Quantum spin Hall insulators (QSHIs) host helical electronic edge states that are protected from backscattering due to time-reversal symmetry (TRS). Despite considerable work investigating QSHI edge states, there is still an open question about their unexpected resilience to large magnetic fields where TRS is undoubtedly broken. In this work, we investigate the transport properties of helical edge states in a QSHI-superconductor (QSHI-SC) junction formed by a $\mathrm{In}\mathrm{As}$(15 nm)/$\mathrm{Ga}\mathrm{Sb}$(5 nm) double quantum well and a superconducting tantalum ($\mathrm{Ta}$) constriction. We observe a robust conductance plateau up to 2 T, signaling resilient edge-state transport. Using a modified Landauer-Büttiker analysis, we find that the zero-field conductance is consistent with 98% Andreev-reflection probability owing to the high transparency of the ($\mathrm{In}\mathrm{As}$/$\mathrm{Ga}\mathrm{Sb}$)-$\mathrm{Ta}$ interface. Such resilience is consistent with the Dirac point for the edge states being buried in the bulk valence band. We further theoretically show that a buried Dirac point does not affect the robustness of the quasi-one-dimensional topological superconducting phase. We find that a buried Dirac point favors the hybridization of Majorana Kramers pairs (MKPs)—predicted to exist in a QSHI-SC constriction—and fermionic modes in the QSHI vacuum edge resulting in extended MKP states, highlighting the subtle role of buried Dirac points in probing MKPs.

The double descent phenomenon challenges traditional statistical learning theory by revealing scenarios where larger models do not necessarily lead to reduced performance on unseen data. While this counterintuitive behavior has been observed in a variety of classical machine learning models, particularly modern neural network architectures, it remains elusive within the context of quantum machine learning. In this work, we analytically demonstrate that linear regression models in quantum feature spaces can exhibit double descent behavior by drawing on insights from classical linear regression and random matrix theory. Additionally, our numerical experiments on quantum kernel methods across different real-world datasets and system sizes further confirm the existence of a test error peak, a characteristic feature of double descent. Our findings provide evidence that quantum models can operate in the modern, overparameterized regime without experiencing overfitting, potentially opening pathways to improved learning performance beyond traditional statistical learning theory.

We construct examples of highly entangled two-dimensional states by exploiting a correspondence between stochastic processes in $d$ dimensions and quantum states in $d+1$ dimensions. The entanglement structure of these states, which we explicitly calculate, can be tuned between area law, sub-volume law, and volume law. This correspondence also enables a sequential generation protocol: the states can be prepared through a series of unitary transformations acting on an auxiliary system. We also discuss the conditions under which these states have local, frustration-free parent Hamiltonians.

To implement arbitrary quantum circuits in architectures with restricted interactions, one may effectively simulate all-to-all connectivity by routing quantum information. We consider the entanglement dynamics and routing between two regions only connected through an intermediate “bottleneck” region with few qubits. In such systems, where the entanglement rate is restricted by a vertex boundary rather than an edge boundary of the underlying interaction graph, existing results such as the small incremental entangling theorem give only a trivial constant lower bound on the routing time (the minimum time to perform an arbitrary permutation). We significantly improve the lower bound on the routing time in systems with a vertex bottleneck. Specifically, for any system with two regions $L,R$ with $N_L,N_R$ qubits, respectively, coupled only through an intermediate region $C$ with $N_C$ qubits, for any $\delta >0$ we show a lower bound of $\mathrm{\Omega }(N_R^{1-\delta }/\sqrt{N_L}{N}_C)$ on the Hamiltonian quantum routing time when using piecewise time-independent Hamiltonians, or time-dependent Hamiltonians subject to a smoothness condition. We also prove an upper bound on the average amount of bipartite entanglement between $L$ and $C,R$ that can be generated in time $t$ by such architecture-respecting Hamiltonians in systems constrained by vertex bottlenecks, improving the scaling in the system size from $O(N_{L}t)$ to $O(\sqrt{N_L}t)$. As a special case, when applied to the star graph (i.e., one vertex connected to $N$ leaves), we obtain an $\mathrm{\Omega }(\sqrt{N^{1-\delta }})$ lower bound on the routing time and on the time to prepare $N/2$ Bell pairs between the vertices. We also show that, in systems of free particles, we can route optimally on the star graph in time $\mathrm{\Theta }(\sqrt{N})$ using Hamiltonian quantum routing, obtaining a speedup over gate-based routing, which takes time $\mathrm{\Theta }(N)$.

