Distributing entanglement between remote sites is integral to quantum networks. Here, we demonstrate the autonomous stabilization of remote entanglement between a pair of noninteracting superconducting qubits connected by an open waveguide on a chip. In this setting, the interplay between a classical continuous drive—supplied through the waveguide—and dissipation into the waveguide stabilizes the qubit pair in a dark state, which, asymptotically, takes the form of a Bell state. We use field-quadrature measurements of the photons emitted to the waveguide to perform quantum state tomography on the stabilized states, where we find a concurrence of ${0.504}_{-0.029}^{+0.007}$ in the optimal setting with a stabilization time constant of $56\pm 4$ ns. We examine the imperfections within our system and discuss avenues for enhancing fidelities and achieving scalability in future work. The decoherence-protected steady-state remote entanglement offered via dissipative stabilization may find applications in distributed quantum computing, sensing, and communication.

We propose an efficient yet simple protocol to generate arbitrary symmetric entangled states with only global single-qubit rotations in a torn Hilbert space. The system is based on spin-1/2 qubits in a resonator such as atoms in an optical cavity or superconducting qubits coupled to a main bus. By sending light or microwave into the resonator, it induces ac Stark shifts on particular angular-momentum eigenstates (Dicke states) of qubits. Then we are able to generate barriers that hinder transitions between adjacent Dicke states and tear the original Hilbert space into pieces. Therefore, a simple global single-qubit rotation becomes highly nontrivial, and thus generates entanglement among the many-body system. By optimal control of energy shifts on Dicke states, we are able to generate arbitrary symmetric entangled states. We also exemplify that we can create varieties of useful states with near-unity fidelities in only one or very few steps, including W states, spin-squeezed states (SSSs), and Greenberger-Horne-Zeilinger states. Particularly, the SSS can be created by only one step with a squeezing parameter ${\xi }_R^2\sim 1/N^{0.843}$ approaching the Heisenberg limit. Our finding establishes a way for universal entanglement generations with only single-qubit drivings where all the multiple-qubit controls are integrated into simply switching on or off microwave. It has direct applications in the variational quantum optimizer, which is available with existing technology.

Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. Recently, it has been shown that the Affleck-Kennedy-Lieb-Tasaki state—a paradigmatic example of an MPS—can be exactly prepared with an adaptive quantum circuit of constant depth, an impossible feat with local unitary gates alone due to its nonzero correlation length [Smith et al., PRX Quantum 4, 020315 (2023)]. In this work, we broaden the scope of this approach and demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming theoretically optimal preparation with unitary circuits. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. We present sufficient conditions for particular MPS to be preparable in constant time, with global on-site symmetry playing a pivotal role. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states and provides explicit algorithms that outperform known protocols to prepare an essential class of states.

A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling algorithms based on Wigner functions, with the important distinction that Wigner functions can take negative values obstructing the sampling. Indeed, negativity in Wigner functions has been identified as a precondition for a quantum speed-up. However, in the present method of classical simulation, negativity of quasiprobability functions never arises. This model remains probabilistic for all quantum computations. In this paper, we analyze the amount of classical data that the simulation procedure must track. We find that this amount is small. Specifically, for any number $n$ of magic states, the number of bits that describe the quantum system at any given time is $2n^2+O(n)$.

In computer and system sciences, higher-order cellular automata (HOCA) are a type of cellular automata that evolve over multiple time steps and generate complex patterns, which have various applications, such as secret-sharing schemes, data compression, and image encryption. In this paper, we introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter, in which symmetries are supported on a great variety of subsystems embbeded in the SPT bulk. We call these phases HOCA-generated SPT (HGSPT) phases. Specifically, we show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., linelike subsystems in the two-dimensional cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems. One example is mixed-subsystem SPT that has either fractal and linelike subsystem symmetries simultaneously or two distinct types of fractal symmetries simultaneously. Another example is chaotic-subsystem SPT in which chaotic-looking symmetries are significantly different from and thus cannot reduce to fractal or regular subsystem symmetries. We also introduce a new notation system to characterize HGSPTs. We prove that all possible subsystem symmetries in a square lattice can be locally simulated by an HOCA-generated symmetry. As the usual two-point strange correlators are trivial in most HGSPTs, we find that the nontrivial SPT orders can be detected by what we call multi point strange correlators. We propose a universal procedure to design the spatial configuration of the multi point strange correlators for a given HGSPT phase. Specifically, we find deep connections between multi point strange correlators and the spurious topological entanglement entropy (STEE), both exhibiting long-range behavior in a short-range entangled state. Our HOCA approaches and multi point strange correlators pave the way for a unified paradigm to design, classify, and detect phases of matter with symmetries supported on a great variety of subsystems, and also provide potential useful perspective in surpassing the computational irreducibility of HOCA in a quantum mechanical way.

