Discrete-modulated (DM) continuous-variable quantum key distribution (CV-QKD) protocols are promising candidates for commercial implementations of quantum communication networks due to their experimental simplicity. While tight security analyses in the asymptotic limit exist, proofs in the finite-size regime are still subject to active research. We present a composable finite-size security proof against independently and identically distributed collective attacks for a general DM CV-QKD protocol. We introduce a new energy testing theorem to bound the effective dimension of Bob’s system and rigorously prove security within Renner’s $ϵ$-security framework and address the issue of acceptance sets in protocols and their security proof. We want to highlight that our method also allows for nonunique acceptance statistics, which is necessary in practise. Finally, we extend and apply a numerical security proof technique to calculate tight lower bounds on the secure key rate. To demonstrate our method, we apply it to a quadrature phase-shift keying protocol for both untrusted, ideal and trusted, nonideal detectors. The results show that our security proof method yields secure finite-size key rates under experimentally viable conditions up to at least 72 km transmission distance.

Measurement noise is a major source of noise in quantum metrology. Here, we explore preprocessing protocols that apply quantum controls to the quantum sensor state prior to the final noisy measurement (but after the unknown parameter has been imparted), aiming to maximize the estimation precision. We define the quantum preprocessing-optimized Fisher information, which determines the ultimate precision limit for quantum sensors under measurement noise, and conduct a thorough investigation into optimal preprocessing protocols. First, we formulate the preprocessing optimization problem as a biconvex optimization using the error observable formalism, based on which we prove that unitary controls are optimal for pure states and derive analytical solutions of the optimal controls in several practically relevant cases. Then we prove that for classically mixed states (whose eigenvalues encode the unknown parameter) under commuting-operator measurements, coarse-graining controls are optimal, while unitary controls are suboptimal in certain cases. Finally, we demonstrate that in multiprobe systems where noisy measurements act independently on each probe, the noiseless precision limit can be asymptotically recovered using global controls for a wide range of quantum states and measurements. Applications to noisy Ramsey interferometry and thermometry are presented, as well as explicit circuit constructions of optimal controls.

We develop a resource-theoretic framework that allows one to bridge the gap between two approaches to quantum thermodynamics based on Markovian thermal processes (which model memoryless dynamics) and thermal operations (which model arbitrarily non-Markovian dynamics). Our approach is built on the notion of memory-assisted Markovian thermal processes, where memoryless thermodynamic processes are promoted to non-Markovianity by explicitly modeling ancillary memory systems initialized in thermal equilibrium states. Within this setting, we propose a family of protocols composed of sequences of elementary two-level thermalizations that approximate all transitions between energy-incoherent states accessible via thermal operations. We prove that, as the size of the memory increases, these approximations become arbitrarily good for all transitions in the infinite temperature limit, and for a subset of transitions in the finite temperature regime. Furthermore, we present solid numerical evidence for the convergence of our protocol to any transition at finite temperatures. We also explain how our framework can be used to quantify the role played by memory effects in thermodynamic protocols such as work extraction. Finally, our results show that elementary control over two energy levels at a given time is sufficient to generate all energy-incoherent transitions accessible via thermal operations if one allows for ancillary thermal systems.

The simulation of chemistry is among the most promising applications of quantum computing. However, most prior work exploring algorithms for block encoding, time evolving, and sampling in the eigenbasis of electronic structure Hamiltonians has either focused on modeling finite-sized systems, or has required a large number of plane-wave basis functions. In this work, we extend methods for quantum simulation with Bloch orbitals constructed from symmetry-adapted atom-centered orbitals so that one can model periodic ab initio Hamiltonians using only a modest number of basis functions. We focus on adapting existing algorithms based on combining qubitization with tensor factorizations of the Coulomb operator. Significant modifications of those algorithms are required to obtain an asymptotic speedup leveraging translational (or, more broadly, Abelian) symmetries. We implement block encodings using known tensor factorizations and a new Bloch orbital form of tensor hypercontraction. Finally, we estimate the resources required to deploy our algorithms to classically challenging model materials relevant to the chemistry of lithium nickel oxide battery cathodes within the surface code. We find that even with these improvements, the quantum runtime of these algorithms is on the order of thousands of days and further algorithmic improvements are required to make realistic quantum simulation of materials practical.

We present a numerical method to simulate the dynamics of continuous-variable quantum many-body systems. Our approach is based on custom neural-network many-body quantum states. We focus on dynamics of two-dimensional quantum rotors and simulate large experimentally relevant system sizes by representing a trial state in a continuous basis and using state-of-the-art sampling approaches based on Hamiltonian Monte Carlo. We demonstrate the method can access quantities like the return probability and vorticity oscillations after a quantum quench in two-dimensional systems of up to 64 ($8\times 8$) coupled rotors. Our approach can be used for accurate nonequilibrium simulations of continuous systems at previously unexplored system sizes and evolution times, bridging the gap between simulation and experiment.

