Quantum error correction is necessary to perform large-scale quantum computation but requires extremely large overheads in both space and time. High-rate quantum low-density-parity-check (qLDPC) codes promise a route to reduce qubit numbers, but performing computation while maintaining low space cost has required serialization of operations and extra time costs. In this work, we design fast and parallelizable logical gates for qLDPC codes and demonstrate their utility for key algorithmic subroutines such as the quantum adder. Our gate gadgets utilize transversal logical cnots between a data qLDPC code and a suitably constructed ancilla code to perform parallel Pauli product measurements (PPMs) on the data logical qubits. For hypergraph product codes, we show that the ancilla can be constructed by simply modifying the base classical codes of the data code, achieving parallel PPMs on a subgrid of the logical qubits with a lower space-time cost than existing schemes for an important class of circuits. Generalizations to 3D and 4D homological product codes further feature fast PPMs in constant depth. While prior work on qLDPC codes has focused on individual logical gates, we initiate the study of fault-tolerant compilation with our expanded set of native qLDPC code operations, constructing algorithmic primitives for preparing $k$-qubit Greenberger-Horne-Zeilinger states and distilling or teleporting $k$ magic states with $O(1)$ space overhead in $O(1)$ and $O(\sqrt{k}\log k)$ logical cycles, respectively. We further generalize this to key algorithmic subroutines, demonstrating the efficient implementation of quantum adders using parallel operations. Our constructions are naturally compatible with reconfigurable architectures such as neutral atom arrays, paving the way to large-scale quantum computation with low space and time overheads.

We propose a tensor network approach known as the locally purified density operator (LPDO) to investigate the classification and characterization of symmetry-protected topological phases in open quantum systems. We extend the concept of injectivity, originally associated with matrix product states and projected entangled pair states, to LPDOs in $(1+1)\mathrm{D}$ and $(2+1)\mathrm{D}$ systems, unveiling two distinct types of injectivity conditions that are inherent for short-range entangled density matrices. Within the LPDO framework, we outline a classification scheme for decohered average symmetry-protected topological (ASPT) phases, consistent with earlier results obtained through spectrum sequence techniques. However, our approach offers an intuitive and explicit construction of ASPT states with the decorated domain-wall picture emerging naturally. We illustrate our framework with ASPT phases protected by a weak global symmetry and strong fermion parity symmetry and then extend it to a general group structure. Moreover, we derive both the classification data and the explicit forms of the obstruction functions using the LPDO formalism, particularly in the case of nontrivial group extension between strong and weak symmetries, where intrinsic ASPT phases may emerge. We demonstrate constructions of fixed-point LPDOs for ASPT phases in both $(1+1)\mathrm{D}$ and $(2+1)\mathrm{D}$ and discuss their physical realization in decohered or disordered systems. In particular, we construct examples of intrinsic ASPT states in $(1+1)\mathrm{D}$ and $(2+1)\mathrm{D}$ using the LPDO formalism.

We analyze the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement entropy of such postmeasurement states, we prove that macroscopic long-ranged entanglement is generated above some constant critical depth in several natural classes of circuit architectures, which include brickwork circuits and random holographic tensor networks. This behavior had been conjectured based on previous works, which utilize nonrigorous methods such as replica theory calculations, or work in regimes where the local Hilbert space dimension grows with system size. To establish our lower bound, we develop new replica-free theoretical techniques that leverage tools from multiuser quantum information theory, which are of independent interest, allowing us to map the problem onto a statistical mechanics model of self-avoiding walks without requiring large local Hilbert space dimension. Our findings have consequences for the complexity of classically simulating sampling from random shallow circuits and of contracting tensor networks. First, we show that standard algorithms based on matrix product states which are used for both these tasks will fail above some constant depth and bond dimension, respectively. In addition, we also prove that these random constant-depth quantum circuits cannot be simulated by any classical circuit of sublogarithmic depth.

Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited scalability of current near-term algorithms. Meanwhile, assuming a typical architecture for fault-tolerant quantum computing (FTQC), realistic applications inevitably require a vast number of qubits, typically exceeding ${10}^6$, which seems far beyond near-term realization. In this work, to bridge the gap between the NISQ and FTQC eras, we propose an alternative approach to achieve practical quantum advantages on early-FTQC devices. Our framework is based on partially fault-tolerant logical operations to minimize spatial overhead and avoids the costly distillation techniques typically required for executing non-Clifford gates. To this end, we develop a space-time efficient state preparation protocol to generate an ancillary non-Clifford state consumed for implementing an analog rotation gate with an arbitrary small angle $\theta$ and a remarkably low worst-case error rate below $\mathcal{O}(|\theta |p_{\mathrm{ph}})$, where $p_{\mathrm{ph}}$ is the physical error rate. Furthermore, we propose several error suppression schemes tailored to our preparation protocol, which are essential to minimize the overhead for mitigating errors. Based on this framework, we present several promising applications that leverage the potential of our framework, including the Trotter simulation and quantum phase estimation (QPE). Notably, we demonstrate that our framework allows us to perform the QPE for an $(8\times 8)$-site Hubbard model with fewer than $6.8\times {10}^4$ qubits and an execution time of 10.6 days (or 14 min with full parallelization) under $p_{\mathrm{ph}}={10}^{-4}$, which is significantly faster than recent classical estimation with tensor network techniques (density matrix renormalization group and projected entangled pair states).

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of approximately 50 qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and, therefore, how much infidelity is suffered) in generating highly entangled states. Here, we describe recent hardware upgrades to Quantinuum’s H2 quantum computer, enabling it to operate on up to 56 qubits with arbitrary connectivity and 99.843(5)% two-qubit gate fidelity. We define a class of circuits with random geometries that become hard to classically simulate in very low depth and implement them utilizing the flexible connectivity of H2. A careful analysis demonstrating the fast saturation of classical simulation complexity with depth indicates that H2 can yield data well beyond the reach of state-of-the art classical simulation methods at unprecedented fidelities. We find that the considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the quantum charge-coupled device architecture as continued progress is made toward building larger machines.

Noise on quantum devices is much more complex than it is commonly given credit. Far from usual models of decoherence, nearly all quantum devices are plagued by both a continuum of environments and temporal instabilities. These induce noisy quantum and classical correlations at the level of the circuit. The relevant spatiotemporal effects are difficult enough to understand, let alone combat. There is presently a lack of either scalable or complete methods to address the phenomena responsible for scrambling and loss of quantum information. Here, we make deep strides to remedy this problem. We establish a theoretical framework that uniformly incorporates and classifies all non-Markovian phenomena. Our framework is universal, assumes no parameters values, and is written entirely in terms of experimentally accessible circuit-level quantities. We formulate an efficient reconstruction using tensor network learning, allowing also for easy modularization and simplification based on the expected physics of the system. This is then demonstrated through both extensive numerical studies and implementations on IBM Quantum devices, estimating a comprehensive set of spacetime correlations. Finally, we conclude our analysis with applications thereof to the efficacy of control techniques to counteract these effects—including noise-aware circuit compilation and optimized dynamical decoupling. We find significant improvements are possible in the diamond norm and average gate fidelity of arbitrary SU(4) operations, as well as related decoupling improvements in contrast to off-the-shelf schemes.

Quantum key distribution (QKD) provides information-theoretic security for communication. The mode-pairing (MP) protocol emerges as a promising solution for long-distance QKD by eliminating the need for a global phase reference while maintaining the repeaterlike rate-loss scaling. Recent implementations have demonstrated its potential, but they either rely on costly ultrastable lasers or struggle with phase fluctuations from commercial lasers, particularly over long distances. As a result, surpassing the repeaterless bound with a practical system remains a challenge. In this work, we demonstrate a practical high-performance MP-QKD system using commercial lasers. To address phase fluctuations, we propose a frequency-tracking scheme based on fast Fourier transformation, enabling us to extend the pairing length to $2\times {10}^5$ pulses ($160\mathrm{\mu }\mathrm{s}$). We propose a model to carefully analyze the phase noise and optimize the system parameters. Our system achieves an optimal secret key rate of $47.8\mathrm{bit}/\mathrm{s}$ over 403 km of standard fiber (76.5 dB loss), exceeding the repeaterless bound by a factor of 2.92. Furthermore, we compare MP-QKD and twin-field QKD under various practical conditions and clarify the distinct application scenarios of the two protocols. These results confirm the feasibility of MP-QKD using cost-effective commercial technologies, paving the way for scalable quantum communication networks.

