Superconducting qubits provide a promising approach to large-scale fault-tolerant quantum computing. However, qubit connectivity on a planar surface is typically restricted to only a few neighboring qubits. Achieving longer-range and more flexible connectivity, which is particularly appealing in light of recent developments in error-correcting codes, however, usually involves complex multilayer packaging and external cabling, which is resource intensive and can impose fidelity limitations. Here, we propose and realize a high-speed on-chip quantum processor that supports reconfigurable all-to-all coupling with a large on-off ratio. We implement the design in a four-node quantum processor, built with a modular design comprising a wiring substrate coupled to two separate qubit-bearing substrates, each including two single-qubit nodes. We use this device to demonstrate reconfigurable controlled-$Z$ gates across all qubit pairs, with a benchmarked average fidelity of $96.00\%\pm 0.08\%$ and best fidelity of $97.14\%\pm 0.07\%$, limited mainly by dephasing in the qubits. We also generate multiqubit entanglement, distributed across the separate modules, demonstrating GHZ-3 and GHZ-4 states with fidelities of $88.15\%\pm 0.24\%$ and $75.18\%\pm 0.11\%$, respectively. This approach promises efficient scaling to larger-scale quantum circuits and offers a pathway for implementing quantum algorithms and error-correction schemes that benefit from enhanced qubit connectivity.

Grover’s algorithm is one of the primary algorithms offered as evidence that quantum computers can provide an advantage over classical computers. It involves an “oracle” (external quantum subroutine), which must be specified for a given application and whose internal structure is not part of the formal scaling of the quadratic quantum speedup guaranteed by the algorithm. Grover’’s algorithm also requires exponentially many calls to the quantum oracle (approximately $\sqrt{2^n}$ calls where n is the number of qubits) to succeed, raising the question of its implementation on both noisy and error-corrected quantum computers. In this work, we construct a quantum-inspired algorithm executable on a classical computer that performs Grover’s task in a linear number of calls to (simulations of) the oracle—an exponentially smaller number than Grover’s algorithm—and demonstrate this algorithm explicitly for Boolean satisfiability problems. The complexity of our algorithm depends on the cost to simulate the oracle once, which may or may not be exponential, depending on its internal structure. Indeed, Grover’s algorithm does not have an a priori quantum speedup as soon as one is given access to the “source code” of the oracle, which may reveal an internal structure of the problem. Our findings illustrate this point explicitly, as our algorithm exploits the structure of the quantum circuit used to program the quantum computer to speed up the search. There are still problems where Grover’s algorithm would provide an asymptotic speedup if it could be run accurately for large enough sizes. Our quantum-inspired algorithm provides lower bounds, in terms of the quantum-circuit complexity, for the quantum hardware to beat classical approaches for these problems. These estimates, combined with the unfavorable scaling of the success probability of Grover’s algorithm, which in the presence of noise decays as the exponential of the exponential of the number of qubits, makes a practical speedup unrealistic even under extremely optimistic assumptions of the evolution of both hardware quality and availability.

Quantum processors based on linear arrays of trapped ions have achieved exceptional performance, but scaling to large qubit numbers requires realizing two-dimensional ion arrays as envisioned in the quantum charge-coupled device (QCCD) architecture. Here, we present a scalable method for the control of ion crystals in a grid-based surface-electrode Paul trap and characterize it in the context of transport operations that sort and reorder multispecies crystals. By combining cowiring of control electrodes at translationally symmetric locations in each grid site with the sitewise ability to exchange the voltages applied to two special electrodes gated by a binary input, site-dependent operations can be achieved using only a fixed number of analog voltage signals and a single digital input per site. In two separate experimental systems containing nominally identical grid traps, one using ${}^{171}{\mathrm{Yb}}^{+}\text{−}{}^{138}{\mathrm{Ba}}^{+}$ crystals and the other ${}^{137}{\mathrm{Ba}}^{+}\text{−}{}^{88}{\mathrm{Sr}}^{+}$, we demonstrate this method by characterizing the conditional intrasite crystal reorder and the conditional exchange of ions between adjacent sites on the grid. Averaged across a multisite region of interest, we measure subquanta motional excitation in the axial in-phase and out-of-phase modes of the crystals following these operations at exchange rates of 2.5 kHz. In this initial demonstration, the logic controlling the voltage exchange occurs in software, but the applied signals mimic a proposed hardware implementation using crossover switches. These techniques can be further extended to implement other conditional operations in the QCCD architecture such as gates, initialization, and measurement.