A quantum register coupled to a spin-photon interface is a key component in quantum communication and information processing. Group-IV color centers in diamond ($\mathrm{Si}$${\mathrm{V}}^{-}$, $\mathrm{Ge}$${\mathrm{V}}^{-}$, and $\mathrm{Sn}$${\mathrm{V}}^{-}$) are promising candidates for this application, comprising an electronic spin with optical transitions coupled to a nuclear spin as the quantum register. However, the creation of a quantum register for these color centers with deterministic and strong coupling to the spin-photon interface remains challenging. Here, we make first-principles predictions of the hyperfine parameters of the group-IV color centers, which we verify experimentally with a comprehensive comparison between the spectra of spin active and spin neutral intrinsic dopant nuclei in single $\mathrm{Ge}$${\mathrm{V}}^{-}$ and $\mathrm{Sn}$${\mathrm{V}}^{-}$ emitters. In line with the theoretical predictions, detailed spectroscopy on large sample sizes reveals that hyperfine coupling causes a splitting of the optical transition of $\mathrm{Sn}$${\mathrm{V}}^{-}$ an order of magnitude larger than the optical line width and provides a magnetic field insensitive transition. This strong coupling provides access to a new regime for quantum registers in diamond color centers, opening avenues for novel spin-photon entanglement and quantum sensing schemes for these well-studied emitters.

Recent work has shown that a self-correcting quantum memory can exist in three spatial dimensions, provided that it is protected by a 1-form symmetry. Requiring that the dynamics of a system obey this type of symmetry is equivalent to enforcing a macroscopic number of symmetry terms throughout the bulk. In this paper, we show how to replace the explicit 1-form symmetry with an emergent 1-form symmetry in the bulk and an explicit 1-form symmetry on the boundary. To do so, we use the extended excitations of a three-dimensional (3D) toric code to confine anyons in a two-dimensional (2D) toric code on the boundary. The boundary anyons are bound to the bulk excitations by the explicit 1-form symmetry. Although the symmetry still has to be explicitly enforced on the boundary, this could conceivably be a more attainable constraint due to the accessibility of the boundary qubits. Furthermore, this only requires $\mathcal{O}(L^2)$ terms for a system of linear size $L$, instead of $\mathcal{O}(L^3)$ terms.

Integrated photonics provides a versatile platform for encoding and processing quantum information. However, the encoded quantum states are sensitive to noise, which limits their capability to perform complicated quantum computations. Here, we use a five-qubit linear cluster state on a silicon photonic chip to implement a quantum error-correction code and demonstrate its capability of identifying and correcting a single-qubit error. The encoded quantum information is reconstructed from a single-qubit error and an average state fidelity of $0.863\pm 0.032$ is achieved for different input states. We further extend the scheme to demonstrate a fault-tolerant measurement-based quantum computation (MBQC) on stabilizer formalism that allows us to redo the qubit operation against the failure of the teleportation process. Our work provides a proof-of-concept working prototype of error correction and MBQC in an integrated photonic chip.

Quasiparticle (QP) effects play a significant role in the coherence and fidelity of superconducting quantum circuits. The Andreev bound states of high-transparency Josephson junctions can act as low-energy traps for QPs, providing a mechanism for studying the dynamics and properties of both the QPs and the junction. Using locally injected and thermal QPs, we study QP loss and QP poisoning in epitaxial $\mathrm{Al}$-$\mathrm{In}\mathrm{As}$ Josephson junctions incorporated in a superconducting quantum interference device (SQUID) galvanically shorting a superconducting resonator to ground. We observe changes in the resonance line shape and frequency shifts consistent with QP trapping into and clearing out of the ABSs of the junctions when the junctions are phase biased. By monitoring the QP trapping and clearing mechanisms in time, we find a time scale of $\mathcal{O}(1\text{μ}\mathrm{s})$ for these QP dynamics, consistent with the presence of phonon-mediated QP-QP interactions. Our measurements suggest that electron-phonon interactions play a significant role in the relaxation mechanisms of our system, while electron-photon interactions and electron-phonon interactions govern the clearing mechanisms. Our results highlight the QP-induced dissipation and complex QP dynamics in superconducting quantum circuits fabricated on superconductor-semiconductor heterostructures.

