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.

Encoding information redundantly using quantum error-correcting (QEC) codes allows one to overcome the inherent sensitivity to noise in quantum computers to ultimately achieve large-scale quantum computation. The Steane QEC method involves preparing an auxiliary logical qubit of the same QEC code as used for the data register. The data and auxiliary registers are then coupled with a logical controlled-not (cnot) gate, enabling a measurement of the auxiliary register to reveal the error syndrome. This study presents the implementation of multiple rounds of fault-tolerant (FT) Steane QEC on a trapped-ion quantum computer. Various QEC codes are employed and the results are compared to a previous experimental approach utilizing flag qubits. Our experimental findings show improved logical fidelities for Steane QEC and accompanying numerical simulations indicate an even larger performance advantage for quantum processors limited by entangling-gate errors. This establishes experimental Steane QEC as a competitive paradigm for FT quantum computing.

We show a dissipative phase transition in a driven nonlinear quantum oscillator in which a discrete time-translation symmetry is spontaneously broken in two different ways. The corresponding regimes display either discrete or incommensurate time-crystal order, which we analyze numerically and analytically beyond the classical limit, addressing observable dynamics, phenomenology in different (laboratory and rotating) frames, Liouvillian spectral features, and quantum fluctuations. Via an effective semiclassical description, we show that phase diffusion dominates in the incommensurate time crystal (or continuous time crystal in the rotating frame), which manifests as a band of eigenmodes with a lifetime growing linearly with the mean-field excitation number. Instead, in the discrete time-crystal phase, the leading fluctuation process corresponds to quantum activation with a single mode that has an exponentially growing lifetime. Interestingly, the transition between these two regimes manifests itself already in the quantum regime as a spectral singularity, namely, as an exceptional point mediating between phase diffusion and quantum activation. Finally, we discuss this transition between different time-crystal orders in the context of synchronization phenomena.

The generation and evolution of entanglement in many-body systems is an active area of research that spans multiple fields, from quantum information science to the simulation of quantum many-body systems encountered in condensed matter, subatomic physics, and quantum chemistry. Motivated by recent experiments exploring quantum information processing systems with electrons trapped above the surface of cryogenic noble gas substrates, we theoretically investigate the generation of motional entanglement between two electrons via their unscreened Coulomb interaction. The model system consists of two electrons confined in separate electrostatic traps that establish microwave-frequency quantized states of their motion. We compute the motional energy spectra of the electrons, as well as their entanglement, by diagonalizing the model Hamiltonian with respect to a single-particle Hartree product basis. We also compare our results with the predictions of an effective Hamiltonian. The computational procedure outlined here can be employed for device design and guidance of experimental implementations. In particular, the theoretical tools developed here can be used for fine-tuning and optimization of control parameters in future experiments with electrons trapped above the surface of superfluid helium or solid neon.

Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage—namely, a significant (in some cases exponential) speedup of numerical simulations. The rapid development of hardware devices with various realizations of qubits enables the execution of small-scale but representative applications on quantum computers. In particular, the high-energy physics community plays a pivotal role in accessing the power of quantum computing, since the field is a driving source for challenging computational problems. This concerns, on the theoretical side, the exploration of models that are very hard or even impossible to address with classical techniques and, on the experimental side, the enormous data challenge of newly emerging experiments, such as the upgrade of the Large Hadron Collider. In this Roadmap paper, led by CERN, DESY, and IBM, we provide the status of high-energy physics quantum computations and give examples of theoretical and experimental target benchmark applications, which can be addressed in the near future. Having in mind hardware with about 100 qubits capable of executing several thousand two-qubit gates, where possible, we also provide resource estimates for the examples given using error-mitigated quantum computing. The ultimate declared goal of this task force is therefore to trigger further research in the high-energy physics community to develop interesting use cases for demonstrations on near-term quantum computers.

Calculating the equilibrium properties of condensed-matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude $⟨\psi |e^{-i\hat{H}t}|\psi ⟩$ from initial states $|\psi ⟩$ and a time evolution under the Hamiltonian $\hat{H}$ up to short times $t$. In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a $16$-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error-mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm.

Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. Here, we introduce a fault-tolerant hybrid quantum computation by building on the advantages of both discrete-variable (DV) and continuous-variable (CV) systems. In particular, we define a CV-DV hybrid qubit with a bosonic cat code and a single photon, which is implementable in current photonic platforms. Due to the cat code encoded in the CV part, the predominant loss errors are readily correctable without multiqubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error-correction code such as a topological code, exploring their potential merit in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource efficient compared to all previous proposals in photonic platforms, allowing us to achieve a record-high loss threshold among existing CV and hybrid approaches. We discuss the realization of our approach not only in all-photonic platforms but also in other hybrid platforms including superconducting and trapped-ion systems, which allows us to find various efficient routes toward fault-tolerant quantum computing.