Estimating the fidelity between a desired target quantum state and an actual prepared state is essential for assessing the success of experiments. For pure target states, we use functional representations that can be measured directly and determine the number of copies of the prepared state needed for fidelity estimation. In continuous variable (CV) systems, we use the Wigner function, which can be measured via displaced parity measurements. We provide upper and lower bounds on the sample complexity required for fidelity estimation, considering the worst-case scenario across all possible prepared states. For target states of particular interest, such as Fock and Gaussian states, we find that this sample complexity is characterized by the $L^1$-norm of the Wigner function, a measure of Wigner negativity widely studied in the literature, in particular in resource theories of quantum computation. For discrete variable systems consisting of $n$ qubits, we explore fidelity estimation protocols using Pauli string measurements. Similarly as for the CV approach, the sample complexity is shown to be characterized by the $L^1$-norm of the characteristic function of the target state for both Haar random states and stabilizer states. Furthermore, in a general black box model, we prove that, for any target state, the optimal sample complexity for fidelity estimation is characterized by the smoothed $L^1$-norm of the target state. To the best of our knowledge, this is the first time the $L^1$-norm of the Wigner function provides a lower bound on the cost of some information processing task.

The simplicity of encoding a qubit in the state of a single electron spin and the potential for their integration into industry-standard microchips continue to drive the field of semiconductor-based quantum computing. After a series of key first-principles demonstrations validating universal gate operations, initialization and readout, three-qubit algorithms have already been realized with silicon-based quantum dots in past years. Devices containing more qubits have become available since then but experiments have not gone beyond meeting the DiVincenzo criteria. In this work, we fully exploit the capacity of a spin-qubit array and implement a six-qubit quantum circuit, the largest utilizing semiconductor quantum technology. By programming the quantum processor, we execute quantum circuits across all permutations of three, four, five, and six neighboring qubits, demonstrating successful programmable multi-qubit operation throughout the array. Using an error model that incorporates quasi-static noise allows us to qualitatively explain some key trends in our experimental results and highlight the necessity to minimize idling times through simultaneous operations, extending dephasing times, and consistently improving state preparation and measurement fidelities.

Many-body localization, an emergent quantum phenomenon, challenges the fundamental principles of thermodynamics and has attracted significant attention. In this study, we demonstrate Stark many-body localization in a one-dimensional Bose gas under the continuous limit, a scenario that extends well beyond the conventional tight-binding model commonly employed in most discussions. This localization occurs within a background harmonic trap without any random disorder, where the potential gradient effectively halts thermalization. Contrary to prior studies on Stark localization, our findings reveal that an increasing gradient does not necessarily lead to greater localization. Instead, we observe a complex transition within this continuous interacting system. Another surprising result is that a higher initial density, which typically correlates with a higher collisional rate and thermalization rate, actually induces stronger localization in this one-dimensional model. Additionally, we observe a density plateau with zero compressibility and low-density fluctuations, which may signal an insulating behavior associated with prethermalization during nonequilibrium dynamics.

Protected superconducting qubits such as the 0-$\pi$ qubit promise to substantially reduce physical error rates. However, a key challenge in the field is designing gates for these qubits that do not compromise their protection or become infeasibly slow as the protection of the qubit is improved. In this work we propose a protected phase gate that is compatible with the protected regime of the 0-$\pi$ qubit and does not suffer from spurious coupling to additional circuit modes. Our gate utilizes an internal mode of the circuit as an ancilla and is achieved by varying the qubit-ancilla coupling via a tunable Josephson element. Through numerical simulations, we study how the gate error scales with the circuit parameters of the 0-$\pi$ qubit and the tunable Josephson element that enacts the gate. Ultimately, we find that a protected gate with the 0-$\pi$ qubit is possible with near-term circuit parameters. Our work opens up the possibility of performing protected gates on protected superconducting qubits, which may significantly reduce hardware overheads for quantum computation.

Understanding quantum noise is an essential step towards building practical quantum information processing systems. Pauli noise is a useful model that has been widely applied in quantum benchmarking, error mitigation, and error correction. Despite intensive study into Pauli noise learning, most existing works focus on learning Pauli channels associated with some specific gates rather than treating the gate set as a whole. A learning algorithm that is self-consistent, complete, and efficient at the same time has yet to be established. In this work, we study the task of gate set Pauli noise learning, where a set of quantum gates, state preparation, and measurements all suffer from unknown Pauli noise channels with a customized noise ansatz. Using tools from algebraic graph theory, we analytically characterize the self-consistently learnable degrees of freedom for Pauli noise models with arbitrary linear ansatz, and design experiments to efficiently learn all the learnable information. Specifically, we show that all learnable information about the gate noise can be learned to relative precision, under mild assumptions on the noise ansatz. We then demonstrate the flexibility of our theory by applying it to concrete physically motivated ansatze (such as spatially local or quasi-local noise) and experimentally relevant gate sets (such as parallel CZ gates). These results not only enhance the theoretical understanding of quantum noise learning, but also provide a feasible recipe for characterizing existing and near-future quantum computing devices.