Tailored topological stabilizer codes in two dimensions have been shown to exhibit high-storage-threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for several advantages including a transversal implementation of non-Clifford logical gates, single-shot decoding strategies, and parallelized decoding in the case of fracton codes, as well as construction of fractal-lattice codes. Motivated by this, we tailor 3D topological codes for enhanced storage performance under biased Pauli noise. We present Clifford deformations of various 3D topological codes, such that they exhibit a threshold error rate of $50\mathrm{\%}$ under infinitely biased Pauli noise. Our examples include the 3D surface code on the cubic lattice, the 3D surface code on a checkerboard lattice that lends itself to a subsystem code with a single-shot decoder, and the 3D color code, as well as fracton models such as the X-cube model, the Sierpiński model, and the Haah code. We use the belief propagation with ordered statistics decoder (BP OSD) to study threshold error rates at finite bias. We also present a rotated layout for the 3D surface code, which uses roughly half the number of physical qubits for the same code distance under appropriate boundary conditions. Imposing coprime periodic dimensions on this rotated layout leads to logical operators of weight $O(n)$ at infinite bias and a corresponding $\exp [-O(n)]$ subthreshold scaling of the logical failure rate, where $n$ is the number of physical qubits in the code. Even though this scaling is unstable due to the existence of logical representations with $O(1)$ low-rate and $O(n^{2/3})$ high-rate Pauli errors, the number of such representations scales only polynomially for the Clifford-deformed code, leading to an enhanced effective distance.

We demonstrate high-fidelity repetitive measurements of nuclear spin qubits in an array of neutral ytterbium-171 (${}^{171}\mathrm{Yb}$) atoms. We show that the qubit state can be measured with a spin-flip probability of $0.004(4)$ for a single tweezer and $0.012(3)$ averaged over the array. This is accomplished by high cyclicity of one of the nuclear spin qubit states with an optically excited state under a magnetic field of $B=58$ G, resulting in a spin-flip probability of approximately ${10}^{-5}$ per scattered photon during fluorescence readout. The performance improves further as $\sim 1/B^2$. The state discrimination fidelity is $0.993(4)$ with a state-averaged readout survival of $0.994(3)$, limited by off-resonant scattering to dark states. We combine our measurement technique with high-contrast rotations of the nuclear spin qubit via an ac magnetic field to explore two paradigmatic scenarios, including the noncommutativity of measurements in orthogonal bases, and the quantum Zeno mechanism in which measurements “freeze” coherent evolution. Finally, we employ real-time feedforward to repetitively and deterministically prepare the qubit in the $+z$ or $-z$ direction after initializing it in a different basis and performing a measurement in the $Z$ basis. These capabilities constitute an important step towards adaptive quantum circuits with atom arrays.

Storing quantum information for an extended period of time is essential for running quantum algorithms with low errors. Currently, superconducting quantum memories have coherence times of a few milliseconds, and surpassing this performance has remained an outstanding challenge. In this work, we report a single-photon qubit encoded in a novel superconducting cavity with a coherence time of 34 ms, representing an order of magnitude improvement compared to previous demonstrations. We use this long-lived quantum memory to store a Schrödinger cat state with a record size of 1024 photons, indicating the cavity’s potential for bosonic quantum error correction.

The quantum approximate optimization algorithm (QAOA) is suggested as a promising application on early quantum computers. Here a quantum-inspired classical algorithm, the mean-field approximate optimization algorithm (mean-field AOA), is developed by replacement of the quantum evolution of the QAOA with classical spin dynamics through the mean-field approximation. Because of the alternating structure of the QAOA, this classical dynamics can be found exactly for any number of QAOA layers. We benchmark its performance against the QAOA on the Sherrington-Kirkpatrick model and the partition problem, and find that the mean-field AOA outperforms the QAOA in both cases for most instances. Our algorithm can thus serve as a tool to delineate optimization problems that can be solved classically from those that cannot, i.e., we believe that it will help to identify instances where a true quantum advantage can be expected from the QAOA. To quantify quantum fluctuations around the mean-field trajectories, we solve an effective scattering problem in time, which is characterized by a spectrum of time-dependent Lyapunov exponents. These provide an indicator for the hardness of a given optimization problem relative to the mean-field AOA.

While standard approaches to quantum simulation require a number of qubits proportional to the number of simulated particles, current noisy quantum computers are limited to tens of qubits. With the technique of holographic quantum simulation, a $D$-dimensional system can be simulated with a $(D-1)$-dimensional subset of qubits, enabling the study of systems significantly larger than current quantum computers. Using circuits derived from the multiscale entanglement renormalization ansatz (MERA), we accurately prepare the ground state of an $L=32$ critical, nonintegrable perturbed Ising model and measure long-range correlations on the ten-qubit Quantinuum trapped-ion computer. We introduce generalized MERA networks that interpolate between MERA and matrix product state networks and demonstrate that generalized MERA can capture far longer correlations than a MERA with the same number of qubits, at the expense of greater circuit depth. Finally, we perform noisy simulations of these two network ansatzes and find that the optimal choice of network depends on the noise level, available qubits, and the state to be represented.