Despite the high measurement fidelity that can now be reached, the dispersive qubit readout of circuit quantum electrodynamics is plagued by a loss of its quantum nondemolition character and a decrease in fidelity with increased measurement strength. In this work, we elucidate the nature of this dynamical process, which we refer to as transmon ionization. We develop a comprehensive framework which provides a physical picture of the origin of transmon ionization. This framework consists of three complementary levels of descriptions: a fully quantized transmon-resonator model, a semiclassical model where the resonator is treated as a classical drive on the transmon, and a fully classical model. Crucially, all three approaches preserve the full cosine potential of the transmon and lead to similar predictions. This framework identifies the multiphoton resonances responsible for transmon ionization. It also allows one to efficiently compute numerical estimates of the photon number threshold for ionization, which are in remarkable agreement with recent experimental results. The tools developed within this work are both conceptually and computationally simple, and we expect them to become an integral part of the theoretical underpinning of all circuit QED experiments.

The performance of superconducting quantum circuits is primarily limited by dielectric loss due to interactions with two-level systems (TLSs). State-of-the-art circuits with engineered material interfaces are approaching a limit where dielectric loss from bulk substrates plays an important role. However, a microscopic understanding of dielectric loss in crystalline substrates is still lacking. In this work, we show that boron acceptors in silicon constitute a TLS bath that leads to an energy dissipation channel for superconducting circuits. We discuss how the electronic structure of boron acceptors leads to an effective TLS response in silicon. We sweep the boron concentration in silicon and demonstrate the bulk dielectric loss limit from boron acceptors. We show that boron-induced dielectric loss can be reduced in a magnetic field due to the spin-orbit structure of boron. This work provides the first detailed microscopic description of a TLS bath for superconducting circuits and demonstrates the need for ultrahigh-purity substrates for next-generation superconducting quantum processors.

We introduce a class of quantum non-Markovian processes—dubbed process trees—that exhibit polynomially decaying temporal correlations and memory distributed across timescales. This class of processes is described by a tensor network with treelike geometry whose component tensors are (1) causality-preserving maps (superprocesses) and (2) locality-preserving temporal change-of-scale transformations. We show that the long-range correlations in this class of processes tends to originate almost entirely from memory effects and can accommodate genuinely quantum power-law correlations in time. Importantly, this class allows efficient computation of multitime correlation functions. To showcase the potential utility of this model-agnostic class for numerical simulation of physical models, we show how it can efficiently approximate the strong memory dynamics of the paradigmatic spin-boson model, in terms of arbitrary multitime features. In contrast to an equivalently costly matrix-product-operator representation, the ansatz produces a fiducial characterization of the relevant physics. Finally, leveraging 2D tensor-network renormalization-group methods, we detail an algorithm for deriving a process tree from an underlying Hamiltonian via the Feynmann-Vernon influence functional. Our work lays the foundation for the development of more efficient numerical techniques in the field of strongly interacting open quantum systems, as well as the theoretical development of a temporal renormalization-group scheme.

Qubits based on ions trapped in linear radio-frequency traps form a successful platform for quantum computing, due to their high fidelity of operations, all-to-all connectivity, and degree of local control. In principle, there is no fundamental limit to the number of ion-based qubits that can be confined in a single 1D register. However, in practice, there are two main issues associated with long trapped-ion crystals, that stem from the “softening” of their modes of motion, upon scaling up: high heating rates of the ions’ motion and a dense motional spectrum; both impede the performance of high-fidelity qubit operations. Here, we propose a holistic, scalable architecture for quantum computing with large ion crystals that overcomes these issues. Our method relies on dynamically operated optical potentials that instantaneously segment the ion crystal into cells of a manageable size. We show that these cells behave as nearly independent quantum registers, allowing for parallel entangling gates on all cells. The ability to reconfigure the optical potentials guarantees connectivity across the full ion crystal and also enables efficient midcircuit measurements. We study the implementation of large-scale parallel multiqubit entangling gates that operate simultaneously on all cells and present a protocol to compensate for crosstalk errors, enabling full-scale usage of an extensively large register. We illustrate that this architecture is advantageous both for fault-tolerant digital quantum computation and for analog quantum simulations.

