We report evidence for the formation of niobium hydride phase within niobium films on silicon substrates in superconducting qubits fabricated at Rigetti Computing. For this study, we combined complementary techniques-including room-temperature and cryogenic atomic force microscopy (AFM), synchrotron x-ray diffraction, and time-of-flight secondary ion mass spectroscopy (ToF-SIMS)-to directly reveal the existence of niobium hydride precipitates on the surface of superconducting qubits. Upon cryogenic cooling, we observed variation in the size and morphology of the hydrides, ranging from small ('5 nm) irregular shapes to large ('10-100 nm) domains within the Nb grains, which were fully converted to niobium hydrides. Since niobium hydrides are nonsuperconducting and can easily change in size and location upon different cooldowns to cryogenic temperature, our finding highlights a previously unknown source of decoherence in superconducting qubits. This contributes to quasiparticle losses, offering a potential explanation for changes in qubit performance upon cooldowns. Finally, by leveraging the RF performance of a 3D bulk Nb resonator, we quantify RF dissipation in a superconducting qubit caused by hydrogen concentration variation, and propose a practical engineering pathway to mitigate the formation of Nb hydrides for superconducting qubit applications.

Disorder in quantum many-body systems can drive transitions between ergodic and non-ergodic phases, yet the nature–and even the existence–of these transitions remains intensely debated. Using a two-dimensional array of superconducting qubits, we study an interacting spin model at finite temperature in a disordered landscape, tracking dynamics both in real space and in Hilbert space. Over a broad disorder range, we observe an intermediate non-ergodic regime with glass-like characteristics: physical observables become broadly distributed and some, but not all, degrees of freedom are effectively frozen. The Hilbert-space return probability shows slow power-law decay, consistent with finite-temperature quantum glassiness. In the same regime, we detect the onset of a finite Edwards-Anderson order parameter and the disappearance of spin diffusion. By contrast, at lower disorder, spin transport persists with a nonzero diffusion coefficient. Our results show that there is a transition out of the ergodic phase in two-dimensional systems.

Disorder-induced phenomena in quantum many-body systems pose significant challenges for analytical methods and numerical simulations at relevant time and system scales. To reduce the cost of disorder-sampling, we investigate quantum circuits initialized in states tunable to superpositions over all disorder configurations. In a translationally-invariant lattice gauge theory (LGT), these states can be interpreted as a superposition over gauge sectors. We observe localization in this LGT in the absence of disorder in one and two dimensions: perturbations fail to diffuse despite fully disorder-free evolution and initial states. However, Rényi entropy measurements reveal that superposition-prepared states fundamentally differ from those obtained by direct disorder sampling. Leveraging superposition, we propose an algorithm with a polynomial speedup in sampling disorder configurations, a longstanding challenge in many-body localization studies.

Quantum error correction (QEC) is the primary strategy for protecting a quantum computer from the environment1,2. The prerequisite of QEC is that errors must remain sufficiently rare, which requires perpetually adapting the control parameters of the computer to the drifting environmental conditions. The current solution to this problem is to terminate the entire quantum computation for recalibration, but it is incompatible with the long runtimes of future quantum algorithms3,4. Here we address this challenge by unifying calibration with computation. We grant the QEC process5-11 a dual role: its error-detection events are not only used to correct the logical quantum state but are also repurposed as a learning signal, teaching a reinforcement learning agent12-16 to continuously steer the control parameters and stabilize the quantum system during computation. We experimentally demonstrate this framework on a Willow superconducting processor, improving the logical stability of the surface code 3.5-fold against injected drift. By synthesizing our full suite of technological advances, we achieve record performance of the surface and colour codes, with average logical error per cycle of 7.72(9) × 10-4 and 8.19(14) × 10-3, respectively. Numerical simulations of large codes with tens of thousands of control parameters confirm the scalability of our RL framework, revealing an optimization speed that is independent of system size. This work thus enables a new paradigm: a quantum computer that learns from its errors and never stops computing.

