We present an end-to-end algorithmic pipeline where a noisy digital quantum computer is used to approximate the value of the Jones polynomial at the fifth root of unity for any input link, i.e., a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is “less quantum,” the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain “more advantage” by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum’s H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterize the effect of noise present in a given quantum processor. In parallel, we develop and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The reconfigurable tools provided in this work allow for precise resource estimation to identify minimum link sizes for near-term quantum advantage in practice for a meaningful quantum-native problem in knot theory, if a candidate set of links are provided.

Multiqubit gates that involve three or more qubits are usually thought to be of little significance for fault-tolerant quantum error correction because single gate faults can lead to errors of high Pauli weight. However, recent works have shown that multiqubit gates can be beneficial for measurement-free fault-tolerant quantum error correction and for fault-tolerant stabilizer readout in unrotated surface codes. In this work, we investigate multiqubit Rydberg gates that are useful for fault-tolerant quantum error correction in single-species neutral-atom platforms and can be implemented with global laser pulses that do not individually address atomic sites. We develop an open-source Python package to generate analytical, few-parameter pulses that implement the desired gates while minimizing gate errors due to Rydberg-state decay. The tool also allows us to identify parameter-optimal pulses, characterized by a minimal parameter count for the pulse ansatz. Measurement-free quantum error correction protocols require controlled-controlled-Z (CCZ) gates, which we analyze for atoms arranged in symmetric and asymmetric configurations. We investigate the performance of these schemes for various single-, two-, and three-qubit gate error rates, showing that break-even performance of measurement-free quantum error correction is within reach of current hardware. Moreover, we study Floquet quantum error correction protocols that comprise two-body stabilizer measurements. Those can be realized using global three-qubit gates, and we show that this can lead to a significant reduction in shuttling operations. Simulations with realistic circuit-level noise indicate that applying three-qubit gates for stabilizer measurements in Floquet codes can yield competitive logical qubit performance in experimentally relevant error regimes.

Quantum phenomena offer the possibility of measuring physical quantities with precision beyond classical limits. However, current progress is constrained by scalability, environmental noise, and challenges in practical integration. This highlights the necessity for novel approaches. An emerging paradigm in this direction is critical quantum metrology, which harnesses the enhanced susceptibility and nonclassical correlations that naturally occur near quantum phase transitions as resources for quantum-enhanced precision. This tutorial provides a pedagogical introduction to key concepts and a detailed overview of prominent quantum sensing strategies that exploit critical phenomena in metrology. Through examples of increasing complexity, the reader is guided through various critical quantum sensing protocols applied to different critical systems. Special emphasis is placed on the optimal scaling of estimation precision with respect to fundamental resources. Finally, we discuss how critical quantum metrology extends from idealized models to realistic open-system, dissipative regimes, and strongly correlated fermionic systems, outlining both the challenges and opportunities for future quantum technologies.

The power of quantum random number generation is more than just the ability to create truly random numbers—it can also enable self-testing, which allows the user to verify the implementation integrity of critical quantum components with minimal assumptions. In this work, we develop and implement a self-testing quantum random number generator (QRNG) chipset capable of generating 15.33 Mbits of certifiable randomness in each run, producing an expansion rate of $5.11\times {10}^{-4}$ at a repetition rate of 10 MHz, with quantum side information considered for a high level of security. The chip design is based on a highly loss-and-noise-tolerant measurement-device-independent protocol, where random coherent states encoded using quadrature phase shift keying are used to self-test the integrated homodyne detectors—well-known to be challenging to characterize in practice. Importantly, this proposal opens up the possibility of implementing miniaturized self-testing QRNG devices at production scale using standard silicon photonics foundry platforms.