Monitored many-body systems fall broadly into two dynamical phases, “entangling” or “disentangling,” separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of this measurement-induced transition is an outstanding challenge. Recent work made progress in the context of tree tensor networks, which can be related to all-to-all quantum circuit dynamics with forced (postselected) measurement outcomes. So far, however, there are no exact solutions for dynamics of spin-1/2 degrees of freedom (qubits) with “real” measurements, whose outcome probabilities are sampled according to the Born rule. Here we define dynamical processes for qubits, with real measurements, that have a treelike space-time interaction graph, either collapsing or expanding the system as a function of time. The former case yields an exactly solvable measurement transition. We explore these processes analytically and numerically, exploiting the recursive structure of the tree. We compare the case of “real” measurements with the case of “forced” measurements. Both cases show a transition at a nontrivial value of the measurement strength, with the real measurement case exhibiting a smaller entangling phase. Both exhibit exponential scaling of the entanglement near the transition, but they differ in the value of a critical exponent. An intriguing difference between the two cases is that the real measurement case lies at the boundary between two distinct types of critical scaling. On the basis of our results, we propose a protocol for realizing a measurement phase transition experimentally via an expansion process.

The orientation of the order parameter of quantum magnets can be used to store information in a dense and efficient way. Switching this order parameter corresponds to writing data. To understand how this can be done, we study a precessional reorientation of the sublattice magnetization in an (an)isotropic quantum antiferromagnet induced by an applied magnetic field. For this intriguing nonequilibrium issue, we introduce a description including the leading quantum and thermal fluctuations, namely time-dependent Schwinger boson mean-field theory, because this theory allows us to describe both ordered phases and the phases in between them, as is crucial for switching. An activation energy has to be overcome, requiring a minimum applied field $h_t$ that is given essentially by the spin gap. It can be reduced significantly for temperatures approaching the Néel temperature, facilitating switching. The time required for switching diverges when the field approaches $h_t$, which is the signature of an inertia in the magnetization dynamics. The temporal evolution of the magnetization and of the energy reveals signs of dephasing. The switched state has lost a part of its coherence because the magnetic modes do not evolve in phase.

We theoretically show that laser recoil heating in free-space levitated optomechanics can be arbitrarily suppressed by shining squeezed light onto an optically trapped nanoparticle. The presence of squeezing modifies the quantum electrodynamical light-matter interaction in a way that enables us to control the amount of information that the scattered light carries about a given mechanical degree of freedom. Moreover, we analyze the trade-off between measurement imprecision and back-action noise and show that optical detection beyond the standard quantum limit can be achieved. We predict that, with state-of-the-art squeezed light sources, laser recoil heating can be reduced by at least $60\mathrm{\%}$ by squeezing a single Gaussian mode with an appropriate incidence direction, and by $98\mathrm{\%}$ by squeezing a properly mode-matched mode. Our results, which are valid both for motional and librational degrees of freedom, will lead to improved feedback cooling schemes as well as boost the coherence time of optically levitated nanoparticles in the quantum regime.

The complexity of quantum many-body systems is manifested in the vast diversity of their correlations, making it challenging to distinguish the generic from the atypical features. This can be addressed by analyzing correlations through ensembles of random states, chosen to faithfully embody the relevant physical properties. Here, we focus on spins with local interactions, whose correlations are extremely well captured by tensor network states. Adopting an operational perspective, we define ensembles of random tensor network states in one and two spatial dimensions that admit a sequential generation. As such, they directly correspond to outputs of quantum circuits with a sequential architecture and random gates. In one spatial dimension, the ensemble explores the entire family of matrix product states, while in two spatial dimensions, it corresponds to random isometric tensor network states. We extract the scaling behavior of the average correlations between two subsystems as a function of their distance. Using elementary concentration results, we then deduce the typical case for measures of correlation such as the von Neumann mutual information and a measure arising from the Hilbert-Schmidt norm. We find for all considered cases that the typical behavior is an exponential decay (for both one and two spatial dimensions). We observe the consistent emergence of a correlation length that depends only on the underlying spatial dimension and not the considered measure. Remarkably, increasing the bond dimension leads to a higher correlation length in one spatial dimension but has the opposite effect in two spatial dimensions.