Micro- and nanoscale optical or microwave cavities are used in a wide range of classical applications and quantum science experiments, ranging from precision measurements, laser technologies to quantum control of mechanical motion. The dissipative photon loss via absorption, present to some extent in any optical cavity, is known to introduce thermo-optical effects and thereby impose fundamental limits on precision measurements. Here, we theoretically and experimentally reveal that such dissipative photon absorption can result in quantum feedback via in-loop field detection of the absorbed optical field, leading to the intracavity field fluctuations to be squashed or antisquashed. A closed-loop dissipative quantum feedback to the cavity field arises. Strikingly, this modifies the optical cavity susceptibility in coherent response measurements (capable of both increasing or decreasing the bare cavity linewidth) and causes excess noise and correlations in incoherent interferometric optomechanical measurements using a cavity, that is parametrically coupled to a mechanical oscillator. We experimentally observe such unanticipated dissipative dynamics in optomechanical spectroscopy of sideband-cooled optomechanical crystal cavitiess at both cryogenic temperature (approximately 8 K) and ambient conditions. The dissipative feedback introduces effective modifications to the optical cavity linewidth and the optomechanical scattering rate and gives rise to excess imprecision noise in the interferometric quantum measurement of mechanical motion. Such dissipative feedback differs fundamentally from a quantum nondemolition feedback, e.g., optical Kerr squeezing. The dissipative feedback itself always results in an antisqueezed out-of-loop optical field, while it can enhance the coexisting Kerr squeezing under certain conditions. Our result applies to cavity spectroscopy in both optical and superconducting microwave cavities, and equally applies to any dissipative feedback mechanism of different bandwidth inside the cavity. It has wide-ranging implications for future dissipation engineering, such as dissipation enhanced sideband cooling and Kerr squeezing, quantum frequency conversion, and nonreciprocity in photonic systems.

The interaction between an atomic ensemble and a light mode in a high-finesse optical cavity can easily reach the strong-coupling regime, where quantum effects dominate. In this regime, the interaction can be used to generate both atom-light and atom-atom entanglement. We analyze the dominant effects on the collective atomic state and the light field, and derive a unified approach that can account for atomic entanglement induced both by measurements on the light field, and by ignoring the state of the light field altogether. We present analytical expressions for the entanglement induced by the interaction, and determine the conditions that maximize the entanglement-induced gain over the standard quantum limit in quantum sensors and atomic clocks.

Random access codes have provided many examples of quantum advantage in communication, but concern only one kind of information retrieval task. We introduce a related task—the Torpedo Game—and show that it admits greater quantum advantage than the comparable random access code. Perfect quantum strategies involving prepare-and-measure protocols with experimentally accessible three-level systems emerge via analysis in terms of the discrete Wigner function. The example is leveraged to an operational advantage in a pacifist version of the strategy game Battleship. We pinpoint a characteristic of quantum systems that enables quantum advantage in any bounded-memory information retrieval task. While preparation contextuality has previously been linked to advantages in random access coding we focus here on a different characteristic called sequential contextuality. It is shown not only to be necessary and sufficient for quantum advantage, but also to quantify the degree of advantage. Our perfect qutrit strategy for the Torpedo Game entails the strongest type of inconsistency with noncontextual hidden variables, revealing logical paradoxes with respect to those assumptions.

Simultaneous ideal quantum measurements of multiple single-photon-level signals would advance applications in quantum information processing, metrology, and astronomy but require the first amplifier to be simultaneously broadband, quantum limited, and directional. However, conventional traveling-wave parametric amplifiers support broadband amplification at the cost of increased added noise and are not genuinely directional due to non-negligible nonlinear backward-wave generation. In this work, we introduce a new class of amplifiers that encode the information in the Floquet modes of the system. Such Floquet-mode amplifiers prevent information leakage and overcome the trade-off between quantum efficiency (QE) and bandwidth. Crucially, Floquet-mode amplifiers strongly suppress the nonlinear forward-backward wave coupling and are therefore genuinely directional and readily integrable with qubits, clearing another major obstacle toward broadband ideal quantum measurements. Furthermore, Floquet-mode amplifiers are insensitive to out-of-band impedance mismatch, which otherwise may lead to gain ripples, parametric oscillations, and instability in conventional traveling-wave parametric amplifiers. Finally, we show that a Floquet-mode Josephson traveling-wave parametric amplifier implementation can simultaneously achieve $>20\mathrm{dB}$ gain and a QE of $\eta /{\eta }_{\mathrm{ideal}}>99.9\mathrm{\%}$ of the quantum limit over more than an octave of bandwidth. The proposed Floquet scheme is also widely applicable to other platforms, such as kinetic inductance traveling-wave amplifiers and optical parametric amplifiers.

