We argue that all locality-preserving mappings between fermionic observables and Pauli matrices on a two-dimensional lattice can be generated from the exact bosonization in Chen et al. [Ann. Phys. (N. Y) 393, 234 (2018)], whose gauge constraints project onto the subspace of the toric code with emergent fermions. Starting from the exact bosonization and applying Clifford finite-depth generalized local unitary transformation, we can achieve all possible fermion-to-qubit mappings (up to the re-pairing of Majorana fermions). In particular, we discover a new supercompact encoding using 1.25 qubits per fermion on the square lattice. We prove the existence of finite-depth quantum circuits to obtain fermion-to-qubit mappings with qubit-fermion ratios $r=1+1/2k$ for positive integers $k$, utilizing the trivialness of quantum cellular automata in two spatial dimensions. Also, we provide direct constructions of fermion-to-qubit mappings with ratios arbitrarily close to 1. When the ratio reaches 1, the fermion-to-qubit mapping reduces to the one-dimensional Jordan-Wigner transformation along a certain path in the two-dimensional lattice. Finally, we explicitly demonstrate that the Bravyi-Kitaev superfast simulation, the Verstraete-Cirac auxiliary method, Kitaev’s exactly solved model, the Majorana loop stabilizer codes, and the compact fermion-to-qubit mapping can all be obtained from the exact bosonization.

Flexible characterization techniques that provide a detailed picture of the experimental imperfections under realistic assumptions are crucial to gain actionable advice in the development of quantum computers. Gate set tomography self-consistently extracts a complete tomographic description of the implementation of an entire set of quantum gates, as well as the initial state and measurement, from experimental data. It has become a standard tool for this task but comes with high requirements on the number of sequences and their design, making it already experimentally challenging for only two qubits. In this work, we show that low-rank approximations of gate sets can be obtained from significantly fewer gate sequences and that it is sufficient to draw them at random. This coherent noise characterization however still contains the crucial information for improving the implementation. To this end, we formulate the data processing problem of gate set tomography as a rank-constrained tensor completion problem. We provide an algorithm to solve this problem while respecting the usual positivity and normalization constraints of quantum mechanics. For this purpose, we combine methods from Riemannian optimization and machine learning and develop a saddle-free second-order geometrical optimization method on the complex Stiefel manifold. Besides the reduction in sequences, we numerically demonstrate that the algorithm does not rely on structured gate sets or an elaborate circuit design to robustly perform gate set tomography. Therefore, it is more flexible than traditional approaches. We also demonstrate how coherent errors in shadow estimation protocols can be mitigated using estimates from gate set tomography.

Dissipative collective effects are ubiquitous in quantum physics and their relevance ranges from the study of entanglement in biological systems to noise mitigation in quantum computers. Here, we put forward the first fully quantum simulation of dissipative collective phenomena on a real quantum computer, based on the recently introduced multipartite-collision model. First, we theoretically study the accuracy of this algorithm on near-term quantum computers with noisy gates and we derive some rigorous error bounds that depend on the time step of the collision model and on the gate errors. These bounds can be employed to estimate the necessary resources for the efficient quantum simulation of the collective dynamics. Then, we implement the algorithm on some IBM quantum computers to simulate superradiance and subradiance between a pair of qubits. Our experimental results successfully display the emergence of collective effects in the quantum simulation. In addition, we analyze the noise properties of the gates that we employ in the algorithm by means of full process tomography, with the aim of improving our understanding of the errors in the near-term devices that are currently accessible to worldwide researchers. We obtain the values of the average gate fidelity, unitarity, incoherence, and diamond error and we establish a connection between them and the accuracy of the experimentally simulated state. Moreover, we build a noise model based on the results of the process tomography for two-qubit gates and show that its performance is comparable with the noise model provided by IBM. Finally, we observe that the scaling of the error as a function of the number of gates is favorable, but at the same time reaching the threshold of the diamond errors for quantum fault-tolerant computation may still be orders of magnitude away in the devices that we employ.