Arrays of gate-defined semiconductor quantum dots are among the leading candidates for building scalable quantum processors. High-fidelity initialization, control, and readout of spin qubit registers require exquisite and targeted control over key Hamiltonian parameters that define the electrostatic environment. However, due to the tight gate pitch, capacitive crosstalk between gates hinders independent tuning of chemical potentials and interdot couplings. While virtual gates offer a practical solution, determining all the required cross-capacitance matrices accurately and efficiently in large quantum dot registers is an open challenge. Here, we establish a modular automated virtualization system (MAViS)—a general and modular framework for autonomously constructing a complete stack of multilayer virtual gates in real time. Our method employs machine learning techniques to rapidly extract features from two-dimensional charge stability diagrams. We then utilize computer vision and regression models to self-consistently determine all relative capacitive couplings necessary for virtualizing plunger and barrier gates in both low- and high-tunnel-coupling regimes. Using MAViS, we successfully demonstrate accurate virtualization of a dense two-dimensional array comprising ten quantum dots defined in a high-quality $\mathrm{Ge}/\mathrm{SiGe}$ heterostructure. Our work offers an elegant and practical solution for the efficient control of large-scale semiconductor quantum dot systems.

Quantum nonlocality describes a stronger form of quantum correlation than that of entanglement. It refutes Einstein’s belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning. Nevertheless, the detection of nonlocality, especially in quantum many-body systems, is notoriously challenging. Here, we report an experimental certification of genuine multipartite Bell-operator correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor. In particular, we employ energy as a Bell-operator correlation witness and variationally decrease the energy of a many-body system across a hierarchy of thresholds, below which an increasing Bell-operator correlation depth can be certified from experimental data. We variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell-operator correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations. In addition, we variationally prepare a sequence of low-energy states and certify their genuine multipartite Bell-operator correlations up to 24 qubits via energies measured efficiently by parity oscillation and multiple quantum coherence techniques. Our results establish a viable approach for preparing and certifying multipartite Bell-operator correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide toward exploiting multipartite Bell correlations in a wide spectrum of practical applications.

Local random circuits scramble efficiently and, accordingly, have a range of applications in quantum information and quantum dynamics. With a global U(1) charge, however, the scrambling ability is reduced; for example, such random circuits do not generate the entire group of number-conserving unitaries. We establish two results using the statistical mechanics of $k$-fold replicated circuits. First, we show that finite moments cannot distinguish the ensemble that local random circuits generate from the Haar ensemble on the entire group of number-conserving unitaries. Specifically, the circuits form a $k_c$-design with $k_c=O(L^d)$ for a system in $d$ spatial dimensions with linear dimension $L$. Second, for $k<k_c$, we derive bounds on the depth $\tau$ required for the circuit to converge to an approximate $k$-design. The depth is lower bounded by diffusion $k{L}^2\ln (L)\lesssim \tau$. In contrast, without number conservation $\tau \sim \mathrm{poly}(k)L$. The convergence of the circuit ensemble is controlled by the low-energy properties of a frustration-free quantum statistical model which spontaneously breaks $k$ U(1) symmetries. We conjecture that the associated Goldstone modes set the spectral gap for arbitrary spatial and qudit dimensions, leading to an upper bound $\tau \lesssim k{L}^{d+2}$.

Many-body open quantum systems, described by Lindbladian master equations, are a rich class of physical models that display complex equilibrium and out-of-equilibrium phenomena which remain to be understood. In this paper, we theoretically analyze noisy analog quantum simulation of geometrically local open quantum systems and provide evidence that this problem both is hard to simulate on classical computers and could be approximately solved on near-term quantum devices. First, given a noiseless quantum simulator, we show that the dynamics of local observables and the fixed-point expectation values of rapidly mixing local observables in geometrically local Lindbladians can be obtained to a precision of $ϵ$ in time that is $\mathrm{poly}({ϵ}^{-1})$ and uniform in system size. Furthermore, we establish that the quantum simulator would provide a superpolynomial advantage, in run-time scaling with respect to the target precision and either the evolution time (when simulating dynamics) or the Lindbladian’s decay rate (when simulating fixed points), over any classical algorithm for these problems, assuming $\mathrm{BQP}\ne \mathrm{BPP}$. We then consider the presence of noise in the quantum simulator in the form of additional geometrically local Lindbladian terms. We show that the simulation tasks considered in this paper are stable to errors; i.e., they can be solved to a noise-limited, but system-size independent, precision. Finally, we establish that, assuming $\mathrm{BQP}\ne \mathrm{BPP}$, there are stable geometrically local Lindbladian simulation problems such that, as the noise rate on the simulator is reduced, classical algorithms must take time superpolynomially longer in the inverse noise rate to attain the same precision as the analog quantum simulator.