We observe the continuous emission of photons into a waveguide from a superconducting qubit without the application of an external drive. To explain this counterintuitive observation, we build a two-bath model where the qubit couples simultaneously to a cold bath (the waveguide) and a hot bath (a secondary environment). Our results show that the thermal-photon occupation of the hot bath is up to $0.14$ photons, 35 times larger than the cold waveguide, leading to nonequilibrium heat transport with a power of up to 132 zW, as estimated from the qubit emission spectrum. By adding more isolation between the sample output and the first cold amplifier in the output line, the heat transport is strongly suppressed. Our interpretation is that the hot bath may arise from active two-level systems being excited by noise from the output line, and that the qubit coherence can be improved significantly by suppressing this noise. We also apply a coherent drive, and use the waveguide to measure thermodynamic work and heat, suggesting waveguide spectroscopy is a useful means to study quantum heat engines and refrigerators. Finally, based on the theoretical model, we propose how a similar setup can be used as a noise spectrometer which provides a solution for calibrating the background noise of hybrid quantum systems.

Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finite-size quantum simulators. In general, this limits their reliability for strongly correlated systems, for instance, in the vicinity of a quantum phase transition (QPT). Here, we propose a protocol that makes optimal use of a given finite-size simulator by directly preparing, on its bulk region, a mixed state representing the reduced density operator of the translation-invariant infinite-sized system of interest. This protocol is based on coherent evolution with a local deformation of the system Hamiltonian. For systems of free fermions in one and two spatial dimensions, we illustrate and explain the underlying physics, which consists of quasiparticle transport towards the system’s boundaries while retaining the bulk “vacuum.” For the example of a nonintegrable extended Su-Schrieffer-Heeger model, we demonstrate that our protocol enables a more accurate study of QPTs. In addition, we demonstrate the protocol for an interacting spinful Fermi-Hubbard model with doping for one-dimensional chains and a small two-leg ladder, where the initial state is a random superposition of energetically low-lying states.

We use the resonant dipole-dipole interaction between Rydberg atoms and a periodic external microwave field to engineer $XXZ$ spin Hamiltonians with tunable anisotropies. The atoms are placed in one-dimensional (1D) and two-dimensional (2D) arrays of optical tweezers. As illustrations, we apply this engineering to two iconic situations in spin physics: the Heisenberg model in square arrays and spin transport in 1D. We first benchmark the Hamiltonian engineering for two atoms and then demonstrate the freezing of the magnetization on an initially magnetized 2D array. Finally, we explore the dynamics of 1D domain-wall systems with both periodic and open boundary conditions. We systematically compare our data with numerical simulations and assess the residual limitations of the technique as well as routes for improvement. The geometrical versatility of the platform, combined with the flexibility of the simulated Hamiltonians, opens up exciting prospects in the fields of quantum simulation, quantum information processing, and quantum sensing.

We can encode a qubit in the energy levels of a quantum system. Relaxation and other dissipation processes lead to decay of the fidelity of this stored information. Is it possible to preserve the quantum information for a longer time by introducing additional drives and dissipation? The existence of autonomous quantum error correcting codes answers this question in the positive. Nonetheless, discovering these codes for a real physical system, i.e., finding the encoding and the associated driving fields and bath couplings, remains a challenge that has required intuition and inspiration to overcome. In this work, we develop and demonstrate a computational approach based on adjoint optimization for discovering autonomous quantum error correcting codes given a Hamiltonian description of a physical system. We implement an optimizer that searches for a logical subspace and control parameters to better preserve quantum information. We demonstrate our method on a system of a harmonic oscillator coupled to a lossy qubit, and find that varying the Hamiltonian distance in Fock space—a proxy for the control hardware complexity—leads to discovery of different and new error correcting schemes. We discover what we call the $\sqrt{3}$ code, realizable with a Hamiltonian distance $d=2$, and propose a hardware-efficient implementation based on superconducting circuits.