Recent studies of monitored quantum dynamics have revealed that projective measurements, traditionally viewed as decohering operations, can instead generate and sustain long-range entanglement. Motivated by these, we ask how many physical qubits must be measured in random basis to irreversibly destroy quantum information encoded in a quantum error-correcting code. We study this problem for a broad class of stabilizer and subsystem codes, derive necessary and sufficient conditions for measurement-induced information destruction, and show that many codes, including concatenated and topological codes, achieve the maximal measurement threshold $p_m^{\mathrm{th}}=1$, meaning that the encoded information survives as long as arbitrarily small but finite fraction of physical qubits remain unmeasured. Beyond this surprising robustness, we find a structural relation underlying maximal thresholds. Namely, we prove that if the Pauli basis of the logical operator measured at full measurement does not concentrate on a single Pauli, then the measurement threshold always satisfies $p_m^{\mathrm{th}}=1$. This result uncovers a structural relation between logical measurement statistics and stability under partial measurement, revealing a general mechanism by which access to measurement outcomes enhances decodability under monitored dynamics.

We introduce Single-Shot Cross-Spectroscopy (SSCS), a method for extracting the auto- and cross-power spectral densities of dephasing noise in a qubit pair. The method uses straightforward input, namely, single-shot readouts from single-qubit Ramsey-type experiments, without requiring the reconstruction of qubit energy fluctuations from repeated measurements, and is resilient against errors in state preparation and measurement. We apply it to experimental data from a semiconductor spin-qubit device and obtain noise spectra over five orders of magnitude in frequency (5 mHz–500 Hz). Compared to other techniques, for spin qubits, SSCS enables access to noise correlations in the previously inaccessible intermediate-frequency range (1–500 Hz), and can be further extended with faster readout. The method is directly applicable to other qubit platforms, and the upper frequency it can probe is set by the repetition rate of a single-qubit preparation and measurement.

We introduce a universal dilation framework to simulate arbitrary non-Hermitian dynamics $\dot{\mathit{x}}=L(t)\mathit{x}$ on unitary quantum processors. By imposing algebraic moment-matching conditions on an ancilla, our framework generates diverse families of dilation schemes that unify existing methods and broaden the design space for hardware-aware implementations. A tight-binding dilation that maps the ancilla to a 1D lattice with nearest-neighbor hopping is derived, overcoming the connectivity bottlenecks of dilation schemes. This construction handles general dynamics, including gain, without a priori rescaling and achieves near-optimal complexity, as demonstrated by benchmarks on dissipative wave propagations.

We develop protocols for generating loss-tolerant quantum tree-codes; these are designed to safeguard information against qubit losses, with wide applications in quantum communications. Contrary to previous proposals, our method enables top-to-bottom fast encoding and decoding, thereby reducing losses due to the lagging and photon-reordering at the repeater stations. At the hardware level, we show how to achieve this with a single quantum emitter equipped with a static feedback mechanism, which we leverage to engineer entangling gates between a fed-back qubit and multiple emitted qubits in parallel. In addition, analyzing typical patterns within the error-correction decoding graphs, we find optimizations of the structure of tree-codes, which enable improved performance by also reducing the code size; these are based on the introduction of asymmetries in the code, which mimic the intrinsic adaptiveness of the recovery procedure. We show numerically that these improvements together significantly enhance the loss-correction performance. Specifically, focusing on quantum repeater protocols, we show that our fast recovery scheme (decoding-encoding) allows for improved repeater rates with smaller photon numbers per code.

Photon blockade—the suppression of multiphoton transmission by quantum nonlinearities—enables on-demand nonclassical light, but it typically requires strong single-emitter coupling and does not improve by simply adding more emitters. We show that this limitation can be overcome when an ensemble of $N$ identical two-level emitters couples to a single cavity mode through a two-photon exchange interaction. Using input-output theory together with a hierarchy of open-system descriptions (exact numerics, a Holstein-Primakoff model, and an approximated analytical treatment), we characterize the steady-state transmission and photon statistics of the two-photon Tavis-Cummings model. We find that blockade is collectively enhanced: the optimal antibunching improves with atom number ($1/N^2$ scaling of the second-order correlation function) while maintaining near-unit transmission, eliminating the usual brightness-purity trade-off of interference-based weak-coupling schemes. We further identify driving configurations that yield collectively enhanced two-photon blockade, with strong suppression of higher-order autocorrelation functions that deepens with increasing $N$. The nonclassicality is ultimately limited by decoherence, with emitter dephasing providing the dominant constraint. These results establish collective two-photon light-matter coupling as a scalable route to photon blockade in platforms where individual strong coupling is not achievable.