Despite their importance in quantum theory, joint quantum measurements remain poorly understood. An intriguing conceptual and practical question is whether joint quantum measurements on separated systems can be performed without bringing them together. Remarkably, by using shared entanglement, this can be achieved perfectly when disregarding the postmeasurement state. However, existing localization protocols typically require unbounded entanglement. In this work, we address the fundamental question: “Which joint measurements can be localized with a finite amount of entanglement?” We develop finite-resource versions of teleportation-based schemes and analytically classify all two-qubit measurements that can be localized in the first levels of the resulting hierarchies. These levels include several measurements with exceptional properties and symmetries, such as the Bell state measurement and the elegant joint measurement. This leads us to propose a systematic classification of joint measurements based on entanglement cost, which we argue directly connects with the complexity of implementing those measurements. We illustrate how to numerically explore higher levels and construct generalizations to higher dimensions and multipartite settings.

Solid-state quantum registers consisting of optically active electron spins with nearby nuclear spins are promising building blocks for future quantum technologies. For electron spin-1 registers, dynamical decoupling (DD) quantum gates have been developed that enable the precise control of multiple nuclear spin qubits. However, for the important class of electron spin-$1/2$ systems, this control method suffers from intrinsic selectivity limitations, resulting in reduced nuclear spin gate fidelities. Here, we demonstrate improved control of single nuclear spins by an electron spin-$1/2$ using dynamically decoupled radio-frequency (DDRF) gates. We make use of the electron spin-$1/2$ of a diamond tin-vacancy center, showing high-fidelity single-qubit gates, single-shot readout, and spin coherence beyond a millisecond. The DD control is used as a benchmark to observe and control a single ${}^{1}3\mathrm{C}$ nuclear spin. Using the DDRF control method, we demonstrate improved control on that spin. In addition, we find and control an additional nuclear spin that is insensitive to the DD control method. Using these DDRF gates, we show entanglement between the electron and the nuclear spin with 72(3)% state fidelity. Our extensive simulations indicate that DDRF gate fidelities well in excess are feasible. Finally, we employ time-resolved photon detection during readout to quantify the hyperfine coupling for the electron’s optically excited state. Our work provides key insights into the challenges and opportunities for nuclear spin control in electron spin-$1/2$ systems, opening the door to multiqubit experiments on these promising qubit platforms.

Spins and oscillators are foundational to much of physics and applied sciences. For quantum information, a spin $1/2$ exemplifies the most basic unit, a qubit. High angular momentum spins (HAMSs) and harmonic oscillators provide multilevel manifolds which have the potential for hardware-efficient protected encodings of quantum information and simulation of many-body quantum systems. In this work, we demonstrate a new quantum control protocol that conceptually merges these disparate hardware platforms. Namely, we show how to modify a harmonic oscillator on demand to implement a continuous range of generators to accomplish linear and nonlinear HAMS dynamics. The spinlike dynamics are verified by demonstration of linear spin coherent [SU(2)] rotations, nonlinear spin rotations, and comparison to other manifolds like simply truncated oscillators. Our scheme allows universal control of a spin cat logical qubit encoding with interpretable drive pulses: We use linear operations to accomplish four logical gates and further show that nonlinear spin rotations can complete the logical gate set. Our results show how motion on a closed Hilbert space can be useful for quantum information processing and opens the door to superconducting circuit simulations of higher angular momentum quantum magnetism.