We develop a comprehensive framework for characterizing fluctuations in quantum transport and nonequilibrium thermodynamics using two complementary approaches: full counting statistics and first-passage times. Focusing on open quantum systems governed by Markovian Lindblad dynamics, we derive general ensemble relations that connect the two approaches at all times, and we clarify how the steady states reached at long times relate to those reached at large jump counts. In regimes of metastability, long-lived intermediate states cause violations of experimentally testable cumulant relations, as we discuss. We also formulate a fluctuation theorem governing the probability of rare fluctuations in the first-passage time distributions based on results from full counting statistics. Our results apply to general integer-valued trajectory observables that do not necessarily increase monotonically in time. Three illustrative applications, a two-state emitter, a driven qubit, and a variant of the Su-Schrieffer-Heeger model, highlight the physical implications of our results and provide guidelines for practical calculations. Our framework provides a complete picture of first-passage time statistics in Markovian quantum systems, encompassing multiple earlier results, and it has direct implications for current experiments in quantum optics, superconducting circuits, and nanoscale heat engines.

This tutorial offers a pedagogical guide to hybrid quantum processors that integrate discrete-variable (DV) qubits and continuous-variable (CV) oscillators. Aimed at computer scientists, engineers, and physicists, it provides an overview of the experimental, algorithmic, and architectural aspects of this novel and rapidly developing hardware model. Experimental realizations of this model include superconducting, trapped-ion, and neutral-atom platforms. By combining DV and CV components, hybrid oscillator-qubit processors enable a powerful new paradigm that offers complementary strengths for quantum control, error correction, computation, and simulation. Working toward the goal of a full-stack system connecting applications to CV-DV hardware, we define and formulate abstract machine models and instruction set architectures. These essential abstractions enable codesign of hardware and software, and resource estimation for exploring the potential of current and future hardware for computational and simulation tasks. Using these abstractions, we present both new and existing examples that illustrate the benefits of hybrid CV-DV processors relative to traditional DV-only hardware in computation as well as quantum simulation of physical models. Examples include algorithms for transferring states between DV and CV systems, performing the quantum Fourier transform, and simulation of lattice gauge theories. Relative to qubit-only hardware, the bosonic degrees of freedom natively available in hybrid architectures can substantially reduce the circuit complexity of simulations for physical models containing bosons. A key technique is the extension of quantum signal processing ideas to CV-DV systems. This work is intended to serve as a timely and comprehensive guide to this relatively unexplored yet promising approach to quantum computation and to provide a road map to guide future development.

Precise state-dependent control of optical potentials is of great importance for various applications utilizing cold neutral atoms. In particular, tune-out wavelengths for the clock state pair in alkaline-earth(-like) atoms provide maximally state-selective trap conditions that hold promise for the realization of novel approaches in quantum computation and simulation. While several ground-state tune-out wavelengths have been determined, similar experimental studies for metastable excited states are challenged by inelastic collisions and Raman losses, so far prohibiting precise measurements of excited-state tune-out conditions. In this work we report on the measurement of a tune-out wavelength for the metastable ${}^3{\mathrm{P}}_0$ clock state in ${}^{\text{174}}\mathrm{Yb}$ at $519.920(9)$ THz. In order to circumvent collisional losses, we isolate individual ${}^3{\mathrm{P}}_0$ atoms in a two-dimensional clock-magic-wavelength lattice at 759 nm. To minimize the limitation imposed by Raman scattering, we further implement resolved sideband cooling on the clock transition, which allows us to reduce the lattice depth and surpass lifetimes of 5 s. The precision of the tune-out measurement is further enhanced by fluorescence imaging in a triple-magic configuration, where we implement molasses cooling on the ${}^3{\mathrm{P}}_1$ intercombination line and identify a magic angle of $38.5(9{)}^{\circ }$ in the clock-magic lattice.