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators1,2. Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble-Zurek scaling predictions3 in the XY model, as well as signatures of the classical Kosterlitz-Thouless phase transition4. Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis5-7 in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum processors has remained elusive. Using a superconducting qubit processor, we show that quantum contextuality enables certain tasks to be performed with success probabilities beyond classical limits. With a few qubits, we illustrate quantum contextuality with the magic square game, as well as quantify it through a Kochen–Specker–Bell inequality violation. To examine many-body contextuality, we implement the N-player GHZ game and separately solve a 2D hidden linear function problem, exceeding classical success rate in both. Our work proposes novel ways to benchmark quantum processors using contextuality-based algorithms.

Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. In experimental systems, repeated time-reversal protocols have been successfully implemented to restore sensitivities of quantum observables. Using a 103-qubit superconducting quantum processor, we characterize ergodic dynamics using the second-order out-of-time-order correlators, OTOC^(2). In contrast to dynamics without time reversal, OTOC^(2) are observed to remain sensitive to the underlying dynamics at long time scales. Furthermore, by inserting Pauli operators during quantum evolution and randomizing the phases of Pauli strings in the Heisenberg picture, we observe substantial changes in OTOC^(2) values. This indicates that OTOC^(2) is dominated by constructive interference between Pauli strings that form large loops in configuration space. The observed interference mechanism endows OTOC^(2) with a high degree of classical simulation complexity, which culminates in a set of large-scale OTOC^(2) measurements exceeding the simulation capacity of known classical algorithms. Further supported by an example of Hamiltonian learning through OTOC^(2), our results indicate a viable path to practical quantum advantage.

We report the evidence of the formation of niobium hydride phase within niobium films on silicon substrates in superconducting qubits fabricated at Rigetti Computing. For this study, we combined complementary techniques, including room-temperature and cryogenic atomic force microscopy (AFM), synchrotron Xray diffraction, and time of flight secondary ion mass spectroscopy (ToF-SIMS), to directly reveal the existence of niobium hydride precipitates in the Rigetti chip area. Upon cryogenic cooling, we observed variation in the size and morphology of the hydrides, ranging from small (5 nm) irregular shapes to large ( 10-100 nm) domain within the Nb grains, fully converted to niobium hydrides. Since niobium hydrides are non-superconducting and can easily change in size and location upon different cooldowns to cryogenic temperature, our finding highlights a new and previously unknown source of decoherence in superconducting qubits. This contributes to both quasiparticle and two level system (TLS) losses, offering a potential explanation for changes in qubit performance upon cooldowns. Finally, by leveraging the RF performance of a 3D bulk Nb resonator, we can quantify RF dissipation on a superconducting qubit, caused by hydrogen concentration variation, and are able to propose a practical engineering pathway to mitigate the formation of the Nb hydrides for superconducting qubit applications.

The promise of fault-tolerant quantum computing is challenged by environmental drift that relentlessly degrades the quality of quantum operations. The contemporary solution, halting the entire quantum computation for recalibration, is unsustainable for the long runtimes of the future algorithms. We address this challenge by unifying calibration with computation, granting the quantum error correction process a dual role: its error detection events are not only used to correct the logical quantum state, but are also repurposed as a learning signal, teaching a reinforcement learning (RL) agent to continuously steer the physical control parameters and stabilize the quantum system during the computation. We experimentally demonstrate this framework on a Willow superconducting processor, improving the logical stability of the surface code 3.5-fold against injected drift. By synthesizing our full suite of technological advances, including RL fine-tuning of the entire system and near-optimal decoding, we achieve record performance of the surface and color codes, with average logical error per cycle of ε_L=7.72(9)×10^-4 and ε_L=8.19(14)×10^-3 respectively. Simulations of surface codes up to distance-15 with tens of thousands control parameters confirm the scalability of our RL framework, revealing an optimization speed that is independent of the system size. This work thus enables a new paradigm: a quantum computer that learns from its errors and never stops computing.

A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome checks, permitting correction of logical information. Recently, the development of time-dynamic approaches to error correction has uncovered new codes and new code implementations. In this work, we experimentally demonstrate three time-dynamic implementations of the surface code, each offering a unique solution to hardware design challenges and introducing flexibility in surface code realization. First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three. Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors. Finally, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead. We measure the error suppression factor when scaling from distance-3 to distance-5 codes of Λ_35,hex = 2.15(2), Λ_35,walk = 1.69(6), and Λ_35,iSWAP = 1.56(2), achieving state-of-the-art error suppression for each. With detailed error budgeting, we explore their performance trade-offs and implications for hardware design. This work demonstrates that dynamic circuit approaches satisfy the demands for fault-tolerance and opens new alternative avenues for scalable hardware design.