Photon-emission-correlation spectroscopy is an indispensable tool for the study of atoms, molecules, and, more recently, solid-state quantum defects. In solid-state systems, its most common use is as an indicator of single-photon emission, a key property for quantum technology. Beyond the single-photon purity of an emitter, however, photon-correlation measurements can provide a wealth of information that can reveal details about its electronic structure and optical dynamics that are hidden by other spectroscopy techniques. This tutorial presents a standardized framework for using photon-emission-correlation spectroscopy to study quantum emitters, including discussion of theoretical background, considerations for data acquisition and statistical analysis, and interpretation. We highlight important nuances and best practices regarding the commonly used $g^{(2)}(\tau =0)<0.5$ test for single-photon emission. Finally, we illustrate how this experimental technique can be paired with optical-dynamics simulations to formulate an electronic model for unknown quantum emitters, enabling the design of quantum control protocols and assessment of their suitability for quantum information science applications.

Individually addressed $\mathrm{Er}$${}^{3+}$ ions in solid-state hosts are promising resources for quantum repeaters, because of their direct emission in the telecom band and their compatibility with silicon photonic devices. While the $\mathrm{Er}$${}^{3+}$ electron spin provides a spin-photon interface, ancilla nuclear spins could enable multiqubit registers with longer storage times. In this work, we demonstrate coherent coupling between the electron spin of a single $\mathrm{Er}$${}^{3+}$ ion and a single $I=1/2$ nuclear spin in the solid-state host crystal, which is a fortuitously located proton (${}^1$$\mathrm{H}$). We control the nuclear spin using dynamical-decoupling sequences applied to the electron spin, implementing one- and two-qubit gate operations. Crucially, the nuclear spin coherence time exceeds the electron coherence time by several orders of magnitude, because of its smaller magnetic moment. These results provide a path toward combining long-lived nuclear spin quantum registers with telecom-wavelength emitters for long-distance quantum repeaters.

Superconducting parametric amplifiers are crucial components in microwave quantum circuits for enabling quantum-limited signal readout. The best-performing such amplifiers are often based on Josephson junctions, which however are sensitive to magnetic fields. Therefore, they require magnetic shields and are not easily integratable with other quantum systems that operate within magnetic fields, such as spin-ensemble quantum memories. To tackle this challenge, we develop a kinetic inductance-based parametric amplifier featuring a NbN nanobridge instead of Josephson junctions, which provides the desired nonlinearity for a strong parametric gain up to 42 dB. The added noise of this nanobridge kinetic-inductance parametric amplifier (hereby referred to as NKPA) is calibrated and found to be $0.59\pm 0.03$ quanta for phase-preserving amplification, approaching the quantum limit of 0.5 quanta. Most importantly, we show that such excellent noise performance is preserved in an in-plane magnetic field up to 427 mT, the maximum field available in our experiment. This magnetic-field-resilient parametric amplifier presents an opportunity towards addressing single electron-spin resonance and more efficient search for axions as well as Majorana fermions.

In Brown et al. [PRX Quantum, 4, 010321 (2023)], we discuss how holographic quantum gravity may be simulated using quantum devices and we give a specific proposal—teleportation by size and the phenomenon of size winding. Here, we elaborate on what it means to do quantum gravity in the lab and how size winding connects to bulk gravitational physics and traversable wormholes. Perfect size winding is a remarkable fine-grained property of the size wave function of an operator; we show from a bulk calculation that this property must hold for quantum systems with a nearly ${\mathrm{Ad}\mathrm{S}}_2$ bulk. We then examine in detail teleportation by size in three systems—the Sachdev-Ye-Kitaev model, random matrices, and spin chains—and discuss prospects for realizing these phenomena in near-term quantum devices.

With the long-term goal of studying models of quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in the recent traversable-wormhole constructions of Gao et al. [J. High Energy Phys., 2017, 151 (2017)] and Maldacena et al. [Fortschr. Phys., 65, 1700034 (2017)]: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of teleportation by size to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semiclassical holographic wormhole corresponds to a rather special property of the operator-size distribution that we call size winding. For more general systems (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversable-wormhole phenomenon. In addition, a form of signaling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole but, rather, to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations that are feasible with current technology in two experimental platforms: Rydberg-atom arrays and trapped ions.