Understanding the computational complexity of quantum states is a central challenge in quantum many-body physics. In qubit systems, fermionic Gaussian states can be efficiently simulated on classical computers and hence can be employed as a natural baseline for evaluating quantum complexity. In this work, we develop a framework for quantifying fermionic magic resources, also referred to as fermionic non-Gaussianity, which constitutes an essential resource for universal quantum computation. We leverage the algebraic structure of the fermionic commutant to define the fermionic antiflatness (FAF)—an efficiently computable and experimentally accessible measure of non-Gaussianity, with a clear physical interpretation in terms of Majorana fermion correlation functions. Studying systems in equilibrium, we show that FAF detects phase transitions, reveals universal features of critical points, and uncovers special solvable points in many-body systems. Extending the analysis to out-of-equilibrium settings, we demonstrate that fermionic magic resources become more abundant in highly excited eigenstates of many-body systems. We further investigate the growth and saturation of FAF under ergodic many-body dynamics, highlighting the roles of conservation laws and locality in constraining the increase of non-Gaussianity during unitary evolution. This work provides a framework for probing quantum many-body complexity from the perspective of fermionic Gaussian states and opens up directions for investigating fermionic magic resources in many-body systems. Our results establish fermionic non-Gaussianity, alongside entanglement and nonstabilizerness, as a resource relevant not only to foundational studies but also to experimental platforms aiming to achieve quantum advantage.

Discovering low-overhead quantum error-correcting codes is of significant interest for fault-tolerant quantum computation. For hardware capable of long-range connectivity, the bivariate bicycle codes offer significant overhead reduction compared to surface codes with similar performance. In this work, we present “Z semidirect Z (ZSZ) codes,” a simple nonabelian generalization of the bivariate bicycle codes based on the group ${\mathbb{Z}}_{\ell }⋊{\mathbb{Z}}_m$. We numerically demonstrate that certain instances of this code family achieve competitive performance with the bivariate bicycle codes under circuit-level depolarizing noise using a belief-propagation and ordered-statistics decoder, with an observed threshold around $0.5\mathrm{\%}$. We also benchmark the performance of this code family under local “self-correcting” decoders, where we observe significant improvements over the bivariate bicycle codes, including evidence of a sustainable threshold around $0.095\mathrm{\%}$, which is higher than the $0.06\mathrm{\%}$ that we estimate for the four-dimensional toric code under the same noise model. These results suggest that ZSZ codes are promising candidates for scalable self-correcting quantum memories. Finally, we describe how ZSZ codes can be realized with neutral atoms trapped in movable tweezer arrays, where a complete round of syndrome extraction can be achieved using simple global motions of the atomic arrays.

We study the interplay between magic and entanglement in quantum many-body systems. We show that nonlocal magic, which is supported by the quantum correlations is lower bounded by the nonflatness of entanglement spectrum and upper bounded by the amount of entanglement in the system. We then argue that a smoothed version of nonlocal magic bounds the hardness of classical simulations for incompressible states. In conformal field theories (CFTs), we conjecture that the nonlocal magic should scale linearly with entanglement entropy but sublinearly when an approximation of the state is allowed. We support the conjectures using both analytical arguments based on unitary distillation and numerical data from an Ising CFT. If the CFT has a holographic dual, then we prove that the nonlocal magic vanishes if and only if there is no gravitational backreaction. Furthermore, we show that nonlocal magic is approximately equal to the rate of change of the minimal surface area in response to the change of cosmic brane tension in the bulk.

We present a quantum process-tomography protocol based on a low-degree ansatz for the quantum channel, i.e., when it can be expressed as a fixed-degree polynomial in terms of Pauli operators. We demonstrate how to perform tomography of such channels with a logarithmic amount of effort relative to the size of the system, by employing random state preparation and measurements in the Pauli basis. We extend the applicability of the protocol to channels consisting of a layer of quantum gates with a polylogarithmic number of non-Clifford gates, followed by a low-degree noise channel. Rather than inverting the layer of quantum gates on the hardware—which would introduce additional errors—we instead carry out the inversion in classical postprocessing, while adding to the sample complexity a factor at most polynomial in system size. Numerical simulations support our theoretical findings and demonstrate the feasibility of our method.

Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. Subaşı et al. [Phys. Rev. Lett. 122, 060504 (2019)] proposed a randomized algorithm inspired by adiabatic quantum computing, based on a sequence of random Hamiltonian simulation steps, with suboptimal scaling in the condition number $\kappa$ of the linear system and the target error $ϵ$. Here we go beyond these results in several ways. Firstly, using filtering [Lin and Tong, Quantum 4, 361 (2020)] and Poissonization techniques [Cunningham and Roland, ArXiv:2406.03972 (2024)], the algorithm complexity is improved to the optimal scaling $O(\kappa \log (1/ϵ))$—an exponential improvement in $ϵ$, and a shaving of a $\log \kappa$ scaling factor in $\kappa$. Secondly, the algorithm is further modified to achieve constant factor improvements, which are vital as we progress towards hardware implementations on fault-tolerant devices. We introduce a cheaper randomized walk operator method replacing Hamiltonian simulation—which also removes the need for potentially challenging classical precomputations; randomized routines are sampled over optimized random variables; circuit constructions are improved. We obtain a closed formula rigorously upper bounding the expected number of times one needs to apply a block-encoding of the linear system matrix to output a quantum state encoding the solution to the linear system. The upper bound is $837\kappa$ at $ϵ={10}^{-10}$ for Hermitian matrices.