Phase slips occur across all Josephson junctions (JJs) at a rate that increases with the impedance of the junction. In superconducting qubits composed of JJ-array superinductors—such as fluxonium—phase slips in the array can lead to decoherence. In particular, phase-slip processes at the individual array junctions can coherently interfere, each with an Aharonov-Casher phase that depends on the offset charges of the array islands. These coherent quantum phase slips (CQPS) perturbatively modify the qubit frequency, and therefore charge noise on the array islands will lead to dephasing. By varying the impedance of the array junctions, we design a set of fluxonium qubits in which the expected phase-slip rate within the JJ array changes by several orders of magnitude. We characterize the coherence times of these qubits and demonstrate that the scaling of CQPS-induced dephasing rates agrees with our theoretical model. Furthermore, we perform noise spectroscopy of two qubits in regimes dominated by either CQPS or flux noise. We find that the noise power spectrum associated with CQPS dephasing appears to be featureless at low frequencies and not $1/f$. Numerical simulations indicate that this behavior is consistent with charge noise generated by charge-parity fluctuations within the array. Our findings broadly inform JJ-array-design trade-offs, relevant for the numerous superconducting-qubit designs employing JJ-array superinductors.

We propose a novel variational ansatz for the ground-state preparation of the ${\mathbb{Z}}_2$ lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve $>99\mathrm{\%}$ precision in energy in both the confined and deconfined phase of the ${\mathbb{Z}}_2$ LGT. We benchmark our proposal against the unitary Hamiltonian variational ansatz showing a reduction in the required number of variational layers to achieve a target precision. After performing a finite-size scaling analysis, we show that our dissipative variational ansatz can predict accurate critical exponents without requiring a number of layers that scales with the system size, which is the standard situation for unitary ansätze. Furthermore, we investigate the performance of this variational eigensolver subject to circuit-level noise, determining variational error thresholds that fix the error rate below which it would be beneficial to increase the number of layers. In light of these quantities and for typical gate errors $p$ in current quantum processors, we provide a detailed assessment of the prospects of our scheme to explore the ${\mathbb{Z}}_2$ LGT on near-term devices.

Quantum simulation traditionally relies on unitary dynamics, inherently imposing efficiency constraints on the generation of intricate entangled states. In principle, these limitations can be superseded by nonunitary, dynamic circuits. These circuits exploit measurements alongside conditional feed-forward operations, providing a promising approach for long-range entangling gates, higher effective connectivity of near-term hardware, and more efficient state preparations. Here, we explore the utility of shallow dynamic circuits for creating long-range entanglement on large-scale quantum devices. Specifically, we study two tasks: controlled-not gate teleportation between up to 101 qubits by feeding forward 99 midcircuit measurement outcomes, and the preparation of Greenberger–Horne–Zeilinger states with genuine entanglement. In the former, we observe that dynamic circuits can outperform their unitary counterparts. In the latter, by tallying instructions of compiled quantum circuits, we provide an error budget detailing the obstacles that must be addressed to unlock the full potential of dynamic circuits. Looking forward, we expect dynamic circuits to be useful for generating long-range entanglement in the near term on large-scale quantum devices.

We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that converge to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful for metrological applications. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust regarding drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberger-Horne-Zeilinger states, observing genuine multipartite entanglement. Then we prepare the ground state of the transverse-field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by our increasing the circuit depth.

The properties of superconducting devices depend sensitively on the parity (even or odd) of the quasiparticles that they contain. Encoding quantum information in the parity degree of freedom is central in several emerging solid-state qubit architectures, including in hybrid superconductor-semiconductor devices. In the latter case, accurate, nondestructive, and time-resolved parity measurements are a challenging issue. Here, we report on control and real-time parity measurement in a superconducting island embedded in a superconducting loop and realized in a hybrid two-dimensional heterostructure using a microwave resonator. To avoid microwave losses impeding time-resolved measurements, the device and readout resonator are located on separate chips, connected via flip-chip bonding, and couple inductively through vacuum. The superconducting resonator detects the parity-dependent circuit inductance, allowing for fast parity readout. We have resolved even- and odd-parity states with a signal-to-noise ratio of $\mathrm{SNR}\approx 3$ for an integration time of $20\text{μ}\mathrm{s}$ and a detection fidelity exceeding $98\mathrm{\%}$. The real-time parity measurement shows a state lifetime extending into the millisecond range. Our approach will lead to a better understanding of coherence-limiting mechanisms in superconducting quantum hardware and help to advance inductive-readout schemes for hybrid qubits.