Bosonic pure-loss channel, which represents the process of photons decaying into a vacuum environment, has zero quantum capacity when the channel’s transmissivity is less than 50%. Modeled as a beam splitter interaction between the system and its environment, the performance of bosonic pure-loss channel can be enhanced by controlling the environment state. We show that by choosing the ideal Gottesman-Kitaev-Preskill (GKP) states for the system and its environment, perfect transmission of quantum information through a beam splitter is achievable at arbitrarily low transmissivities. Our explicit constructions allow for experimental demonstration of the improved performance of a quantum channel through passive environment assistance, which is potentially useful for quantum transduction where the environment state can be naturally controlled. In practice, it is crucial to consider finite-energy constraints, and high-fidelity quantum communication through a beam splitter remains achievable with GKP states at the few-photon level.

Following a consistent geometrical description previously introduced [Quantum 8, 1466 (2024)], we present an exact method for obtaining canonically quantizable Hamiltonian descriptions of nonlinear, nonreciprocal quasilumped electrical networks. We identify and classify singularities arising in the quest for Hamiltonian descriptions of general quasilumped element networks via the Faddeev-Jackiw technique. We offer systematic solutions to cases previously considered singular—a major challenge in the context of canonical circuit quantization. The solution relies on the correct identification of the reduced classical circuit-state manifold, i.e., a mix of flux and charge fields and functions. Starting from the geometrical description of the transmission line, we provide a complete program including lines coupled to one-port lumped-element networks, as well as multiple lines connected to multiport nonreciprocal lumped-element networks, with intrinsic ultraviolet cutoff. On the way, we naturally extend the canonical quantization of transmission lines coupled through frequency-dependent, nonreciprocal linear systems, such as practical circulators. Additionally, we demonstrate how our method seamlessly facilitates the characterization of general nonreciprocal, dissipative linear environments. This is achieved by extending the Caldeira-Leggett formalism, using continuous limits of series of immittance matrices. We provide a tool in the analysis and design of electrical circuits and of special interest in the context of canonical quantization of superconducting networks. For instance, this work provides a solid ground for a precise nondivergent input-output theory in the presence of nonreciprocal devices, e.g., within (chiral) waveguide QED platforms.

Entanglement between photons and a quantum memory is a key component of quantum repeaters, which allow long-distance quantum entanglement distribution in the presence of fiber losses. Spin-photon entanglement has been implemented with a number of different atomic and solid-state qubits with long spin coherence times, but none directly emit photons into the $1.5\text{−}\mathrm{\mu }\mathrm{m}$ telecom band where losses in optical fibers are minimized. Here, we demonstrate spin-photon entanglement using a single rare earth ion in the solid-state ${\mathrm{Er}}^{3+}$ coupled to a silicon nanophotonic cavity, which directly emits photons at 1532.6 nm. We infer an entanglement fidelity of 73(3)% after propagating through 15.6 km of optical fiber. This work opens the door to large-scale quantum networks based ${\mathrm{Er}}^{3+}$ ions, leveraging scalable silicon device fabrication and spectral multiplexing.

Cat qubits, a type of bosonic qubit encoded in a harmonic oscillator, can exhibit an exponential noise bias against bit-flip errors with increasing mean photon number. Here, we focus on cat qubits stabilized by two-photon dissipation, where pairs of photons are added and removed from a harmonic oscillator by an auxiliary, lossy buffer mode. This process requires a large loss rate and strong nonlinearities of the buffer mode that must not degrade the coherence and linearity of the oscillator. In this work, we show how to overcome this challenge by coloring the loss environment of the buffer mode with a multipole filter and optimizing the circuit to take into account additional inductances in the buffer mode. Using these techniques, we achieve near-ideal enhancement of cat-qubit bit-flip times with increasing photon number, reaching over 0.1 s with a mean photon number of only 4. Concurrently, our cat qubit remains highly phase coherent, with phase-flip times corresponding to an effective lifetime of $T_{1,\mathrm{eff}}\simeq 70\mathrm{\mu }\mathrm{s}$, comparable with the bare oscillator lifetime. We achieve this performance even in the presence of an ancilla transmon, used for reading out the cat-qubit states, by engineering a tunable oscillator-ancilla dispersive coupling. Furthermore, the low nonlinearity of the harmonic oscillator mode allows us to perform pulsed cat-qubit stabilization, an important control primitive, where the stabilization can remain off for a significant fraction (e.g., two-thirds) of a $3\mathrm{\mu }\mathrm{s}$ cycle without degrading bit-flip times. These advances are important for the realization of scalable error correction with cat qubits, where large noise bias and low phase-flip error rate enable the use of hardware-efficient outer error-correcting codes.