The negatively charged tin-vacancy (${\mathrm{SnV}}^{-}$) center in diamond is a promising solid-state qubit for applications in quantum networking due to its high quantum efficiency, strong zero phonon emission, and reduced sensitivity to electrical noise. The ${\mathrm{SnV}}^{-}$ has a large spin-orbit coupling, which allows for long spin lifetimes at elevated temperatures, but unfortunately suppresses the magnetic dipole transitions desired for quantum control. Here, by use of a naturally strained center, we overcome this limitation and achieve high-fidelity microwave spin control. We demonstrate a $\pi$-pulse fidelity of up to $99.51\pm 0.03\%$ and a Hahn-echo coherence time of $T_2^{\mathrm{echo}}=170.0\pm 2.8\mathrm{\mu }\mathrm{s}$, both the highest yet reported for ${\mathrm{SnV}}^{-}$ platform. This performance comes without compromise to optical stability, and is demonstrated at 1.7 K where ample cooling power is available to mitigate drive-induced heating. These results pave the way for ${\mathrm{SnV}}^{-}$ spins to be used as a building block for future quantum technologies.

Symmetry-protected topological (SPT) phases are many-body quantum states that are topologically nontrivial as long as the relevant symmetries are unbroken. In this work we show that SPT phases are also well defined for average symmetries, where quenched disorders locally break the symmetries, but restore the symmetries upon disorder averaging. An example would be crystalline SPT phases with imperfect lattices. Specifically, we define the notion of average SPT phase for disordered ensembles of quantum states. We then classify and characterize a large class of average SPT phases using a decorated domain wall approach, in which domain walls (and more general defects) of the average symmetries are decorated with lower-dimensional topological states. We then show that if the decorated domain walls have dimension higher than $(0+1)\mathrm{D}$, then the boundary states of such average SPT phases will almost certainly be long-range entangled, with probability approaching 1 as the system size approaches infinity. This generalizes the notion of t’Hooft anomaly to average symmetries, which we dub “average anomaly.” The average anomaly can also manifest as constraints on lattice systems similar to the Lieb-Schultz-Mattis theorems, but with only average lattice symmetries. We also generalize our problem to “quantum disorders” that can admit short-range entanglement on their own, and develop a theory of such generalized average SPT phases purely based on density matrices and quantum channels. Our results indicate that topological quantum phenomena associated with average symmetries can be at least as rich as those with ordinary exact symmetries.

Continuous monitoring of driven-dissipative quantum-optical systems is a crucial element in the implementation of quantum metrology, providing essential strategies for achieving highly precise measurements beyond the classical limit. In this context, the relevant figure of merit is the quantum Fisher information of the radiation field emitted by the driven-dissipative sensor. Saturation of the corresponding precision limit as defined by the quantum Cramér-Rao bound is typically not achieved by conventional, temporally local continuous-measurement schemes such as counting or homodyning. To address the outstanding open challenge of efficient retrieval of the quantum Fisher information of the emission field, we design a novel continuous-measurement strategy featuring temporally quasilocal measurement bases as captured by matrix-product states. Such a measurement can be implemented effectively by injecting the emission field of the sensor into an auxiliary open system, a “quantum-decoder” module, which “decodes” specific input matrix-product states into simple product states as its output field, and performing conventional continuous measurement at the output. We devise a universal recipe for the construction of the decoder by exploiting the time-reversal transformation of quantum-optical input-output channels, thereby establishing a universal method to achieve the quantum Cramér-Rao precision limit for generic sensor designs based on continuous measurement. As a by-product, we establish an effective formula for the evaluation of the quantum Fisher information of the emission field of generic driven-dissipative open sensors. We illustrate the power of our scheme with paramagnetic open sensor designs including linear force sensors, fiber-interfaced nonlinear emitters, and driven-dissipative many-body sensors, and demonstrate that it can be robustly implemented under realistic experimental imperfections.

Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in fewer logical qubits, enabling the identification of errors through a decoding process. This process increases the logical fidelity (or accuracy) making the computation more reliable. However, most fast (efficient run-time) decoders neglect important noise characteristics, thereby reducing their accuracy. In this work, we introduce decoders that are both fast and accurate, and can be used with a wide class of QEC codes including the surface code. Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC. Using the surface code threshold as a performance metric, we observe a threshold at 0.94% error probability for our decoders, outperforming the 0.82% threshold for a standard minimum-weight perfect matching decoder. We also test our belief-matching decoders in a theoretical case study of codes tailored to a biased noise model. We find that the decoders lead to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code. Surprisingly, in the well-below-threshold regime, the rectangular surface code becomes more resource efficient than the tailored surface code due to a previously unnoticed phenomenon that we call “fragile boundaries.” Our decoders outperform all other fast decoders in terms of threshold and accuracy, enabling better results in current quantum-error-correction experiments and opening up new areas for theoretical case studies.

Cat states and Gottesman-Kitaev-Preskill (GKP) states play a key role in quantum computation and communication with continuous variables. The creation of such states relies on strong nonlinear light-matter interactions, which are widely available in microwave frequencies as in circuit quantum electrodynamics platforms. However, strong nonlinearities are hard to come by in optical frequencies, severely limiting the development and applications of quantum-information science with continuous variable in the optical range. Here we propose using the strong interaction of free electrons with light to implement the desired nonlinear mechanism, showing its implication by creating optical cat and GKP states. The key to our finding is identifying conditions on the electron for which its interaction mimics the conditional displacement quantum gate. The strong interactions can be realized by phase matching of free electrons with photonic structures such as optical waveguides and photonic crystals in an ultrafast transmission electron microscope (UTEM). Our approach enables the generation of optical GKP states with above 10 dB squeezing and fidelities above 90% at postselection probability of 10%, even reaching $>30\%$ using an initially squeezed-vacuum state. We analyze the different factors that affect the fidelity, such as electron dispersion, inhomogeneity, nonideal interaction, and limited detection efficiency. Furthermore, the free-electron interaction allows two qubit gates between a pair of GKP states, which can entangle them into a GKP Bell state. We present a roadmap for realizing such experiments in a UTEM. Since electrons can interact resonantly with light across the electromagnetic spectrum, our approach could apply for a generation of cat and GKP states also in other platforms of free-electron radiation, from klystrons to free-electron lasers.

Quantum-computation architecture based on $d$-level systems, or qudits, has attracted considerable attention recently due to their enlarged Hilbert space. Extensive theoretical and experimental studies have addressed aspects of algorithms and benchmarking techniques for qudit-based quantum computation and quantum-information processing. Here, we report a physical realization of a qudit with up to four embedded levels in a superconducting transmon demonstrating high-fidelity initialization, manipulation, and simultaneous multilevel readout. In addition to constructing $\mathrm{SU}(d)$ operations and benchmarking protocols for quantum-state tomography, quantum-process tomography, randomized benchmarking, etc., we experimentally carry out these operations for $d=3$ and $d=4$. Moreover, we perform prototypical quantum algorithms and observe outcomes consistent with expectations. Our work will hopefully stimulate further research interest in developing manipulation protocols and efficient applications for quantum processors with qudits.

The theory of circuit quantum electrodynamics has successfully analyzed superconducting circuits on the basis of the classical Lagrangian, and the corresponding quantized Hamiltonian describing these circuits. In many simplified versions of these networks, the modeling involves a singular Lagrangian that employs Kirchhoff’s laws to eliminate inherent constraints of the system. In this work, we demonstrate the failure of such singular theories for the quantization of realistic, nearly singular superconducting circuits. Instead, we rigorously prove the validity of a perturbative analysis within the Born-Oppenheimer approximation. In particular, we find that the limiting behavior of the low-energy dynamics obtained from the regularized approach exhibits a fixed-point structure flowing to one of a few universal fixed points as parasitic capacitance values go to zero. This singular limit of the regularized analysis is, in many cases, completely unlike the singular theory. Consequently, we conclude that classical network synthesis techniques which build on Kirchhoff’s laws must be critically examined prior to applying circuit quantization.

Cat states, with their unique phase-space interference properties, are ideal candidates for understanding fundamental principles of quantum mechanics and performing key quantum information processing tasks. However, they are highly susceptible to photon loss, which inevitably diminishes their quantum non-Gaussian features. Here, we protect these non-Gaussian features against photon loss by compressing the phase-space distribution of a cat state. We achieve this compression with a deterministic technique based on the echoed conditional displacement operation in a circuit QED device. We present a versatile technique for creating robust non-Gaussian continuous-variable resource states in a highly linear bosonic mode and manipulating their phase-space distribution to achieve enhanced resilience against photon loss. Such compressed cat states offer an attractive avenue for obtaining new insights into quantum foundations and quantum metrology, as well as for developing inherently more protected bosonic code words for quantum error correction.