Maintaining or even improving gate performance with growing numbers of parallel controlled qubits is a vital requirement for fault-tolerant quantum computing. For superconducting quantum processors, though isolated one- or two-qubit gates have been demonstrated with high fidelity, implementing these gates in parallel commonly shows worse performance. Generally, this degradation is attributed to various crosstalks between qubits, such as quantum crosstalk due to residual inter-qubit coupling. An understanding of the exact nature of these crosstalks is critical to figuring out respective mitigation schemes and improved qubit architecture designs with low crosstalk. Here we give a theoretical analysis of quantum crosstalk impact on simultaneous gate operations in a qubit architecture, where fixed-frequency transmon qubits are coupled via a tunable bus, and sub-100-ns controlled-Z (cz) gates can be realized by applying a baseband flux pulse on the bus. Our analysis shows that for microwave-driven single-qubit gates, the dressing from the qubit-qubit coupling can cause non-negligible cross-driving errors when qubits operate near frequency collision regions. During cz gate operations, although unwanted nearest-neighbor interactions are nominally turned off, sub-MHz parasitic next-nearest-neighbor interactions involving spectator qubits can still exist, causing considerable leakage or control error when one operates qubit systems around these parasitic resonance points. To ensure high-fidelity simultaneous operations, a request could be raised to figure out a better way to balance the gate error from target qubit systems themselves and the error from nonparticipating spectator qubits. Overall, our analysis suggests that towards useful quantum processors, the qubit architecture should be examined carefully in the context of high-fidelity simultaneous gate operations in a scalable qubit lattice.

Present protocols of criticality-enhanced sensing with open quantum sensors assume direct measurement of the sensor and omit the radiation quanta emitted to the environment, thereby potentially missing valuable information. Here we propose a protocol for criticality-enhanced sensing via continuous observation of the emitted radiation quanta. Under general assumptions, we establish a scaling theory for the global quantum Fisher information of the joint system and environment state at dissipative critical points. We derive universal scaling laws featuring transient and long-time behavior governed by the underlying critical exponents. Importantly, such scaling laws exceed the standard quantum limit and can in principle saturate the Heisenberg limit. To harness such advantageous scaling, we propose a practical sensing scheme based on continuous detection of the emitted quanta as realized experimentally in various quantum-optical setups. In such a scheme a single interrogation corresponds to a (stochastic) quantum trajectory of the open system evolving under the nonunitary dynamics dependent on the parameter to be sensed and the backaction of the continuous measurement. Remarkably, we demonstrate that the associated precision scaling significantly exceeds that based on direct measurement of the critical steady state, thereby establishing the metrological value of the continuous detection of the emitted quanta at dissipative criticality. We illustrate our protocol via counting the photons emitted by the open Rabi model, a paradigmatic model for the study of dissipative phase transition with finite components. Our protocol is applicable to generic quantum-optical open sensors permitting continuous readout, and may find applications at the frontier of quantum sensing, such as the human-machine interface, magnetic diagnosis of heart disease, and zero-field nuclear magnetic resonance.

We construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a ${\mathbb{Z}}_4$ toric code, where the condensation is implemented at the level of the ground states by two-body measurements. We rigorously verify the topological order of the DS stabilizer model by identifying an explicit finite-depth quantum circuit (with ancillary qubits) that maps its ground-state subspace to that of a DS string-net model. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes—in fact, exhausting all Abelian anyon theories that admit a gapped boundary. We also demonstrate that symmetry-protected topological phases of matter characterized by type-I and type-II cocycles can be modeled by Pauli stabilizer Hamiltonians by gauging certain $1$-form symmetries of the TQD stabilizer models.

We demonstrate rapid high-fidelity state preparation and measurement in exchange-only $\mathrm{Si}$/$\mathrm{Si}\mathrm{Ge}$ triple-quantum-dot qubits. Fast measurement integration (980-ns) and initialization (approximately 300-ns) operations are performed with all-electrical baseband control. We emphasize a leakage-sensitive joint initialization and measurement metric, developed in the context of exchange-only qubits but applicable more broadly, and report an infidelity of $2.5\pm 0.5\times {10}^{-3}$. This result is enabled by a high-valley-splitting heterostructure, initialization at the two- to three-electron charge boundary, and careful assessment and mitigation of $T_1$ during spin-to-charge conversion. The ultimate fidelity is limited by a number of comparably important factors and we identify clear paths toward further improved fidelity and speed. Along with an observed single-qubit randomized benchmarking error rate of $1.7\times {10}^{-3}$, this work demonstrates initialization, control, and measurement of $\mathrm{Si}$/$\mathrm{Si}\mathrm{Ge}$ triple-dot qubits at fidelities and durations that are promising for scalable quantum information processing.