Proposals for large-scale semiconductor spin-based quantum computers require high-fidelity single-shot qubit readout to perform error correction and read out qubit registers at the end of a computation. However, as devices scale to larger qubit numbers integrating readout sensors into densely packed qubit chips is a critical challenge. Two promising approaches are minimizing the footprint of the sensors, and extending the range of each sensor to read more qubits. Here we show high-fidelity single-shot electron spin readout using a nanoscale single-lead quantum dot (SLQD) sensor that is both compact and capable of reading multiple qubits. Our gate-based SLQD sensor is deployed in an all-epitaxial silicon donor spin-qubit device, and we demonstrate single-shot readout of three ${}^{31}\mathrm{P}$ donor quantum dot electron spins with a maximum fidelity of 95%. Importantly, in our device the quantum dot confinement potentials are provided inherently by the donors, removing the need for additional metallic confinement gates and resulting in strong capacitive interactions between sensor and donor quantum dots. Our results are consistent with a $1/d^{1.4}$ scaling of the capacitive coupling between sensor and ${}^{31}\mathrm{P}$ dots (where $d$ is the sensor-dot distance), compared to $1/d^{2.5-3.0}$ in gate-defined quantum dot devices. Due to the small qubit size and strong capacitive interactions in all-epitaxial donor devices, we estimate a single sensor can achieve single-shot readout of approximately 15 qubits in a linear array, compared to 3–4 qubits for a similar sensor in a gate-defined quantum dot device. Our results highlight the potential for spin-qubit devices with significantly reduced sensor densities.

The operator entanglement (OE) is a key quantifier of the complexity of a reduced density matrix. In out-of-equilibrium situations, e.g., after a quantum quench of a product state, it is expected to exhibit an entanglement barrier. The OE of a reduced density matrix initially grows linearly as entanglement builds up between the local degrees of freedom; it then reaches a maximum and ultimately decays to a small finite value as the reduced density matrix converges to a simple stationary state through standard thermalization mechanisms. Here, by performing a new data analysis of the published experimental results of Brydges et al. [Science 364, 260 (2019)], we obtain the first experimental estimation of the OE of a subsystem reduced density matrix in a quantum many-body system. We employ the randomized-measurements toolbox and we introduce and develop a new efficient method to postprocess experimental data in order to extract higher-order density-matrix functionals and access the OE. The OE thus obtained displays the expected barrier as long as the experimental system is large enough. For smaller systems, we observe a barrier with a double-peak structure, the origin of which can be interpreted in terms of pairs of quasiparticles being reflected at the boundary of the qubit chain. As $U(1)$ symmetry plays a key role in our analysis, we introduce the notion of symmetry-resolved operator entanglement (SROE), in addition to the total OE. To gain further insights into the SROE, we provide a thorough theoretical analysis of this new quantity in chains of noninteracting fermions, which, in spite of their simplicity, capture most of the main features of OE and SROE. In particular, we uncover three main physical effects: the presence of a barrier in any charge sector, a time delay for the onset of the growth of SROE, and an effective equipartition between charge sectors.

Google’s tensor processing units (TPUs) are integrated circuits specifically built to accelerate and scale up machine learning workloads. They can perform fast distributed matrix multiplications and therefore be repurposed for other computationally intensive tasks. In this work we demonstrate the use of TPUs for accelerating and scaling up the density matrix renormalization group (DMRG), a powerful numerical approach to compute the ground state of a local quantum many-body Hamiltonian. The cost of DMRG scales with system size $N$ as $O(N{D}^3)$, where the so-called bond dimension $D$ regulates how expressive the underlying matrix product state (MPS) variational ansatz is. We consider lattice models in two spatial dimensions, with square lattices of size $10\times 10$ (free fermions) and $20\times 20$ (transverse field Ising model), for which the required MPS bond dimension is known to scale at least as $\exp (\sqrt{N})$. Using half of a TPU v3 pod (namely $1024$ TPU v3 cores), we reach an unprecedentedly large bond dimension $D=2^{16}=65536$, for which optimizing a single MPS tensor takes about 2 min.

Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms [Ebadi et al., Science, 376, 1209 (2022)] with hundreds of qubits. In particular, the maximum independent set problem on so-called unit-disk graphs, was shown to be efficiently encodable in such a quantum system. Here, we extend the classes of problems that can be efficiently encoded in Rydberg arrays by constructing explicit mappings from a wide class of problems to maximum-weighted independent set problems on unit-disk graphs, with at most a quadratic overhead in the number of qubits. We analyze several examples, including maximum-weighted independent set on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization. Numerical simulations on small system sizes indicate that the adiabatic time scale for solving the mapped problems is strongly correlated with that of the original problems. Our work provides a blueprint for using Rydberg atom arrays to solve a wide range of combinatorial optimization problems with arbitrary connectivity, beyond the restrictions imposed by the hardware geometry.

The development of quantum optomechanics now allows mechanical sensors with femtogram masses to be controlled and measured in the quantum regime. If the mechanical element contains isotopes that undergo nuclear decay, measuring the recoil of the sensor following the decay allows reconstruction of the total momentum of all emitted particles, including any neutral particles that may escape detection in traditional detectors. As an example, for weak nuclear decays the momentum of the emitted neutrino can be reconstructed on an event-by-event basis. We present the concept that a single nanometer-scale optically levitated sensor operated with sensitivity near the standard quantum limit can search for heavy sterile neutrinos in the keV-MeV mass range with sensitivity significantly beyond existing laboratory constraints. We also comment on the possibility that mechanical sensors operated well into the quantum regime might ultimately reach the sensitivities required to provide an absolute measurement of the mass of the light neutrino states.

Tunable coupling of superconducting qubits has been widely studied due to its importance for isolated gate operations in scalable quantum processor architectures. Here, we demonstrate a tunable qubit-qubit coupler based on a floating transmon device, which allows us to place qubits at least 2 mm apart from each other while maintaining over 50-MHz coupling between the coupler and the qubits. In the introduced tunable-coupler design, both the qubit-qubit and the qubit-coupler couplings are mediated by two waveguides instead of relying on direct capacitive couplings between the components, reducing the impact of the qubit-qubit distance on the couplings. This leaves space for each qubit to have an individual readout resonator and a Purcell filter, which is needed for fast high-fidelity readout. In addition, simulations show that the large qubit-qubit distance significantly lowers unwanted non-nearest-neighbor coupling and allows multiple control lines to cross over the structure with minimal crosstalk. Using the proposed flexible and scalable architecture, we demonstrate a controlled-$Z$ gate with ($99.81\pm 0.02$)% fidelity.

The swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform swap for the task of permuting qubits within an architecture, which we call routing. We consider quantum routing in two models: (i) allowing arbitrary two-qubit unitaries, or (ii) allowing Hamiltonians with norm-bounded interactions. We lower bound the circuit depth or time of quantum routing in terms of spectral properties of graphs representing the architecture interaction constraints, and give a generalized upper bound for all simple connected $n$-vertex graphs. In particular, we give conditions for a superpolynomial classical-quantum routing separation, which exclude graphs with a small spectral gap and graphs of bounded degree. Finally, we provide examples of a quadratic separation between gate-based and Hamiltonian routing models with a constant number of local ancillas per qubit and of an $\mathrm{\Omega }\left(n\right)$ speedup if we also allow fast local interactions.

Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and adiabatic quantum computation. The problem of speeding up these processes has garnered a large amount of interest, resulting in a menagerie of approaches, most notably quantum optimal control and shortcuts to adiabaticity. The two approaches are complementary: optimal control manipulates control fields to steer the dynamics in the minimum allowed time, while shortcuts to adiabaticity aims to retain the adiabatic condition upon speed-up. We outline a new method that combines the two methodologies and takes advantage of the strengths of each. The new technique improves upon approximate local counterdiabatic driving with the addition of time-dependent control fields. We refer to this new method as counterdiabatic optimized local driving (COLD) and we show that it can result in a substantial improvement when applied to annealing protocols, state preparation schemes, entanglement generation, and population transfer on a lattice. We also demonstrate a new approach to the optimization of control fields that does not require access to the wave function or the computation of system dynamics. COLD can be enhanced with existing advanced optimal control methods and we explore this using the chopped randomized basis method and gradient ascent pulse engineering.

Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the dynamics of thermalization. While contemporary methods in quantum chaos often rely on random ensembles of quantum states and Hamiltonians, this is not reflective of most real-world systems. In this paper, we introduce a new perspective: across a wide range of examples, a single nonrandom quantum state is shown to encode universal and highly random quantum state ensembles. We characterize these ensembles using the notion of quantum state $k$-designs from quantum information theory and investigate their universality using a combination of analytic and numerical techniques. In particular, we establish that $k$-designs emerge naturally from generic states in a Hilbert space as well as physical states associated with strongly interacting Hamiltonian dynamics. Our results offer a new approach for studying quantum chaos and provide a practical method for sampling approximately uniformly random states; the latter has wide-ranging applications in quantum information science from tomography to benchmarking.

Quantum error correction is crucial for any quantum computing platform to achieve truly scalable quantum computation. The surface code and its variants have been considered the most promising quantum error correction scheme due to their high threshold, low overhead, and relatively simple structure that can naturally be implemented in many existing qubit architectures, such as superconducting qubits. The recent development of Floquet codes by Hastings and Haah offers another promising approach. By going beyond the usual paradigm of stabilizer codes, Floquet codes achieve similar performance while being constructed entirely from two-qubit measurements. This makes them particularly suitable for platforms where two-qubit measurements can be implemented directly, such as the measurement-only topological qubits based on Majorana zero modes (MZMs) proposed by Karzig et al. Here, we explain how two variants of Floquet codes can be implemented on MZM-based architectures without any auxiliary qubits for syndrome measurement and with shallow syndrome-extraction sequences. We then numerically demonstrate their favorable performance. In particular, we show that they improve the threshold for scalable quantum computation in MZM-based systems by an order of magnitude and significantly reduce space and time overheads below threshold.

The impressive progress in quantum hardware of the last years has raised the interest of the quantum computing community in harvesting the computational power of such devices. However, in the absence of error correction, these devices can only reliably implement very shallow circuits or comparatively deeper circuits at the expense of a nontrivial density of errors. In this work, we obtain extremely tight limitation bounds for standard noisy intermediate-scale quantum proposals in both the noisy and noiseless regimes, with or without error-mitigation tools. The bounds limit the performance of both circuit model algorithms, such as the quantum approximate optimization algorithm, and also continuous-time algorithms, such as quantum annealing. In the noisy regime with local depolarizing noise $p$, we prove that at depths $L=\mathcal{O}(p^{-1})$ it is exponentially unlikely that the outcome of a noisy quantum circuit outperforms efficient classical algorithms for combinatorial optimization problems like max-cut. Although previous results already showed that classical algorithms outperform noisy quantum circuits at constant depth, these results only held for the expectation value of the output. Our results are based on newly developed quantum entropic and concentration inequalities, which constitute a homogeneous toolkit of theoretical methods from the quantum theory of optimal mass transport whose potential usefulness goes beyond the study of variational quantum algorithms.

Intense laser-matter interactions are at the center of interest in research and technology since the development of high-power lasers. They have been widely used for fundamental studies in atomic, molecular, and optical physics, and they are at the core of attosecond physics and ultrafast optoelectronics. Although the majority of these studies have been successfully described using classical electromagnetic fields, recent investigations based on fully quantized approaches have shown that intense laser-atom interactions can be used for the generation of controllable high-photon-number entangled coherent states and coherent state superpositions. In this tutorial, we provide a comprehensive fully quantized description of intense laser-atom interactions. We elaborate on the processes of high-harmonic generation, above-threshold ionization, and we discuss new phenomena that cannot be revealed within the context of semiclassical theories. We provide the description for conditioning the light field on different electronic processes, and their consequences for quantum state engineering of light. Finally, we discuss the extension of the approach to more complex materials, and the impact to quantum technologies for a new photonic platform composed of the symbiosis of attosecond physics and quantum information science.