Entanglement distribution via photons over long distances enables many applications, including quantum key distribution, which provides unprecedented privacy. The inevitable degradation of entanglement through noise accumulated over long distances remains one of the key challenges in this area. Exploiting the potential of higher-dimensional entangled photons promises to address this challenge, but poses extreme demands on the experimental implementation. Here, we present a long-range free-space quantum link, distributing entanglement over 10.2 km with flexible dimensionality of encoding by deploying a phase-stable nonlocal Franson interferometer. With this distribution of multidimensional energy-time entangled photons, we analyze the achievable key rate in a dimensionally adaptive quantum key distribution protocol that can be optimized with respect to any environmental noise conditions. Our approach enables and emphasizes the power of high-dimensional entanglement for quantum communication, yielding a positive asymptotic key rate well into the dawn of the day.

A central challenge in analog quantum simulation is to characterize desirable physical properties of quantum states produced in experiments. However, in conventional approaches, the extraction of arbitrary information requires performing measurements in many different bases, which necessitates a high level of control that present-day quantum devices may not have. Here, we propose and analyze a scalable protocol that leverages the ergodic nature of generic quantum dynamics, enabling the efficient extraction of many physical properties. The protocol does not require sophisticated controls and can be generically implemented in analog quantum simulation platforms today. Our protocol involves introducing ancillary degrees of freedom in a predetermined state to a system of interest, quenching the joint system under Hamiltonian dynamics native to the particular experimental platform, and then measuring globally in a single, fixed basis. We show that arbitrary information of the original quantum state is contained within such measurement data and can be extracted using a classical data-processing procedure. We numerically demonstrate our approach with a number of examples, including the measurements of entanglement entropy, many-body Chern number, and various superconducting orders in systems of neutral atom arrays, bosonic and fermionic particles on optical lattices, respectively, only assuming existing technological capabilities. Our protocol excitingly promises to overcome limited controllability and, thus, enhance the versatility and utility of near-term quantum technologies.

The quantum Hall states at filling factors $\nu =5/2$ and $7/2$ are expected to have Abelian charge-$e/2$ quasiparticles and non-Abelian charge-$e/4$ quasiparticles. The non-Abelian statistics of the latter is predicted to display a striking interferometric signature, the even-odd effect. By measuring resistance oscillations as a function of the magnetic field in Fabry-Pérot interferometers using new high-purity heterostructures, we for the first time report experimental evidence for the non-Abelian nature of excitations at $\nu =7/2$. At both $\nu =5/2$ and $7/2$, we also examine, for the first time, the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near both filling factors, indicating stability of the fermion parity. At both fractions, when phase fluctuations are observed, they are predominantly $\pi$ phase flips, consistent with either fermion parity change or change in the number of the enclosed $e/4$ quasiparticles. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e/4$ quasiparticles; the observed lifetime of their combined fermion parity further strengthens the case for their utility for topological quantum computation.

Photons and nuclear spins are two well-known building blocks in quantum information science and technology. Establishing an efficient interface between optical photons and nuclear spins, while highly desirable for hybridizing these two quantum systems, is challenging, because the interactions between nuclear spins and the environment are usually weak in magnitude, and there is also a formidable gap between nuclear spin frequencies and optical frequencies. In this work, we propose an optonuclear quadrupolar (ONQ) effect, whereby optical photons can be efficiently coupled to nuclear spins, similar to Raman scattering. Compared to previous works, ancilla electron spins are not required for the ONQ effect. This leads to advantages such as applicability in defect-free nonmagnetic crystals and longer nuclear spin coherence time. In addition, the frequency of the optical photons can be arbitrary, so they can be fine-tuned to minimize the material heating and to match telecom wavelengths for long-distance communications. Using perturbation theory and first-principles calculations, we demonstrate that the ONQ effect is stronger by several orders of magnitude than other nonlinear optical effects that could couple to nuclear spins. Based on this rationale, we propose promising applications of the ONQ effect, including quantum memory, quantum transduction, and materials isotope spectroscopy. We also discuss issues relevant to the experimental demonstration of the ONQ effect.