Encoding quantum information in quantum states with disjoint wave-function support and noise-insensitive energies is the key behind the idea of qubit protection. While fully protected qubits are expected to offer exponential protection against both energy relaxation and pure dephasing, simpler circuits may grant partial protection with currently achievable parameters. Here, we study a fluxonium circuit in which the wave functions are engineered to minimize their overlap while benefiting from a first-order-insensitive flux sweet spot. Taking advantage of a large superinductance ($L\sim 1\mathrm{\mu }\mathrm{H}$), our circuit incorporates a resonant tunneling mechanism at zero external flux that couples states with the same fluxon parity, thus enabling bifluxon tunneling. The states $|0⟩$ and $|1⟩$ are encoded in wave functions with parities 0 and 1, respectively, ensuring a minimal form of protection against relaxation. Two-tone spectroscopy reveals the energy-level structure of the circuit and the presence of $4\pi$ quantum-phase slips between different potential wells corresponding to $m=\pm 1$ fluxons, which can be precisely described by a simple fluxonium Hamiltonian or by an effective bifluxon Hamiltonian. Despite suboptimal fabrication, the measured relaxation ($T_1=177\pm 3\mathrm{\mu }\mathrm{s}$) and dephasing ($T_2^{\mathrm{E}}=75\pm 5\mathrm{\mu }\mathrm{s}$) times not only demonstrate the relevance of our approach but also open an alternative direction toward quantum computing using partially protected fluxonium qubits.

Efficient coupling of optically active qubits to optical cavities is a key challenge for solid-state-based quantum optics experiments and future quantum technologies. Here we present a quantum photonic interface based on a single tin-vacancy center in a micrometer-thin diamond membrane coupled to a tunable open microcavity. We use the full tunability of the microcavity to selectively address individual tin-vacancy centers within the cavity mode volume. Purcell enhancement of the tin-vacancy center optical transition is evidenced both by optical excited state lifetime reduction and by optical linewidth broadening. As the emitter selectively reflects the single-photon component of the incident light, the coupled emitter-cavity system exhibits strong quantum nonlinear behavior. On resonance, we observe a transmission dip of 50% for low incident photon number per Purcell-reduced excited state lifetime, while the dip disappears as the emitter is saturated with higher photon number. Moreover, we demonstrate that the emitter strongly modifies the photon statistics of the transmitted light by observing photon bunching. This work establishes a versatile and tunable platform for advanced quantum optics experiments and proof-of-principle demonstrations on quantum networking with solid-state qubits.

To control and measure the state of a quantum system, it must necessarily be coupled to external degrees of freedom. This inevitably leads to spontaneous emission via the Purcell effect, photon-induced dephasing from measurement backaction, and errors caused by unwanted interactions with nearby quantum systems. To tackle this fundamental challenge, we make use of the design flexibility of superconducting quantum circuits to form a multimode element—an artificial molecule—with symmetry-protected modes. The proposed circuit consists of three superconducting islands coupled to a central island via Josephson junctions. It exhibits two essential nonlinear modes, one of which is flux insensitive and used as the protected qubit mode. The second mode is flux tunable and serves via a cross-Kerr-type coupling as a mediator to control the dispersive coupling of the qubit mode to the readout resonator. We demonstrate the Purcell protection of the qubit mode by measuring relaxation times that are independent of the mediated dispersive coupling. We show that the coherence of the qubit is not limited by photon-induced dephasing when detuning the mediator mode from the readout resonator and thereby reducing the dispersive coupling. The resulting highly protected qubit, which we refer to as P-mon, with tunable interactions may serve as a basic building block of a scalable quantum processor architecture, in which qubit decoherence is strongly suppressed.