We study the behavior of errors in the quantum simulation of spin systems with long-range multibody interactions resulting from the Trotter-Suzuki decomposition of the time-evolution operator. We identify a regime where the Floquet operator underlying the Trotter decomposition undergoes sharp changes even for small variations in the simulation step size. This results in a time evolution operator that is very different from the dynamics generated by the targeted Hamiltonian, which leads to a proliferation of errors in the quantum simulation. These regions of sharp change in the Floquet operator, referred to as structural instability regions, appear typically at intermediate Trotter step sizes and in the weakly interacting regime, and are thus complementary to recently revealed quantum chaotic regimes of the Trotterized evolution [L. M. Sieberer et al. npj Quantum Inf. 5, 78 (2019); M. Heyl, P. Hauke, and P. Zoller, Sci. Adv. 5, eaau8342 (2019)]. We characterize these structural instability regimes in $p$-spin models, transverse-field Ising models with all-to-all $p$-body interactions, and analytically predict their occurrence based on unitary perturbation theory. We further show that the effective Hamiltonian associated with the Trotter decomposition of the unitary time-evolution operator, when the Trotter step size is chosen to be in the structural instability region, is very different from the target Hamiltonian, which explains the large errors that can occur in the simulation in the regions of instability. These results have implications for the reliability of near-term gate-based quantum simulators, and reveal an important interplay between errors and the physical properties of the system being simulated.

Scaling of quantum computers to fault-tolerant levels relies critically on the integration of energy-efficient, stable, and reproducible qubit control and readout electronics. In comparison to traditional semiconductor-control electronics (TSCE) located at room temperature, the signals generated by rf sources based on Josephson-junctions (JJs) benefit from small device sizes, low power dissipation, intrinsic calibration, superior reproducibility, and insensitivity to ambient fluctuations. Previous experiments to colocate qubits and JJ-based control electronics have resulted in quasiparticle poisoning of the qubit, degrading the coherence and lifetime of the qubit. In this paper, we digitally control a 0.01-K transmon qubit with pulses from a Josephson pulse generator (JPG) located at the 3-K stage of a dilution refrigerator. We directly compare the qubit lifetime $T_1$, the coherence time $T_2^{\ast }$, and the thermal occupation $P_{\mathrm{th}}$ when the qubit is controlled by the JPG circuit versus the TSCE setup. We find agreement to within the daily fluctuations of $\pm 0.5\mu \mathrm{s}$ and $\pm 2\mu \mathrm{s}$ for $T_1$ and $T_2^{\ast }$, respectively, and agreement to within the 1% error for $P_{\mathrm{th}}$. Additionally, we perform randomized benchmarking to measure an average JPG gate error of $2.1\times {10}^{-2}$. In combination with a small device size ($<25{\mathrm{mm}}^2$) and low on-chip power dissipation ($\ll 100\mu \mathrm{W}$), these results are an important step toward demonstrating the viability of using JJ-based control electronics located at temperature stages higher than the mixing-chamber stage in highly scaled superconducting quantum information systems.

The development of a future global quantum communication network (or quantum Internet) will enable high-rate private communication and entanglement distribution over very long distances. However, the large-scale performance of ground-based quantum networks (which employ photons as information carriers through optical fibers) is fundamentally limited by fiber quality and link length, with the latter being a primary design factor for practical network architectures. While these fundamental limits are well established for arbitrary network topologies, the question of how to best design global architectures remains open. In this work, we introduce a large-scale quantum network model called weakly regular architectures. Such networks are capable of idealizing network connectivity, provide freedom to capture a broad class of spatial topologies, and remain analytically treatable. This allows us to investigate the effectiveness of large-scale networks with consistent connective properties and unveil critical conditions under which end-to-end rates remain optimal. Furthermore, through a strict performance comparison of ideal ground-based quantum networks with that of realistic satellite quantum communication protocols, we establish conditions for which satellites can be used to outperform fiber-based quantum infrastructure, rigorously proving the efficacy of satellite-based technologies for global quantum communications.

Although it is well known that the amount of resources that can be asymptotically distilled from a quantum state or channel does not exceed the resource cost needed to produce it, the corresponding relation in the nonasymptotic regime hitherto has not been well understood. Here, we establish a quantitative relation between the one-shot distillable resource yield and dilution cost in terms of transformation errors involved in these processes. Notably, our bound is applicable to quantum state and channel manipulation with respect to any type of quantum resource and any class of free transformations thereof, encompassing broad types of settings, including entanglement, quantum thermodynamics, and quantum communication. We also show that our techniques provide strong converse bounds relating the distillable resource and the resource dilution cost in the asymptotic regime. Moreover, we introduce a class of channels that generalize the twirling maps encountered in many resource theories, and by directly connecting it with resource quantification, we compute analytically several smoothed resource measures and improve our one-shot yield-cost bound in relevant theories. We use these operational insights to exactly evaluate important measures for various resource states in the resource theory of magic states.