The resource theory of quantum thermodynamics has been a very successful theory and has generated much follow-up work in the community. It requires energy-preserving unitary operations to be implemented over a system, bath, and catalyst as part of its paradigm. So far, such unitary operations have been considered a “free” resource in the theory. However, this is only an idealization of a necessarily inexact process. Here, we include an additional auxiliary control system which can autonomously implement the unitary by turning an interaction “on or off.” However, the control system will inevitably be degraded by the backaction caused by the implementation of the unitary. We derive conditions on the quality of the control device so that the laws of thermodynamics do not change and prove—by utilizing a good quantum clock—that the laws of quantum mechanics allow the backreaction to be small enough so that these conditions are satisfiable. Our inclusion of nonidealized control into the resource framework also raises interesting prospects, which were absent when considering idealized control. Among other things, the emergence of a third law without the need for the assumption of a light cone. Our results and framework unify the field of autonomous thermal machines with the thermodynamic quantum resource-theoretic one, and lay the groundwork for all quantum processing devices to be unified with fully autonomous machines.

Quantum networks play an indispensable role in quantum information tasks such as secure communications, enhanced quantum sensing, and distributed computing. Among the most mature and promising platforms for quantum networking are nitrogen-vacancy (NV) centers in diamond and other color centers in solids. One of the challenges in using these systems for networking applications is to controllably manipulate entanglement between the electron and the nuclear spin register despite the always-on nature of the hyperfine interactions, which makes this an inherently many-body quantum system. Here, we develop a general formalism to quantify and control the generation of entanglement in an arbitrarily large nuclear spin register coupled to a color center electronic spin. We provide a reliable measure of nuclear spin selectivity, by exactly incorporating into our treatment the dynamics with unwanted nuclei. We also show how to realize direct multipartite gates through the use of dynamical decoupling sequences, drastically reducing the total gate time compared to protocols based on sequential entanglement with individual nuclear spins. We quantify the performance of such gate operations in the presence of unwanted residual entanglement links, capturing the dynamics of the entire nuclear spin register. Finally, using experimental parameters of a well-characterized 27 nuclear spin register device, we show how to prepare with high-fidelity entangled states for quantum error correction. While in this analysis we focus on a particular NV-diamond-based register, our framework is completely general and applicable to other defects in diamond and in SiC.

A primary requirement for a robust and unconditionally secure quantum network is the establishment of quantum nonlocal correlations over a realistic channel. While loophole-free tests of Bell nonlocality allow for entanglement certification in such a device-independent setting, they are extremely sensitive to loss and noise, which naturally arise in any practical communication scenario. Quantum steering relaxes the strict technological constraints of Bell nonlocality by reframing it in an asymmetric manner, with a trusted party only on one side. However, tests of quantum steering still require either extremely high-quality entanglement or very low loss. Here we introduce a test of quantum steering that harnesses the advantages of high-dimensional entanglement to be simultaneously noise robust and loss tolerant. Despite being constructed for qudits, our steering test is designed for single-detector measurements and is able to close the fair-sampling loophole in a time-efficient manner. We showcase the improvements over qubit-based systems by experimentally demonstrating quantum steering in up to 53 dimensions, free of the fair-sampling loophole, through simultaneous loss and noise conditions corresponding to 14.2-dB loss equivalent to 79 km of telecommunication fiber, and 36% of white noise. We go on to show how the use of high dimensions counterintuitively leads to a dramatic reduction in total measurement time, enabling a quantum steering violation almost 2 orders of magnitude faster obtained by simply doubling the Hilbert space dimension. Our work conclusively demonstrates the significant resource advantages that high-dimensional entanglement provides for quantum steering in terms of loss, noise, and measurement time, and opens the door toward practical quantum networks with the ultimate form of security.