The emergence of states with long-range correlations in a disordered landscape is rare, as disorder typically suppresses the particle mobility required for long-range coherence. But when more than two energy levels are available per site, disorder can induce resonances that locally enhance mobility. Here we explore phases arising from the interplay between disorder, kinetic energy, and interactions on a superconducting processor with qutrit readout and control. Compressibility measurements distinguish an incompressible Mott insulator from surrounding compressible phases and reveal signatures of glassiness, reflected in non-ergodic behavior. Spatially-resolved two-point correlator measurements identify regions of the phase diagram with a non-vanishing condensate fraction. We also visualize the spectrum by measuring the dynamical structure factor. A linearly-dispersing phonon mode materializes in the superfluid, appearing even when disorder is introduced to the clean Mott insulator. Our results provide strong experimental evidence for disorder-induced superfluidity.

A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome checks, permitting correction of logical information. Recently, the development of time-dynamic approaches to error correction has enabled different codes and implementations that do not rely on static syndrome measurements. Here we experimentally demonstrate three time-dynamic implementations of the surface code, each offering a distinct solution to hardware design challenges faced by surface code realizations. First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three. Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors. Finally, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead. We measure the error suppression factor when scaling from distance-3 to distance-5 codes of Lambda 35,hex = 2.15(2), Lambda 35,walk = 1.69(6) and Lambda 35,iSWAP = 1.56(2), achieving state-of-the-art error suppression for each. Our work demonstrates that dynamic circuit approaches meet the demands for fault tolerance and enable alternative strategies for scalable hardware design.

Lattice gauge theories (LGTs)1-4 can be used to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials5-7. Studying dynamical properties of emergent phases can be challenging, as it requires solving many-body problems that are generally beyond perturbative limits8-10. Here we investigate the dynamics of local excitations in a Z 2 LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit that prepares low-energy states that have a large overlap with the ground state; then we create charge excitations with local gates and simulate their quantum dynamics by means of a discretized time evolution. As the electric field coupling constant is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the electric field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT, from which we uncover two distinct regimes inside the confining phase: for weak confinement, the string fluctuates strongly in the transverse direction, whereas for strong confinement, transverse fluctuations are effectively frozen11,12. We also demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a new set of techniques for investigating emergent excitations and string dynamics.

Quantum science and technology promise the realization of a powerful computational resource that relies on a network of quantum processors connected with low loss and low noise communication channels capable of distributing entangled states [1,2]. While superconducting microwave qubits (3-8 GHz) operating in cryogenic environments have emerged as promising candidates for quantum processor nodes due to their strong Josephson nonlinearity and low loss [3], the information between spatially separated processor nodes will likely be carried at room temperature via telecommunication photons (200 THz) propagating in low loss optical fibers. Transduction of quantum information [4-10] between these disparate frequencies is therefore critical to leverage the advantages of each platform by interfacing quantum resources. Here, we demonstrate coherent optical control of a superconducting qubit. We achieve this by developing a microwave-optical quantum transducer that operates with up to 1.18% conversion efficiency (1.16% cooperativity) and demonstrate optically-driven Rabi oscillations (2.27 MHz) in a superconducting qubit without impacting qubit coherence times (800 ns). Finally, we discuss outlooks towards using the transducer to network quantum processor nodes.

Fault-tolerant quantum computing requires a universal gate set, but the necessary non-Clifford gates represent a significant resource cost for most quantum error correction architectures. Magic state cultivation offers an efficient alternative to resource-intensive distillation protocols; however, testing the proposal's assumptions represents a challenging departure from quantum memory experiments. We present an experimental study of magic state cultivation on a superconducting quantum processor. We implement cultivation, including code-switching into a surface code, and develop a fault-tolerant measurement protocol to bound the magic state fidelity. Cultivation reduces the error by a factor of 40, with a state fidelity of 0.9999(1) (retaining 8