We use a bulk acoustic wave resonator to demonstrate coherent control of the excited orbital states in a diamond nitrogen-vacancy ($\text{N}$$\mathrm{V}$) center at cryogenic temperature. Coherent quantum control is an essential tool for understanding and mitigating decoherence. Moreover, characterizing and controlling orbital states is a central challenge for quantum networking, where optical coherence is tied to orbital coherence. We study resonant multiphonon orbital Rabi oscillations in both the frequency and time domain, extracting the strength of the orbital-phonon interactions and the coherence of the acoustically driven orbital states. We reach the strong-driving limit, where the physics is dominated by the coupling induced by the acoustic waves. We find agreement between our measurements, quantum master-equation simulations, and a Landau-Zener transition model in the strong-driving limit. Using perturbation theory, we derive an expression for the orbital Rabi frequency versus the acoustic drive strength that is nonperturbative in the drive strength and agrees well with our measurements for all acoustic powers. Motivated by continuous-wave spin-resonance-based decoherence protection schemes, we model the orbital decoherence and find good agreement between our model and our measured few-to-several-nanoseconds orbital decoherence times. We discuss the outlook for orbital decoherence protection.

The coupling of an isolated quantum state to a continuum is typically associated with decoherence and decreased lifetime. For coupling rates larger than the bandwidth of the associated continuum, decoherence can be mitigated, and new stable eigenstates emerge. Here, we laser-couple diatomic molecules of highly excited Rydberg atoms, so-called Rydberg macrodimers, to a continuum of free motional states. Enabled by their small vibrational eigenfrequencies, we achieve the regime of strong continuum couplings and observe the appearance of new resonances. We explain the observed spectroscopic features as molecular states emerging in the presence of the light field using a Fano model. For atoms arranged on a lattice, we predict the strong continuum coupling to even stabilize triatomic molecules and find the first signatures of these by observing three-atom loss correlations using quantum gas microscopy. Our results present a mechanism to control decoherence and bind polyatomic molecules using strong light-matter interactions.

We introduce binary randomized benchmarking (BiRB), a protocol that streamlines traditional RB by using circuits consisting almost entirely of independent identically distributed (IID) layers of gates. BiRB reliably and efficiently extracts the average error rate of a Clifford gate set by sending tensor-product eigenstates of random Pauli operators through random circuits with IID layers. Unlike existing RB methods, BiRB does not use motion reversal circuits—i.e., circuits that implement the identity (or a Pauli) operator—which simplifies both the method and the theory proving its reliability. Furthermore, this simplicity enables scaling BiRB to many more qubits than the most widely used RB methods.

In ab initio electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step from the problem of fermions into a problem of qubits. This work introduces a physically inspired method for constructing mappings that significantly simplify entanglement requirements when one is simulating states of interest. The presence of electronic excitations drives the construction of our mappings, reducing correlations for target states in the qubit space. To benchmark our method, we simulate ground-states of small molecules and observe an enhanced performance when compared with classical and quantum variational approaches from prior research using conventional mappings. In particular, on the quantum side, our mappings require a reduced number of entangling layers to achieve accuracy for $\mathrm{LiH}$, ${\mathrm{H}}_2$, $({\mathrm{H}}_2{)}_2$, ${\mathrm{H}}_4^{\ne }$ stretching, and benzene’s $\pi$ system using the RY hardware-efficient ansatz. In addition, our mappings also provide an enhanced ground-state simulation performance in the density matrix renormalization group algorithm for the ${\mathrm{N}}_2$ molecule.

The classical simulation of highly entangling quantum dynamics is conjectured to be generically hard. Thus, recently discovered measurement-induced transitions between highly entangling and low-entanglement dynamics are phase transitions in classical simulability. Here, we study simulability transitions beyond entanglement: noting that some highly entangling dynamics (e.g., integrable systems or Clifford circuits) are easy to classically simulate, thus requiring “magic”—a subtle form of quantum resource—to achieve computational hardness, we ask how the dynamics of magic competes with measurements. We study the resulting “dynamical magic transitions” focusing on random monitored Clifford circuits doped by $T$ gates (injecting magic). We identify dynamical “stabilizer purification”—the collapse of a superposition of stabilizer states by measurements—as the mechanism driving this transition. We find cases where transitions in magic and entanglement coincide, but also others with a magic and simulability transition in a highly (volume-law) entangled phase. In establishing our results, we use Pauli-based computation, a scheme distilling the quantum essence of the dynamics to a magic state register subject to mutually commuting measurements. We link stabilizer purification to “magic fragmentation” wherein these measurements separate into disjoint, $\mathcal{O}(1)$-weight blocks, and relate this to the spread of magic in the original circuit becoming arrested.