Entanglement is an extraordinary feature of quantum mechanics. Sources of entangled optical photons were essential to test the foundations of quantum physics through violations of Bell’s inequalities. More recently, entangled many-body states have been realized via strong nonlinear interactions in microwave circuits with superconducting qubits. Here, we demonstrate a chip-scale source of entangled optical and microwave photonic qubits. Our device platform integrates a piezo-optomechanical transducer with a superconducting resonator which is robust under optical illumination. We drive a photon-pair generation process and employ a dual-rail encoding intrinsic to our system to prepare entangled states of microwave and optical photons. We place a lower bound on the fidelity of the entangled state by measuring microwave and optical photons in two orthogonal bases. This entanglement source can directly interface telecom wavelength time-bin qubits and gigahertz frequency superconducting qubits, two well-established platforms for quantum communication and computation, respectively.

Open system quantum dynamics can generate a variety of long-range entangled mixed states, yet it has been unclear in what sense they constitute phases of matter. To establish that two mixed states are in the same phase, as defined by their two-way connectivity via local quantum channels, we use the renormalization group (RG) and decoders of quantum error correcting codes. We introduce a real-space RG scheme for mixed states based on local channels which ideally preserve correlations with the complementary system, and we prove this is equivalent to the reversibility of the channel’s action. As an application, we demonstrate an exact RG flow of finite temperature toric code in two dimensions to infinite temperature, thus proving it is in the trivial phase. In contrast, for toric code subject to local dephasing, we establish a mixed-state toric code phase using local channels obtained by truncating an RG-type decoder and the minimum weight perfect matching decoder. We also discover a precise relation between mixed-state phase and decodability, by proving that local noise acting on toric code cannot destroy logical information without bringing the state out of the toric code phase.

By applying a microwave drive to a specially designed Josephson circuit, we have realized a double-well model system: a Kerr oscillator submitted to a squeezing force. We have observed, for the first time, the spectroscopic fingerprint of a quantum double-well Hamiltonian when its barrier height is increased: a pairwise level kissing (coalescence) corresponding to the exponential reduction of tunnel splitting in the excited states as they sink under the barrier. The discrete levels in the wells also manifest themselves in the activation time across the barrier which, instead of increasing smoothly as a function of the barrier height, presents steps each time a pair of excited states is captured by the wells. This experiment illustrates the quantum regime of Arrhenius’s law, whose observation is made possible here by the unprecedented combination of low dissipation, time-resolved state control, 98.5% quantum nondemolition single shot measurement fidelity, and complete microwave control over all Hamiltonian parameters in the quantum regime. Direct applications to quantum computation and simulation are discussed.

Group-IV color centers in diamond are promising candidates for quantum networks due to their dominant zero-phonon line and symmetry-protected optical transitions that connect to coherent spin levels. The negatively charged tin-vacancy (SnV) center possesses long electron spin lifetimes due to its large spin-orbit splitting. However, the magnetic dipole transitions required for microwave spin control are suppressed, and strain is necessary to enable these transitions. Recent work has shown spin control of strained emitters using microwave lines that suffer from Ohmic losses, restricting coherence through heating. We utilize a superconducting coplanar waveguide to measure SnV centers subjected to strain, observing substantial improvement. A detailed analysis of the SnV center electron spin Hamiltonian based on the angle-dependent splitting of the ground and excited states is performed. We demonstrate coherent spin manipulation and obtain a Hahn echo coherence time of up to $T_2=430\mathrm{\mu }\mathrm{s}$. With dynamical decoupling, we can prolong coherence to $T_2=10\mathrm{ms}$, about a sixfold improvement compared to earlier works. We also observe a nearby coupling ${}^{13}\mathrm{C}$ spin, which may serve as a quantum memory, thus substantiating the potential of SnV centers in diamond and demonstrates the benefit of superconducting microwave structures.

Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical postprocessing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix, which allow us to reconstruct entropies and PT moments from information on local subsystems. This identification yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements providing a practical and common measurement scheme, we prove that our protocol requires only polynomially many measurements and postprocessing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators and provide numerical evidence that they are satisfied in more general, physically interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today’s quantum platforms.

