous proposals and implementations, requiring only three microwave pumps. It offers the advantage of flexibility, as it can dynamically switch between modes of operation as its pump conditions are changed. Moreover, by demonstrating that a single three-wave process yields nonreciprocal devices with reconfigurable functions, our work breaks the ground for the development of future, more complex directional circuits, and has excellent prospects for on-chip integration.

Field-orthogonal temporal modes of photonic quantum states provide a new framework for quantum information science (QIS). They intrinsically span a high-dimensional Hilbert space and lend themselves to integration into existing single-mode fiber communication networks. We show that the three main requirements to construct a valid framework for QIS—the controlled generation of resource states, the targeted and highly efficient manipulation of temporal modes, and their efficient detection—can be fulfilled with current technology. We suggest implementations of diverse QIS applications based on this complete set of building blocks.

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.

Work and quantum correlations are two fundamental resources in thermodynamics and quantum information theory. In this work, we study how to use correlations among quantum systems to optimally store work. We analyze this question for isolated quantum ensembles, where the work can be naturally divided into two contributions: a local contribution from each system and a global contribution originating from correlations among systems. We focus on the latter and consider quantum systems that are locally thermal, thus from which any extractable work can only come from correlations. We compute the maximum extractable work for general entangled states, separable states, and states with fixed entropy. Our results show that while entanglement gives an advantage for small quantum ensembles, this gain vanishes for a large number of systems.

We introduce a new continuous-variable quantum key distribution (CV-QKD) protocol, self-referenced CV-QKD, that eliminates the need for transmission of a high-power local oscillator between the communicating parties. In this protocol, each signal pulse is accompanied by a reference pulse (or a pair of twin reference pulses), used to align Alice’s and Bob’s measurement bases. The method of phase estimation and compensation based on the reference pulse measurement can be viewed as a quantum analog of intradyne detection used in classical coherent communication, which extracts the phase information from the modulated signal. We present a proof-of-principle, fiber-based experimental demonstration of the protocol and quantify the expected secret key rates by expressing them in terms of experimental parameters. Our analysis of the secret key rate fully takes into account the inherent uncertainty associated with the quantum nature of the reference pulse(s) and quantifies the limit at which the theoretical key rate approaches that of the respective conventional protocol that requires local oscillator transmission. The self-referenced protocol greatly simplifies the hardware required for CV-QKD, especially for potential integrated photonics implementations of transmitters and receivers, with minimum sacrifice of performance. As such, it provides a pathway towards scalable integrated CV-QKD transceivers, a vital step towards large-scale QKD networks.

Continuous-variable quantum key distribution (CV-QKD) protocols based on coherent detection have been studied extensively in both theory and experiment. In all the existing implementations of CV-QKD, both the quantum signal and the local oscillator (LO) are generated from the same laser and propagate through the insecure quantum channel. This arrangement may open security loopholes and limit the potential applications of CV-QKD. In this paper, we propose and demonstrate a pilot-aided feedforward data recovery scheme that enables reliable coherent detection using a “locally” generated LO. Using two independent commercial laser sources and a spool of 25-km optical fiber, we construct a coherent communication system. The variance of the phase noise introduced by the proposed scheme is measured to be 0.04 (${\text{rad}}^2$), which is small enough to enable secure key distribution. This technology also opens the door for other quantum communication protocols, such as the recently proposed measurement-device-independent CV-QKD, where independent light sources are employed by different users.

We present an operational framework for Einstein-Podolsky-Rosen steering as a physical resource. For arbitrary-dimensional bipartite systems composed of a quantum subsystem and a black-box device, we show that local operations assisted by one-way classical communication (1W-LOCCs) from the quantum part to the black box cannot create steering. Based on this, we build a resource theory of steering with 1W-LOCCs as the free operations. We introduce the notion of convex steering monotones as the fundamental axiomatic quantifiers of steering. As a convenient example thereof, we present the relative entropy of steering. In addition, we prove that two previously proposed quantifiers, the steerable weight and the robustness of steering, are also convex steering monotones. To end up with for minimal-dimensional systems, we establish, on the one hand, necessary and sufficient conditions for pure-state steering conversions under stochastic 1W-LOCCs and prove, on the other hand, the nonexistence of steering bits, i.e., measure-independent maximally steerable states from which all states can be obtained by means of the free operations. Our findings reveal unexpected aspects of steering and lay the foundations for further research, with potential implications in Bell nonlocality.

Linear optical quantum computing (LOQC) seems attractively simple: Information is borne entirely by light and processed by components such as beam splitters, phase shifters, and detectors. However, this very simplicity leads to limitations, such as the lack of deterministic entangling operations, which are compensated for by using substantial hardware overheads. Here, we quantify the resource costs for full-scale LOQC by proposing a specific protocol based on the surface code. With the caveat that our protocol can be further optimized, we report that the required number of physical components is at least 5 orders of magnitude greater than in comparable matter-based systems. Moreover, the resource requirements grow further if the per-component photon-loss rate is worse than $10^{-3}$ or the per-component noise rate is worse than $10^{-5}$. We identify the performance of switches in the network as the single most influential factor influencing resource scaling.

Symmetric informationally complete positive operator-valued measures provide efficient quantum state tomography in any finite dimension. In this work, we implement state tomography using symmetric informationally complete positive operator-valued measures for both pure and mixed photonic qudit states in Hilbert spaces of orbital angular momentum, including spaces whose dimension is not power of a prime. Fidelities of reconstruction within the range of 0.81–0.96 are obtained for both pure and mixed states. These results are relevant to high-dimensional quantum information and computation experiments, especially to those where a complete set of mutually unbiased bases is unknown.

Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here, I show that for suitable topological codes, a single round of local measurements is enough. This feature is generic and is related to self-correction and confinement phenomena in the corresponding quantum Hamiltonian model. Three-dimensional gauge color codes exhibit this single-shot feature, which also applies to initialization and gauge fixing. Assuming the time for efficient classical computations to be negligible, this yields a topological fault-tolerant quantum computing scheme where all elementary logical operations can be performed in constant time.

Multipartite entanglement is very poorly understood despite all the theoretical and experimental advances of the last decades. Preparation, manipulation, and identification of this resource is crucial for both practical and fundamental reasons. However, the difficulty in the practical manipulation and the complexity of the data generated by measurements on these systems increase rapidly with the number of parties. Therefore, we would like to experimentally address the problem of how much information about multipartite entanglement we can access with incomplete measurements. In particular, it was shown that some types of pure multipartite entangled states can be witnessed without measuring the correlations [M. Walter et al., Science 340, 1205 (2013)] between parties, which is strongly demanding experimentally. We explore this method using an optical setup that permits the preparation and the complete tomographic reconstruction of many inequivalent classes of three- and four-partite entangled states, and compare complete versus incomplete information. We show that the method is useful in practice, even for nonpure states or nonideal measurement conditions.

We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezoactive materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers, or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range and can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface acoustic excitation can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavity-QED equivalent of microwave photons and enabling long-range coupling of a wide range of qubits.

In the quantum version of a Trojan-horse attack, photons are injected into the optical modules of a quantum key distribution system in an attempt to read information direct from the encoding devices. To stop the Trojan photons, the use of passive optical components has been suggested. However, to date, there is no quantitative bound that specifies such components in relation to the security of the system. Here, we turn the Trojan-horse attack into an information leakage problem. This allows us to quantify the system security and relate it to the specification of the optical elements. The analysis is supported by the experimental characterization, within the operation regime, of reflectivity and transmission of the optical components most relevant to security.

There has been considerable progress in the design and construction of quantum annealing devices. However, a conclusive detection of quantum speedup over traditional silicon-based machines remains elusive, despite multiple careful studies. In this work we outline strategies to design hard tunable benchmark instances based on insights from the study of spin glasses—the archetypal random benchmark problem for novel algorithms and optimization devices. We propose to complement head-to-head scaling studies that compare quantum annealing machines to state-of-the-art classical codes with an approach that compares the performance of different algorithms and/or computing architectures on different classes of computationally hard tunable spin-glass instances. The advantage of such an approach lies in having to compare only the performance hit felt by a given algorithm and/or architecture when the instance complexity is increased. Furthermore, we propose a methodology that might not directly translate into the detection of quantum speedup but might elucidate whether quantum annealing has a “quantum advantage” over corresponding classical algorithms, such as simulated annealing. Our results on a 496-qubit D-Wave Two quantum annealing device are compared to recently used state-of-the-art thermal simulated annealing codes.

Under ideal conditions, quantum metrology promises a precision gain over classical techniques scaling quadratically with the number of probe particles. At the same time, no-go results have shown that generic, uncorrelated noise limits the quantum advantage to a constant factor. In frequency estimation scenarios, however, there are exceptions to this rule and, in particular, it has been found that transversal dephasing does allow for a scaling quantum advantage. Yet, it has remained unclear whether such exemptions can be exploited in practical scenarios. Here, we argue that the transversal-noise model applies to the setting of recent magnetometry experiments and show that a scaling advantage can be maintained with one-axis-twisted spin-squeezed states and Ramsey-interferometry-like measurements. This is achieved by exploiting the geometry of the setup that, as we demonstrate, has a strong influence on the achievable quantum enhancement for experimentally feasible parameter settings. When, in addition to the dominant transversal noise, other sources of decoherence are present, the quantum advantage is asymptotically bounded by a constant, but this constant may be significantly improved by exploring the geometry.

We demonstrate a photonic circuit with integrated long-lived quantum memories. Precharacterized quantum nodes—diamond microwaveguides containing single, stable, negatively charged nitrogen-vacancy centers—are deterministically integrated into low-loss silicon nitride waveguides. These quantum nodes efficiently couple into the single-mode waveguides with $>1\mathrm{Mcps}$ collected into the waveguide, have narrow single-scan linewidths below 400 MHz, and exhibit long electron spin coherence times up to $120\mu \mathrm{s}$. Our system facilitates the assembly of multiple quantum nodes with preselected properties into a photonic integrated circuit with near unity yield, paving the way towards the scalable fabrication of quantum information processors.

Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit quantum electrodynamics setup. We make use of the exchange interaction naturally present in the simulator to construct a digital decomposition of the model-specific evolution and extract its full dynamics. This approach is universal and efficient, employing only resources that are polynomial in the number of spins, and indicates a path towards the controlled simulation of general spin dynamics in superconducting qubit platforms.

Macroscopic quantum tunneling is a fundamental phenomenon of quantum mechanics related to the actively debated topic of quantum-to-classical transition. The ability to realize macroscopic quantum tunneling affects implementation of qubit-based quantum computing schemes and their protection against decoherence. Decoherence in qubits can be reduced by means of topological protection, e.g., by exploiting various parity effects. In particular, paired phase slips can provide such protection for superconducting qubits. Here, we report on the direct observation of quantum paired phase slips in thin-wire superconducting loops. We show that in addition to conventional single phase slips that change the superconducting order parameter phase by $2\pi$, there are quantum transitions that change the phase by $4\pi$. Quantum paired phase slips represent a synchronized occurrence of two macroscopic quantum tunneling events, i.e., cotunneling. We demonstrate the existence of a remarkable regime in which paired phase slips are exponentially more probable than single ones.