A leading approach to implementing small-scale quantum computers has been to use laser beams, focused to micron spot sizes, to address and entangle trapped ions in a linear crystal. Here we propose a method to implement individually addressed entangling gate interactions, but driven by microwave fields, with a spatial resolution of a few microns, corresponding to ${10}^{-5}$ microwave wavelengths. We experimentally demonstrate the ability to suppress the effect of the state-dependent force using a single ion, and find the required interaction introduces $3.7(4)\times {10}^{-4}$ error per emulated gate in a single-qubit benchmarking sequence. We model the scheme for a 17-qubit ion crystal, and find that any pair of ions should be addressable with an average crosstalk error of approximately ${10}^{-5}$.

Exploiting the power of quantum computation to realize superior machine learning algorithms has been a major research focus of recent years, but the prospects of quantum machine learning (QML) remain dampened by considerable technical challenges. A particularly significant issue is that generic QML models suffer from so-called barren plateaus in their training landscapes—large regions where cost function gradients vanish exponentially in the number of qubits employed, rendering large models effectively untrainable. A leading strategy for combating this effect is to build problem-specific models that take into account the symmetries of their data in order to focus on a smaller, relevant subset of Hilbert space. In this work, we introduce a family of rotationally equivariant QML models built upon the quantum Fourier transform, and leverage recent insights from the Lie-algebraic study of QML models to prove that (a subset of) our models do not exhibit barren plateaus. In addition to our analytical results we numerically test our rotationally equivariant models on a dataset of simulated scanning tunneling microscope images of phosphorus impurities in silicon, where rotational symmetry naturally arises, and find that they dramatically outperform their generic counterparts in practice.

We propose to use a quantum spin chain as a device to store and release energy coherently and we investigate the interplay between its internal correlations and outside decoherence. We employ the quantum Ising chain in a transverse field and our charging protocol consists of a sudden global quantum quench in the external field to take the system out of equilibrium. Interactions with the environment and decoherence phenomena can dissipate part of the work that the chain can supply after being charged, measured by the ergotropy. We find that overall, the system shows remarkably better performance, in terms of resilience, charging time, and energy storage, when topological frustration is introduced by setting antiferromagnetic interactions with an odd number of sites and periodic boundary conditions. Moreover, we show that in a simple discharging protocol to an external spin, only the frustrated chain can transfer work and not just heat.

We investigate and ascertain the ideal inputs to any finite-time physical process. We demonstrate that the expectation values of entropy flow, heat, and work can all be determined via Hermitian observables of the initial state. These Hermitian operators encapsulate the breadth of behavior and the ideal inputs for common thermodynamic objectives. We show how to construct these Hermitian operators from measurements of thermodynamic output from a finite number of effectively arbitrary inputs. The behavior of a small number of test inputs thus determines the full range of thermodynamic behavior from all inputs. For any process, entropy flow, heat, and work can all be extremized by pure input states—eigenstates of the respective operators. In contrast, the input states that minimize entropy production or maximize the change in free energy are nonpure mixed states obtained from the operators as the solution of a convex-optimization problem. To attain these, we provide an easily implementable gradient-descent method on the manifold of density matrices, where an analytic solution yields a valid direction of descent at each iterative step. Ideal inputs within a limited domain, and their associated thermodynamic operators, are obtained with less effort. This allows analysis of ideal thermodynamic inputs within quantum subspaces of infinite-dimensional quantum systems; it also allows analysis of ideal inputs in the classical limit. Our examples illustrate the diversity of “ideal” inputs: distinct initial states minimize entropy production, extremize the change in free energy, and maximize work extraction.

In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical nonunital noise sources with constant noise rates. We show that even in the presence of unital sources such as the depolarizing channel, the distribution, under the combined noise channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates—meaning that it is never too “flat”—regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths. As a consequence, our results shows that the complexity of random-circuit sampling under realistic noise is still an open question, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results.