Wide-band gap oxides such as $\mathrm{Zn}\mathrm{O}$ are favorable hosts for spin defect qubits due to their dilute nuclear spin background and potential for ultrahigh purity. Yet, a deep-level defect qubit with robust optical and spin properties has not been identified in this material. Here, using first-principles calculations, we predict that the molybdenum-vacancy complex, $({\mathrm{Mo}}_{\mathrm{Zn}}{\mathrm{v}}_{\mathrm{O}}{)}^{2+}$, exhibits the essential characteristics of an optically addressable spin qubit: a spin-triplet ground state, visible-range optical transitions with high quantum yield, and an unusually small Huang-Rhys factor ($\sim 5$, compared to 10–30 in known $\mathrm{Zn}\mathrm{O}$ defects). We further find long spin coherence times (${\mathrm{T}}_2\sim 4\mathrm{ms}$) when both nuclear and impurity spin baths are considered, with paramagnetic impurities setting a threshold concentration of 0.035 ppm. Importantly, the combination of strong spin-orbit coupling and the absence of Jahn-Teller distortion supports spin-selective intersystem crossing and high-fidelity single-shot readout at elevated temperatures and across wide magnetic field ranges. By identifying ZnO as a host for deep-level defect qubits, our work points toward a pathway to scalable, integrable oxide-based quantum technologies and broadens the material foundation for solid-state quantum information science.

Variational counterdiabatic (CD) driving is a disciplined and widely used method to robustly control quantum many-body systems by mimicking adiabatic processes with high fidelity and reduced duration. Central to this technique is a universal structure of the adiabatic gauge potential (AGP) over a parameterized Hamiltonian. Here, we reveal that introducing a new degree of freedom into the theory of the AGP can significantly improve variational CD driving. Specifically, we find that the algebraic characterization of the AGP is not unique, and we exploit this nonuniqueness to develop the weighted variational method for deriving a refined driving protocol. This approach extends the conventional method in two aspects: it assigns customized weights to matrix elements relevant to specific problems, and it effectively incorporates nonlocal information into local driving coefficients. We also develop an efficient numerical algorithm to compute the refined driving protocol using computer algebra. Our framework is broadly applicable and, in principle, it can replace any previous use of variational CD driving. We demonstrate its practicality by applying it to adiabatic evolution along the ground state of a parameterized Hamiltonian. This proposal outperforms the conventional method in terms of fidelity, as confirmed by extensive numerical simulations on quantum Ising models.

Quantum compilers that reduce the number of $T$ gates are essential for minimizing the overhead of fault-tolerant quantum computation. Achieving further $T$-count reduction calls for identifying equivalent circuit transformation rules beyond those utilized in existing tools. In this paper, we rewrite any given $\mathrm{Clifford}+T$ circuit using a Clifford block followed by a sequential Pauli-based computation and introduce a nontrivial, ancilla-free transformation rule, the multiproduct commutation relation (MCR). MCR constructs gate sequences based on specific commutation properties among multi-Pauli operators, yielding seemingly noncommutative instances that can be commuted, thereby enabling gate orderings that cannot be derived from pairwise commutation alone. We also propose the MCR Compiler, which incorporates MCR-based transformations as an optimization pass. To evaluate its effect, we use a benchmark circuit dataset generated through quantum circuit unoptimization. This approach intentionally adds redundancy to the circuit while keeping its equivalence, allowing a quantitative evaluation of compiler performance by comparison with the original circuit. Our numerical experiments reveal that the MCR Compiler achieves further $T$-count reduction beyond current compilers, establishing MCR-based transformations as a practical optimization primitive. These results highlight an untapped opportunity to enhance the optimization capabilities of quantum compilers.

