Preparation of the ground state of a Hamiltonian is a problem of great significance in physics, with deep implications in the field of combinatorial optimization. The adiabatic algorithm is known to return the ground state for sufficiently long preparation times that depend on the a priori unknown spectral gap. Our work relates in a twofold way. First, we propose a method to obtain information about the spectral profile of the adiabatic evolution. Second, we present the concept of a variational quantum adiabatic algorithm (VQAA) for optimized adiabatic paths. We aim at combining the strengths of the adiabatic and the variational approaches for fast and high-fidelity ground-state preparation while keeping the number of measurements as low as possible. Our algorithms build upon ancilla protocols that we present, which allow us to directly evaluate the ground-state overlap. We benchmark for a nonintegrable spin-1/2 transverse and longitudinal Ising chain with $N=53$ sites using tensor-network techniques. Using a black-box gradient-based approach, we report a reduction in the total evolution time for a given desired ground-state fidelity by a factor of 10, which makes our method suitable for the limited decoherence time of noisy-intermediate scale quantum devices.

We study the dynamical properties of the bosonic quantum East model at low temperature. We show that a naive generalization of the corresponding spin-1/2 quantum East model does not possess analogous slow dynamical properties. In particular, conversely to the spin case, the bosonic ground state turns out to be not localized. We restore localization by introducing a repulsive interaction term. The bosonic nature of the model allows us to construct rich families of many-body localized states, including coherent, squeezed, and cat states. We formalize this finding by introducing a set of superbosonic creation-annihilation operators that satisfy the bosonic commutation relations and, when acting on the vacuum, create excitations that are exponentially localized around a certain site of the lattice. Given the constrained nature of the model, these states retain memory of their initial conditions for long times. Even in the presence of dissipation, we show that quantum information remains localized within decoherence times that are tunable with the parameters of the system. We propose an implementation of the bosonic quantum East model based on state-of-the-art superconducting circuits, which could be used in the near future to explore the dynamical properties of kinetically constrained models in modern platforms.

Quantum technologies are currently the object of high expectations from governments and private companies, as they hold the promise to shape safer and faster ways to extract, exchange, and treat information. However, despite its major potential impact for industry and society, the question of their energetic footprint has remained in a blind spot of current deployment strategies. In this Perspective, I argue that quantum technologies must urgently plan for the creation and structuration of a transverse quantum energy initiative, connecting quantum thermodynamics, quantum information science, quantum physics, and engineering. Such an initiative is the only path towards energy-efficient, sustainable quantum technologies, and to possibly bring out an energetic quantum advantage.

Disorder-free localization is a recently discovered phenomenon of nonergodicity that can emerge in quantum many-body systems hosting gauge symmetries when the initial state is prepared in a superposition of gauge superselection sectors. Thermalization is then prevented up to all accessible evolution times despite the model being nonintegrable and translation invariant. In a recent work [Halimeh et al., arXiv:2111.02427 (2021)], it has been shown that terms linear in the gauge-symmetry generator stabilize disorder-free localization in U(1) gauge theories against gauge errors that couple different superselection sectors. Here, we show in the case of ${\mathbb{Z}}_2$ gauge theories that disorder-free localization can not only be stabilized, but also enhanced by the addition of translation-invariant terms linear in a local ${\mathbb{Z}}_2$ pseudogenerator that acts identically to the full generator in a single superselection sector, but not necessarily outside of it. We show analytically and numerically how this leads through the quantum Zeno effect to the dynamical emergence of a renormalized gauge theory with an enhanced local symmetry, which contains the ${\mathbb{Z}}_2$ gauge symmetry of the ideal model, associated with the ${\mathbb{Z}}_2$ pseudogenerator. The resulting proliferation of superselection sectors due to this dynamically emergent gauge theory creates an effective disorder greater than that in the original model, thereby enhancing disorder-free localization. We demonstrate the experimental feasibility of the ${\mathbb{Z}}_2$ pseudogenerator by providing a detailed readily implementable experimental proposal for the observation of disorder-free localization in a Rydberg setup.

Characterization protocols have so far played a central role in the development of noisy intermediate-scale quantum (NISQ) computers capable of impressive quantum feats. This trajectory is expected to continue in building the next generation of devices—ones that can surpass classical computers for particular tasks—but progress in characterization must keep up with the complexities of intricate device noise. A missing piece in the zoo of characterization procedures is tomography, which can completely describe non-Markovian dynamics over a given time frame. Here, we formally introduce a generalization of quantum process tomography, which we call process tensor tomography. We detail the experimental requirements, construct the necessary postprocessing algorithms for maximum-likelihood estimation, outline the best-practice aspects for accurate results, and make the procedure efficient for low-memory processes. The characterization is a pathway to diagnostics and informed control of correlated noise. As an example application of the hardware-agnostic technique, we show how its predictive control can be used to substantially improve multitime circuit fidelities on superconducting quantum devices. Our methods could form the core for carefully developed software that may help hardware consistently pass the fault-tolerant noise threshold.