Quantum computers are expected to achieve a significant speed-up over classical computers in solving a range of computational problems. Chains of ions held in a linear Paul trap are a promising platform for constructing such quantum computers, due to their long coherence times and high quality of control. Here, we report on the construction of a small five-qubit universal quantum computer using ${}^{88}$$\mathrm{Sr}$${}^{+}$ ions in a radio-frequency (rf) trap. All basic operations, including initialization, quantum logic operations, and readout, are performed with high fidelity. Selective two-qubit and single-qubit gates, implemented using a narrow-line-width laser, comprise a universal gate set, allowing realization of any unitary on the quantum register. We review the main experimental tools and describe in detail unique aspects of the computer: the use of robust entangling gates and the development of a quantum coherent feedback system through electron-multiplying CCD camera acquisition. The latter is necessary for carrying out quantum error-correction protocols in future experiments.

We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the system dimension, where the interactions between divided subsystems are taken as an effective Hamiltonian expanded by the reduced basis. Then the effective Hamiltonian is further solved by the VQE, which we call deep VQE. Deep VQE allows us to apply quantum-classical hybrid algorithms on small-scale quantum computers to large systems with strong intrasubsystem interactions and weak intersubsystem interactions, or strongly correlated spin models on large regular lattices. As proof-of-principle numerical demonstrations, we use the proposed method for quasi-one-dimensional models, including one-dimensionally coupled 12-qubit Heisenberg antiferromagnetic models on kagome lattices as well as two-dimensional Heisenberg antiferromagnetic models on square lattices. The largest problem size of 64 qubits is solved by simulating 20-qubit quantum computers with a reasonably good accuracy approximately a few $\mathrm{\%}$. The proposed scheme enables us to handle the problems of $>1000$ qubits by concatenating VQEs with a few tens of qubits. While it is unclear how accurate ground-state energy can be obtained for such a large system, our numerical results on a 64-qubit system suggest that deep VQE provides a good approximation (discrepancy within a few percent) and has room for further improvement. Therefore, deep VQE provides us a promising pathway to solve practically important problems on noisy intermediate-scale quantum computers.

In the early years of fault-tolerant quantum computing (FTQC), it is expected that the available code distance and the number of magic states will be restricted due to the limited scalability of quantum devices and the insufficient computational power of classical decoding units. Here, we integrate quantum error correction and quantum error mitigation into an efficient FTQC architecture that effectively increases the code distance and $T$-gate count at the cost of constant sampling overheads in a wide range of quantum computing regimes. For example, while we need ${10}^4$ to ${10}^{10}$ logical operations for demonstrating quantum advantages from optimistic and pessimistic points of view, we show that we can reduce the required number of physical qubits by 80% and 45% in each regime. From another perspective, when the achievable code distance is up to about 11, our scheme allows executing ${10}^3$ times more logical operations. This scheme will dramatically alleviate the required computational overheads and hasten the arrival of the FTQC era.

We propose a hardware architecture and protocol for connecting many local quantum processors contained within an optical cavity. The scheme is compatible with trapped ions or Rydberg arrays, and realizes teleported gates between any two qubits by distributing entanglement via single-photon transfers through a cavity. Heralding enables high-fidelity entanglement even for a cavity of moderate quality. For processors composed of trapped ions in a linear chain, a single cavity with realistic parameters successfully transfers photons every few $\mu \mathrm{s}$, increasing the interchain entanglement rate over 2 orders of magnitude beyond current methods and eliminating a major bottleneck for scaling trapped-ion systems. For one realistic scenario, we outline how to achieve the any-to-any entanglement of 20 ion chains containing a total of 500 qubits in $200\mu \mathrm{s}$, with both fidelities and rates limited only by local operations and ion readout. For processors composed of Rydberg atoms, our method fully connects a large array of thousands of neutral atoms. The connectivity afforded by our architecture is extendable to tens of thousands of qubits using multiple overlapping cavities, expanding capabilities for noisy intermediate-scale quantum era algorithms and Hamiltonian simulations, as well as enabling more robust high-dimensional error-correcting schemes.