Optical quantum information processing relies critically on Bell-state measurement, a ubiquitous operation for quantum communication and computing. Its practical realization involves the interference of optical modes and the detection of a single photon in an indistinguishable manner. Yet, in the absence of efficient photon-number-resolution capabilities, errors arise from multiphoton components, decreasing the overall process fidelity. Here, we introduce a hybrid detection scheme for Bell-state measurement, leveraging both on-off single-photon detection and quadrature conditioning via homodyne detection. We derive explicit fidelities for quantum teleportation and entanglement-swapping processes employing this strategy, demonstrating its efficacy. We also compare with photon-number-resolving detectors and find a strong advantage of the hybrid scheme in a wide range of parameters. This work provides a new tool for linear-optics schemes, with applications to quantum state engineering and quantum interconnects.

The distribution of high-fidelity high-rate entanglement over telecommunication infrastructure is one of the main paths toward large-scale quantum networks, enabling applications such as quantum encryption and network protection, blind quantum computing, distributed quantum computing, and distributed quantum sensing. However, the fragile nature of entangled photons operating in real-world fiber infrastructure has historically limited continuous operation of such networks. Here, we present a fully automated system capable of distributing polarization-entangled photons over a 34-km deployed fiber in New York City, achieving high rates of nearly $5\times {10}^5$ pairs/s. Separately, we demonstrate a high fidelity of approximately $99\mathrm{\%}$ for rates up to $2\times {10}^4$ pairs/s. Lastly, we achieve 15 days of continuous distribution, with a network up-time of $99.84\mathrm{\%}$. Our work paves the way for practical deployment of always-on entanglement-based networks with rates and fidelity adequate for many current and future use cases.

Monitored quantum many-body systems display a rich pattern of entanglement dynamics, which is unique to this nonunitary setting. This work studies the effect of quantum jumps on the entanglement dynamics beyond the no-click limit corresponding to a deterministic non-Hermitian evolution. To this aim, we introduce a new tool that looks at the statistics of entanglement-entropy gain and loss after and in between quantum jumps. This insight allows us to build a simple stochastic model of a random walk with partial resetting, which reproduces the entanglement dynamics, and to dissect the mutual role of jumps and non-Hermitian evolution on the entanglement scaling. We apply these ideas to the study of measurement-induced transitions in monitored fermions. We demonstrate that significant deviations from the no-click limit arise whenever quantum jumps strongly renormalize the non-Hermitian dynamics, as in the case of models with $U(1)$ symmetry at weak monitoring. On the other hand, we show that the weak-monitoring phase of the Ising chain leads to a robust subvolume logarithmic phase due to weakly renormalized non-Hermitian dynamics.

In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The algorithm applies to ${\mathbb{Z}}_d$ qudits, including instances where $d$ is a nonprime number. This capability allows the identification of topological orders that differ from the ${\mathbb{Z}}_d$ toric codes. It extends our understanding beyond the established theorem that Pauli stabilizer codes for ${\mathbb{Z}}_p$ qudits (with $p$ being a prime) are equivalent to finite copies of ${\mathbb{Z}}_p$ toric codes and trivial stabilizers. The algorithm is designed to determine all anyons and their string operators, enabling the computation of their fusion rules, topological spins, and braiding statistics. The method converts the identification of topological orders into computational tasks, including Gaussian elimination, the Hermite normal form, and the Smith normal form of truncated Laurent polynomials. Furthermore, the algorithm provides a systematic approach for studying quantum error-correcting codes. We apply it to various codes, such as self-dual CSS quantum codes modified from the two-dimensional honeycomb color code and non-CSS quantum codes that contain the double semion topological order or the six-semion topological order.

We investigate phase transitions in the encoding of quantum information in a quantum many-body system due to the competing effects of unitary scrambling and boundary dissipation. Specifically, we study the fate of quantum information in a one-dimensional qudit chain, subject to local unitary quantum circuit evolution in the presence of depolarizing noise at the boundary. If the qudit chain initially contains a finite amount of locally accessible quantum information, unitary evolution in the presence of boundary dissipation allows this information to remain partially protected when the dissipation is sufficiently weak, and up to timescales growing linearly in the system size $L$. In contrast, for strong enough dissipation, this information is completely lost to the dissipative environment. We analytically investigate this “quantum coding transition” by considering dynamics involving Haar-random, local unitary gates, and confirm our predictions in numerical simulations of Clifford quantum circuits. Scrambling the quantum information in the qudit chain with a unitary circuit of depth $\mathcal{O}(\log L)$ before the onset of dissipation can perfectly protect the information until late times. The nature of the coding transition changes when the dynamics extend for times much longer than $L$. We further show that at weak dissipation, it is possible to code at a finite rate, i.e., a fraction of the many-body Hilbert space of the qudit chain can be used to encode quantum information.