Nondegenerate Josephson mixers (JMs), formed by coupling two different transmission-line resonators to Josephson ring modulators (JRMs), are vital and versatile devices capable of processing microwave signals at the quantum limit. Owing to the lossless nondegenerate three-wave mixing process enabled by the JRM, JMs can perform phase-preserving amplification of quantum signals, generate two-mode squeezed states, and perform noiseless frequency conversion. However, due to their limited bandwidth and saturation power, such resonator-based JMs are generally unable to simultaneously process frequency-multiplexed signals required in large quantum processors. To overcome this longstanding dual challenge, we redesign the JRM parameters by optimizing its inductances to suppress higher order mixing products and engineer its electromagnetic environment by incorporating lumped-element coupled-mode networks between the JRM and the two distinct ports of the JM. By implementing these strategies, we measure for JMs realized with four coupled modes per port, operated in amplification (conversion), bandwidths of about 400 MHz (700 MHz) with power reflections above 10 dB (below $-10$ dB) and saturation powers of about $-110$ dBm at 15 dB ($-91$ dBm at $-26$ dB). Similarly, we demonstrate for a low external quality factor resonant-mode JM operated in conversion, a maximum bandwidth of about 670 MHz with power reflections below $-10$ dB and a maximum saturation power of about $-86$ dBm at $-17$ dB. Such nondegenerate JMs with enhanced bandwidths and saturation powers could serve in a variety of frequency-multiplexed settings ranging from high-fidelity qubit readout and unidirectional routing of quantum signals to the generation of remote entanglement with continuous variables.

Quantum computing experiments have made remarkable progress in demonstrating key components of error-corrected quantum computing, a prerequisite for scalable quantum computation. While we anticipate the near-term arrival of early fault-tolerant quantum hardware capable of a million reliable quantum operations, the cost of preparing low-noise “magic resource states,” which are necessary for performing universal quantum computation, presents a formidable challenge. The recently proposed partially fault-tolerant architecture based on a space-time efficient analog rotation (STAR) approach attempts to address this challenge by using postselection to prepare low-noise, arbitrary small-angle magic states. Its proposed physical implementation, however, assumes fixed qubit connectivity, resulting in implementation costs closer to leading fully fault-tolerant approaches. In this work, we propose the transversal STAR architecture and co-design it with neutral-atom quantum hardware, deriving explicit and significant savings in logical layout, time, and space overhead. Through detailed circuit-level simulations, we derive the logical noise model for surface-code-based transversal STAR gadgets and verify their composability. At its limit, the transversal STAR architecture with neutral atoms can efficiently simulate local Hamiltonians with a total simulation volume exceeding 600, defined as the product of the number of logical qubits and Hamiltonian evolution timescales. Achieving this limit would require approximately 10 000 physical qubits at a physical error rate of ${10}^{-3}$. This is equivalent to a fully fault-tolerant computation requiring over ${10}^6$–${10}^{7}T$ gates and a potential $>100\times$ saving on space-time volume for equivalent simulation over current, state-of-the-art protocols. Finally, we extend the transversal STAR architecture to high-rate quantum low-density parity-check codes, demonstrating how a limited set of highly parallel transversal Clifford gates and generalized small-angle magic injection can be utilized for effective quantum simulation. We anticipate that the co-designed transversal STAR architecture could substantially reduce the physical resources necessary for early fault-tolerant quantum simulation at the megaquop scale.

Typical security proofs for quantum key distribution (QKD) rely on having some model for the devices, with the security guarantees implicitly relying on the values of various parameters of the model, such as dark count rates or detector efficiencies. Hence to deploy QKD in practice, we must establish how to certify or characterize the model parameters of a manufacturer’s QKD devices. We present a rigorous framework for analyzing such procedures, laying out concrete requirements for both the security proofs and the certification or characterization procedures. In doing so, we describe various forms of conclusions that can and cannot be validly drawn from such procedures, addressing some potential misconceptions. We also discuss connections to composable security frameworks and some technical aspects that remain to be resolved in that direction.

Protecting qubits from perturbations is a central challenge in quantum computing. Topological superconductors with separated Majorana bound states (MBSs) provide a strong form of protection that only depends on the locality of perturbations. While the link between MBS separation, robust degeneracy, and protected braiding is well understood in noninteracting systems, recent experimental progress in short quantum-dot-based Kitaev chains highlights the need to establish these connections rigorously for interacting systems. We do this by defining MBSs from many-body ground states and show how their locality constrains their coupling to an environment. This, in turn, quantifies the protection of the energy degeneracy and the feasibility of non-abelian braiding.