In circuit-based quantum state preparation, qubit loss and coherent errors are circuit imperfections that imperil the formation of long-range entanglement beyond a certain threshold. The critical theory at the threshold is a continuous entanglement transition known to be described by a $(2+0)$-dimensional nonunitary conformal field theory which, for the two types of imperfections of certain circuits, is described by either percolation or Nishimori criticality, respectively. Here we study the threshold behavior when the two types of errors simultaneously occur and show that, when moving away from the Clifford regime of projective stabilizer measurements, the percolation critical point becomes unstable and the critical theory flows to Nishimori universality. We track this critical renormalization group (RG) crossover flow by mapping out the entanglement phase diagrams, parametrized by the probability and strength of random weak measurements, of two dual protocols preparing surface code or GHZ-class cat states from a parent cluster state via constant-depth circuits. Extensive numerical simulations, using hybrid Gaussian fermion and tensor network/Monte Carlo sampling techniques on systems with more than a million qubits, demonstrate that an infinitesimal deviation from the Clifford regime leads to a sudden, strongly nonmonotonic entanglement growth at the incipient nonunitary RG flow. We argue that spectra of scaling dimensions of both the percolation and Nishimori fixed points exhibit multifractality. For percolation, we provide the exact (nonquadratic) multifractal spectrum of exponents, while for the Nishimori fixed point we show high-precision numerical results for five leading exponents characterizing multifractality.

Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications. Recently, as a new approach to this problem, the task of agnostic state tomography was defined, in which one aims to approximate an arbitrary quantum state by a simpler one in a given class. Generalizing this notion to quantum processes, we initiate the study of agnostic process tomography: given query access to an unknown quantum channel $\mathrm{\Phi }$ and a known concept class $\mathcal{C}$ of channels, output a quantum channel that approximates $\mathrm{\Phi }$ as well as any channel in the concept class $\mathcal{C}$, up to some error. In this work, we propose several natural applications for this new task in quantum machine learning, quantum metrology, classical simulation, and error mitigation. In addition, we give efficient agnostic process tomography algorithms for a wide variety of concept classes, including Pauli strings, Pauli channels, quantum junta channels, low-degree channels, and a class of channels produced by ${\mathsf{Q}\mathsf{A}\mathsf{C}}^0$ circuits. The main technical tool we use is Pauli spectrum analysis of operators and superoperators. We also prove that, using ancilla qubits, any agnostic state tomography algorithm can be extended to one solving agnostic process tomography for a compatible concept class of unitaries, immediately giving us efficient agnostic learning algorithms for Clifford circuits, Clifford circuits with few T gates, and circuits consisting of a tensor product of single-qubit gates. Together, our results provide insight into the conditions and new algorithms necessary to extend the learnability of a concept class from the standard tomographic setting to the agnostic one.

The electronic energy level structure of yttrium monoxide (YO) provides a long-lived, low-lying ${}^2\mathrm{\Delta }$ state ideal for high-precision molecular spectroscopy, narrowline laser cooling at the single photon-recoil limit, and studying dipolar physics with unprecedented interaction strength. High-resolution laser spectroscopy of ultracold laser-cooled YO molecules is used to study the Stark effect in the ${\mathrm{A}}^{\mathrm{\prime }}{}^2{\mathrm{\Delta }}_{3/2}J=3/2$ state. An immediate onset of the linear Stark effect is observed in the presence of weak applied electric fields due to the near-degenerate $\mathrm{\Lambda }$ doublet and the large electric dipole moment. By applying a small electric field the Stark-insensitive state is spectroscopically isolated and the absolute transition frequency to the $\mathrm{X}{}^2{\mathrm{\Sigma }}^{+}$ electronic ground state is determined with a fractional frequency uncertainty of $9\times {10}^{-12}$. This electric field control is necessary to implement a quasi-closed photon-cycling scheme that preserves parity. With this scheme the first narrowline laser cooling of a molecule is demonstrated, reducing the temperature of sub-Doppler cooled YO in two dimensions.