Quantum error correction1-4 is essential for bridging the gap between the error rates of physical devices and the extremely low error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors5-8 have focused primarily on the surface code9, which offers a high error threshold but poses limitations for logical operations. The colour code10 enables more efficient logic, but it requires more complex stabilizer measurements and decoding. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and realizations of colour codes11-19 have not addressed performance scaling with code size on any platform. Here we present a comprehensive demonstration of the colour code on a superconducting processor8. Scaling the code distance from three to five suppresses logical errors by a factor of Λ3/5 = 1.56(4). Simulations indicate this performance is below the threshold of the colour code, and the colour code may become more efficient than the surface code following modest device improvements. We test transversal Clifford gates with logical randomized benchmarking20 and inject magic states21, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection. Finally, we teleport logical states between colour codes using lattice surgery22. This work establishes the colour code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

Theoretically understanding and experimentally characterizing and modifying the underlying Hamiltonian of a quantum system is of utmost importance in achieving high-fidelity quantum gates for quantum computing. In this work, we explore the use of dynamical decoupling (DD) in characterizing undesired two-qubit couplings as well as the underlying single-qubit decoherence, and in suppressing them. We develop a syncopated dynamical decoupling technique which protects against decoherence and selectively targets unwanted two-qubit interactions, overcoming both significant hurdles to achieving precise quantum control and realizing quantum computing on many hardware prototypes. On a transmon-qubit-based superconducting quantum device, we identify separate white and 1/f noise components underlying the single-qubit decoherence and a static ZZ coupling between pairs of qubits. We suppress these errors using syncopated dynamical decoupling in two-qubit benchmarking experiments and significantly boost performance in a realistic algorithmic quantum circuit.

We present a novel transmon qubit fabrication technique that yields systematic improvements in T$_1$ relaxation times. We fabricate devices using an encapsulation strategy that involves passivating the surface of niobium and thereby preventing the formation of its lossy surface oxide. By maintaining the same superconducting metal and only varying the surface structure, this comparative investigation examining different capping materials, such as tantalum, aluminum, titanium nitride, and gold, and film substrates across different qubit foundries definitively demonstrates the detrimental impact that niobium oxides have on the coherence times of superconducting qubits, compared to native oxides of tantalum, aluminum or titanium nitride. Our surface-encapsulated niobium qubit devices exhibit T$_1$ relaxation times 2 to 5 times longer than baseline niobium qubit devices with native niobium oxides. When capping niobium with tantalum, we obtain median qubit lifetimes above 300 microseconds, with maximum values up to 600 microseconds, that represent the highest lifetimes to date for superconducting qubits prepared on both sapphire and silicon. Our comparative structural and chemical analysis suggests why amorphous niobium oxides may induce higher losses compared to other amorphous oxides. These results are in line with high-accuracy measurements of the niobium oxide loss tangent obtained with ultra-high Q superconducting radiofrequency (SRF) cavities. This new surface encapsulation strategy enables even further reduction of dielectric losses via passivation with ambient-stable materials, while preserving fabrication and scalable manufacturability thanks to the compatibility with silicon processes.

Advanced simulations and calculations on quantum computers require high fidelity implementations of quantum circuits. The universal gateset approach builds complex unitaries from many gates drawn from a small set of calibrated high-fidelity primitive gates, which results in a lower combined fidelity. Compiling a complex unitary for processors with higher-dimensional logical elements, such as qutrits, exacerbates the accumulated error per unitary because a longer gate sequence is needed. Optimal control methods promise time and resource efficient compact gate sequences and, therefore, higher fidelity. These methods generate pulses that can, in principle, directly implement any complex unitary on a quantum device. In this work, we demonstrate that any arbitrary qutrit gate can be realized with high fidelity. We generated and tested pulses for a large set of randomly selected arbitrary unitaries on two separate qutrit compatible processors, LLNL Quantum Device and Integration Testbed (QuDIT) standard QPU and Rigetti Aspen-11, achieving an average fidelity around 99 %. We show that the optimal control gates do not require recalibration for at least three days and the same calibration parameters can be used for all implemented gates. Our work shows that the calibration overheads for optimal control gates can be made small enough to enable efficient quantum circuits based on this technique.

We describe coherent optical control of a superconducting qubit with an electro-optic transducer as a step towards enabling optical interconnects between superconducting processor nodes.