Trapped-ion systems are a leading platform for quantum information processing, but they are currently limited to 1D and 2D arrays, which imposes restrictions on both their scalability and their range of applications. Here, we propose a path to overcome this limitation by demonstrating that Penning traps can be used to realize remarkably clean bilayer crystals, wherein hundreds of ions self-organize into two well-defined layers. These bilayer crystals are made possible by the inclusion of an anharmonic trapping potential, which is readily implementable with current technology. We study the normal modes of this system and discover salient differences compared to the modes of single-plane crystals. The bilayer geometry and the unique properties of the normal modes open new opportunities—in particular, in quantum sensing and quantum simulation—that are not straightforward in single-plane crystals. Furthermore, we illustrate that it may be possible to extend the ideas presented here to realize multilayer crystals with more than two layers. Our work increases the dimensionality of trapped-ion systems by efficiently utilizing all three spatial dimensions, and it lays the foundation for a new generation of quantum information processing experiments with multilayer 3D crystals of trapped ions.

Dynamical decoupling and Hamiltonian engineering are well-established techniques that have been used to control qubit systems. However, designing the corresponding methods for qudit systems has been challenging due to the lack of a Bloch sphere representation, more complex interactions, and additional control constraints. By identifying several general structures associated with such problems, we develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems. Our formalism significantly simplifies qudit pulse-sequence design while naturally incorporating robustness conditions necessary for experimental practicality. We experimentally demonstrate these techniques in a strongly interacting, disordered ensemble of spin-1 nitrogen-vacancy centers, achieving more than an order-of-magnitude improvement in coherence time over existing pulse sequences. We further describe how our techniques enable the engineering of exotic many-body phenomena such as quantum many-body scars, and open up new opportunities for quantum metrology with enhanced sensitivities. These results enable wide-reaching new applications for dynamical decoupling and Hamiltonian engineering in many-body physics and quantum metrology.

Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control. Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single-photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction requires only dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is comprised of only a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits.

A characteristic feature of “quantum chaotic” systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure beyond RMT. To capture this feature, we introduce a framework that allows us to compare the ensemble properties of eigenstates in local systems with those of pure random states. In particular, our framework defines a notion of distance between quantum state ensembles that utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints). This notion gives rise to a quantitative metric for quantum chaos that not only accounts for averages of the distributions but also higher moments. The differences in moments are compared on a highly resolved scale set by the standard deviation of the RMT distribution, which is exponentially small in system size. As a result, the metric can distinguish between chaotic and integrable behaviors and, in addition, quantify and compare the degree of chaos (in terms of proximity to RMT behavior) between two systems that are assumed to be chaotic. We implement our framework in local, minimally structured, Floquet random circuits, as well as a canonical family of many-body Hamiltonians, the mixed-field Ising model (MFIM). Importantly, for Hamiltonian systems, we find that the reference random distribution must be appropriately constrained to incorporate the effect of energy conservation in order to describe the ensemble properties of midspectrum eigenstates. The metric captures deviations from RMT across all models and parameters, including those that have been previously identified as strongly chaotic, and for which other diagnostics of chaos such as level spacing statistics look strongly thermal. In Floquet circuits, the dominant source of deviations is the second moment of the distribution, and this persists for all system sizes. For the MFIM, we find significant variation of the KL divergence in parameter space. Notably, we find a small region where deviations from RMT are minimized, suggesting that “maximally chaotic” Hamiltonians may exist in fine-tuned pockets of parameter space.

A relevant problem in the theory of open quantum systems is the lack of complete positivity of dynamical maps obtained after weak-coupling approximations, a famous example being the Redfield master equation. A number of approaches exist to recover well-defined evolutions under additional Markovian assumptions, but much less is known beyond this regime. Here, we propose a numerical method to cure the complete-positivity violation issue while preserving the non-Markovian features of an arbitrary original dynamical map. The idea is to replace its unphysical Choi operator with its closest physical one, mimicking recent work on quantum process tomography. We also show that the regularized dynamics is more accurate in terms of reproducing the exact dynamics, which allows us to heuristically push the utilization of these master equations in moderate coupling regimes, where the loss of positivity can have a relevant impact.