Exploiting near-term quantum computers and achieving practical value is a considerable and exciting challenge. Most prominent candidates as variational algorithms typically aim to find the ground state of a Hamiltonian by minimizing a single classical (energy) surface which is sampled from by a quantum computer. Here, we introduce a method we call CoVaR, an alternative means to exploit the power of variational circuits: We find eigenstates by finding joint roots of a polynomially growing number of properties of the quantum state as covariance functions between the Hamiltonian and an operator pool of our choice. The most remarkable feature of our CoVaR approach is that it allows us to fully exploit the extremely powerful classical shadow techniques; i.e., we simultaneously estimate a very large number $>{10}^4–{10}^7$ of covariances. We randomly select covariances and estimate analytical derivatives at each iteration applying a stochastic Levenberg-Marquardt step via a large but tractable linear system of equations that we solve with a classical computer. We prove that the cost in quantum resources per iteration is comparable to a standard gradient estimation; however, we observe in numerical simulations a very significant improvement by many orders of magnitude in convergence speed. CoVaR is directly analogous to stochastic gradient-based optimizations of paramount importance to classical machine learning while we also offload significant but tractable work onto the classical processor. As we demonstrate numerically, the approach shares features with phase-estimation protocols that prepare eigenstates with a dominant initial fidelity contribution.

As in conventional computing, memories for quantum information benefit from high storage density and, crucially, random access, or the ability to read from or write to an arbitrarily chosen register. However, achieving such random access with quantum memories in a dense, hardware-efficient manner remains a challenge. Here we introduce a protocol using chirped pulses to encode qubits within an ensemble of quantum two-level systems, offering both random access and naturally supporting dynamical decoupling to enhance the memory lifetime. We demonstrate the protocol in the microwave regime using donor spins in silicon coupled to a superconducting cavity, storing up to four weak, coherent microwave pulses in distinct memory modes and retrieving them on demand up to 2 ms later. This approach offers the potential for microwave random access quantum memories with lifetimes exceeding seconds, while the chirped pulse phase encoding could also be applied in the optical regime to enhance quantum repeaters and networks.

The realization of a scalable architecture for quantum information processing is a major challenge for quantum science. A promising approach is based on emitters in nanostructures that are coupled by light. Here, we show that erbium dopants can be reproducibly integrated at well-defined lattice sites by implantation into pure silicon. We thus achieve a narrow inhomogeneous broadening, less than 1 GHz, strong optical transitions, and an outstanding optical coherence even at temperatures of 8 K, with an upper bound to the homogeneous linewidth of around 10 kHz. Our study thus introduces a promising materials platform for the implementation of on-chip quantum memories, microwave-to-optical conversion, and distributed quantum information processing.

Fault-tolerant quantum computing requires initializing the quantum register in a well-defined fiducial state. In solid-state systems, this is typically achieved through thermalization to a cold reservoir, such that the initialization fidelity is fundamentally limited by temperature. Here, we present a method of preparing a fiducial quantum state with a confidence beyond the thermal limit. It is based on real-time monitoring of the qubit through a negative-result measurement—the equivalent of a “Maxwell’s demon” that triggers the experiment only upon the appearance of a qubit in the lowest-energy state. We experimentally apply it to initialize an electron spin qubit in silicon, achieving a ground-state initialization fidelity of 98.9(4)%, corresponding to a $20\times$ reduction in initialization error compared to the unmonitored system. A fidelity approaching 99.9% could be achieved with realistic improvements in the bandwidth of the amplifier chain or by slowing down the rate of electron tunneling from the reservoir. We use a nuclear spin ancilla, measured in quantum nondemolition mode, to prove the value of the electron initialization fidelity far beyond the intrinsic fidelity of the electron readout. However, the method itself does not require an ancilla for its execution, saving the need for additional resources. The quantitative analysis of the initialization fidelity reveals that a simple picture of spin-dependent electron tunneling does not correctly describe the data. Our digital Maxwell’s demon can be applied to a wide range of quantum systems, with minimal demands on control and detection hardware.

Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disentangling projective measurements. We study how entanglement dynamics in nonunitary quantum circuits can be enriched in the presence of charge conservation, using a combination of exact numerics and a mapping onto a statistical mechanics model of constrained hard-core random walkers. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement, distinguished by whether measurements can efficiently reveal the total charge of the system. We find that while Rényi entropies grow sub-ballistically as $\sqrt{t}$ in the absence of measurement, for even an infinitesimal rate of measurements, all average Rényi entropies grow ballistically with time $\sim t$. We study numerically the critical behavior of the charge-sharpening and entanglement transitions in U(1) circuits, and show that they exhibit emergent Lorentz invariance and can also be diagnosed using scalable local ancilla probes. Our statistical mechanical mapping technique readily generalizes to arbitrary Abelian groups, and offers a general framework for studying dissipatively stabilized symmetry-breaking and topological orders.