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains challenging due to the exponential growth of Hilbert space dimension and rapid spreading of entanglement. In this work, we introduce Fourier neural operators (FNOs) as an efficient, accurate, and scalable framework for nonequilibrium quantum dynamics. Parameterized in Fourier space, FNO naturally captures temporal correlations and remains minimally dependent on discretization of time. We demonstrate the versatility of FNO through three complementary learning paradigms: reconstructing effective Floquet Hamiltonians, predicting expectation values of local observables, and learning quantum information spreading. For each learning task, FNO achieves remarkable accuracy, while attaining a significant speedup, compared to exact numerical methods. Moreover, FNO possesses capabilities beyond that of conventional methods, such as predicting all local observables from a subset of measurements without information about the Hamiltonian, as well as extrapolating beyond the time window provided by training data, enabling access to observables and operator-spreading dynamics that might be beyond the coherence time. By employing a spatially local basis, we argue that the computational cost of FNOs scales only polynomially with the system size. Our results establish FNO as a versatile and scalable computation framework that integrates numerical simulations and experimental data seamlessly, with direct implications for extracting meaningful physics from measurements by near-term quantum computers.

We propose an erasure conversion scheme on the $|e⟩-|f⟩$ and $|g⟩-|f⟩$ qubits in integer fluxonium qubits (IFQs), which are both first-order insensitive to $1/f$ flux noise. The $|e⟩-|f⟩$ transition is identical to that of a usual fluxonium qubit and hence is expected to have excellent coherence time, while the $|g⟩-|f⟩$ transition is additionally protected from the energy relaxation by the parity symmetry. The dominant error in both qubits arises due to the energy relaxation: from $|e⟩$ to $|g⟩$ in the e-f qubit and from $|f⟩$ to $|e⟩$ in the g-f qubit. Such errors can be treated as erasure events, and their efficient detection improves the performance of quantum error-correcting codes. We consider a protocol for such erasure conversion based on the dispersive readout. Our main finding is that, with proper circuit parameter choice, carefully designed gate sets, and the integration of erasure conversion, IFQs promise highly effective coherence times.

Dynamical decoupling is a central technique in quantum computing for actively suppressing decoherence and systematic imperfections through sequences of single-qubit operations. Conventional sequences typically aim to completely freeze system dynamics, often resulting in long protocols whose length scales exponentially with system size. In this work, we introduce a general framework for constructing time-optimal, selectively tailored sequences that remove only specific local interactions. By combining techniques from graph coloring and classical coding theory, our approach enables compact and hardware-tailored sequences across diverse qubit platforms, efficiently canceling undesired Hamiltonian terms while preserving target interactions. This opens up broad applications in quantum computing and simulation. At the core of our method is a mapping between dynamical decoupling sequence design and error-detecting codes, which allows us to leverage powerful coding-theoretic tools to construct customized sequences. To overcome exponential overheads, we exploit symmetries in colored interaction hypergraphs, extending graph-coloring strategies to arbitrary many-body Hamiltonians. We demonstrate the effectiveness of our framework through concrete examples, including compact sequences that suppress residual ZZ and ZZZ interactions in superconducting qubits and Heisenberg exchange coupling in spin qubits. We also show how it enables Hamiltonian engineering by simulating the anisotropic Kitaev honeycomb model using only isotropic Heisenberg interactions.

Identifying the symmetry properties of quantum states is a central theme in quantum information theory and quantum many-body physics. In this work, we investigate quantum learning problems in which the goal is to identify a hidden symmetry of an unknown quantum state. Building on the recent formulation of the state hidden subgroup problem (StateHSP), we focus on abelian groups and develop an efficient quantum algorithm that learns any hidden symmetry subgroup using a generalized form of Fourier sampling. We showcase the versatility of the approach in three concrete applications: These are learning (i) qubit and qudit stabilizer groups, (ii) cuts along which a state is unentangled, and (iii) hidden translation symmetries. Through these applications, we reveal that well-known quantum learning primitives, such as Bell sampling and Bell difference sampling, are, in fact, special cases of Fourier sampling. Our results highlight the broad potential of the StateHSP framework for symmetry-based quantum learning tasks and provide protocols that are easier to implement on near-term quantum devices.