Assembling and maintaining large arrays of individually addressable atoms is a key requirement for continued scaling of neutral-atom-based quantum computers and simulators. In this work, we demonstrate a new paradigm for assembly of atomic arrays, based on a synergistic combination of optical tweezers and cavity-enhanced optical lattices, and the incremental filling of a target array from a repetitively filled reservoir. In this protocol, the tweezers provide microscopic rearrangement of atoms, while the cavity-enhanced lattices enable the creation of large numbers of optical traps with sufficient depth for rapid low-loss imaging of atoms. We apply this protocol to demonstrate near-deterministic filling (99% per-site occupancy) of 1225-site arrays of optical traps. Because the reservoir is repeatedly filled with fresh atoms, the array can be maintained in a filled state indefinitely. We anticipate that this protocol will be compatible with mid-circuit reloading of atoms into a quantum processor, which will be a key capability for running large-scale error-corrected quantum computations whose durations exceed the lifetime of a single atom in the system.

Generalized measurements, also called positive operator-valued measures (POVMs), can offer advantages over projective measurements in various quantum information tasks. Here, we realize a generalized measurement of one and two superconducting qubits with high fidelity and in a single experimental setting. To do so, we propose a hybrid method, the “Naimark-terminated binary tree,” based on a hybridization of Naimark’s dilation and binary tree techniques that leverages emerging hardware capabilities for midcircuit measurements and feed-forward control. Furthermore, we showcase a highly effective use of approximate compiling to enhance POVM fidelity in noisy conditions. We argue that our hybrid method scales better toward larger system sizes than its constituent methods and demonstrate its advantage by performing detector tomography of symmetric, informationally complete POVM (SIC POVM). Detector fidelity is further improved through a composite error-mitigation strategy that incorporates twirling and a newly devised conditional readout error mitigation. Looking forward, we expect improvements in approximate compilation and hardware noise for dynamic circuits to enable generalized measurements of larger multiqubit POVMs on superconducting qubits.

Geometric quantum machine learning based on equivariant quantum neural networks (EQNNs) recently appeared as a promising direction in quantum machine learning. Despite encouraging progress, studies are still limited to theory, and the role of hardware noise in EQNN training has never been explored. This work studies the behavior of EQNN models in the presence of noise. We show that certain EQNN models can preserve equivariance under Pauli channels, while this is not possible under the amplitude damping channel. We claim that the symmetry breaks linearly in the number of layers and noise strength. We support our claims with numerical data from simulations as well as hardware up to 64 qubits. Furthermore, we provide strategies to enhance the symmetry protection of EQNN models in the presence of noise.

We provide the first tensor-network method for computing quantum weight enumerator polynomials in the most general form. If a quantum code has a known tensor-network construction of its encoding map, our method is far more efficient, and in some cases exponentially faster than the existing approach. As a corollary, it produces decoders and an algorithm that computes the code distance. For non-(Pauli)-stabilizer codes, this constitutes the current best algorithm for computing the code distance. For degenerate stabilizer codes, it can be substantially faster compared to the current methods. We also introduce novel weight enumerators and their applications. In particular, we show that these enumerators can be used to compute logical error rates exactly and thus construct (optimal) decoders for any independent and identically distributed single qubit or qudit error channels. The enumerators also provide a more efficient method for computing nonstabilizerness in quantum many-body states. As the power for these speedups rely on a quantum Lego decomposition of quantum codes, we further provide systematic methods for decomposing quantum codes and graph states into a modular construction for which our technique applies. As a proof of principle, we perform exact analyses of the deformed surface codes, the holographic pentagon code, and the two-dimensional Bacon-Shor code under (biased) Pauli noise and limited instances of coherent error at sizes that are inaccessible by brute force.

Generating macroscopic nonclassical quantum states is a long-standing challenge in physics. Anharmonic dynamics is an essential ingredient to generate these states, but for large mechanical systems, the effect of the anharmonicity tends to become negligible compared with the effect of decoherence. As a possible solution to this challenge, we propose using a motional squeezed state as a resource to effectively increase the anharmonicity. We analyze the production of negativity in the Wigner distribution of a quantum anharmonic resonator initially in a squeezed state. We find that initial squeezing increases the rate at which negativity is generated. We also analyze the effect of two common sources of decoherence—namely, energy damping and dephasing—and find that the detrimental effects of energy damping are suppressed by strong squeezing. In the limit of large squeezing, which is needed for state-of-the-art systems, we find good approximations for the Wigner function. Our analysis is significant for current experiments attempting to prepare macroscopic mechanical systems in genuine quantum states. We provide an overview of several experimental platforms featuring nonlinear behaviors and low levels of decoherence. In particular, we discuss the feasibility of our proposal with carbon nanotubes and levitated nanoparticles.