Electrostatically defined quantum dots in bilayer graphene offer a promising platform for spin qubits with presumably long coherence times due to low spin-orbit coupling and low nuclear spin density. We demonstrate two different experimental approaches to measure the decay times of excited states. The first is based on direct current measurements through the quantum device. Pulse sequences are applied to control the occupation of ground and excited states. We observe a lower bound for the excited state decay on the order of a hundred microseconds. The second approach employs a capacitively coupled charge sensor to study the time dynamics of the excited state using the Elzerman technique. We perform single-shot readout of our two-level system with a signal-to-noise ratio of about 7 and find relaxation times up to 50 ms for the spin-excited state, with a strong magnetic field dependence, promising even higher values for smaller magnetic fields. This is an important step for developing a quantum-information processor in graphene.

We provide an efficient algorithm to compile quantum circuits for fault-tolerant execution. We target surface codes, which form a two-dimensional grid of logical qubits with nearest-neighbor logical operations. Embedding an input circuit’s qubits in surface codes can result in long-range two-qubit operations across the grid. We show how to prepare many long-range Bell pairs on qubits connected by edge-disjoint paths of ancillae in constant depth that can be used to perform these long-range operations. This forms one core part of our edge-disjoint path compilation (EDPC) algorithm, by easily performing many parallel long-range Clifford operations in constant depth. It also allows us to establish a connection between surface code compilation and several well-studied edge-disjoint path problems. Similar techniques allow us to perform non-Clifford single-qubit rotations far from magic state distillation factories. In this case, we can easily find the maximum set of paths by a max-flow reduction, which forms the other major part of EDPC. EDPC has the best asymptotic worst-case performance guarantees on the circuit depth for compiling parallel operations when compared to related compilation methods based on swap gates and network coding. EDPC also shows a quadratic depth improvement over sequential Pauli-based compilation for parallel rotations requiring magic resources. We implement EDPC and find significantly improved performance for circuits built from parallel controlled-not (cnot) gates, and for circuits that implement the multicontrolled $X$ gate ${\mathrm{C}}^k\mathrm{NOT}$.

We present a scalable star-shaped quantum-key-distribution (QKD) optical-fiber network. We use wavelength-division demultiplexing (WDM) of broadband photon pairs to establish key exchange between multiple pairs of participants simultaneously. Our QKD system is the first entanglement-based network of four participants using BBM92 time-bin coding and the first network to achieve timing synchronization solely by clock recovery based on the photon arrival times. We demonstrate simultaneous bipartite key exchange between any possible combination of participants and show that the quantum bit error rate (QBER) itself can be used to stabilize the phase in the interferometers by small temperature adjustments. The key distribution is insensitive to polarization fluctuations in the network, enabling key distribution using deployed fibers even under challenging environmental conditions. We show that our network can be readily extended to 34 participants by using a standard arrayed-waveguide grating for WDM with 100 GHz channel spacing and that reconfigurable network connections are possible with a wavelength-selective switch. In a field test, we demonstrate secure key rates of 6.3 bits/s with a QBER of 4.5% over a total fiber length of 108 km with 26.8 km of deployed fiber between two participants with high stability. Our system features a relatively simple design of the receiver modules and enables scaling QKD networks without trusted nodes to distances up to more than 100 km and to more than 100 users. With such a network, a secure communication infrastructure on a metropolitan scale can be established.

We present a voltage gate-based method for controlling the Majorana transmon, using a sinusoidal modulation of the induced offset charge $n_g$. Working in the transmon regime and in the instantaneous eigenstates basis, we find the time evolution under this protocol that realizes tunable $X$-$Z$ rotations. We optimize the parameters of the system for different single-qubit gates in both the laboratory frame and the qubit rotating frame, obtaining qubit control errors $1-\mathcal{F}$ smaller than about $2\times {10}^{-4}$. In addition to this, we conduct an analysis of the effects of the charge noise, assuming wide-band $1/f$ additive noise in $n_g$, both for the free and the driven evolutions. For the free evolution, the relaxation and dephasing rates are calculated perturbatively, obtaining long dephasing times of the order of milliseconds at the system’s sweet spots. For the driven case, the average fidelity for the $X$ gate is obtained via a numerical simulation, demonstrating remarkable resilience.

Quantum error correction with biased-noise qubits can drastically reduce the hardware overhead for universal and fault-tolerant quantum computation. Cat qubits are a promising realization of biased-noise qubits as they feature an exponential error bias inherited from their nonlocal encoding in the phase space of a quantum harmonic oscillator. To confine the state of an oscillator to the cat-qubit manifold, two main approaches have been considered so far: a Kerr-based Hamiltonian confinement with high gate performances, and a dissipative confinement with robust protection against a broad range of noise mechanisms. We introduce a new combined dissipative and Hamiltonian confinement scheme based on two-photon dissipation together with a two-photon exchange (TPE) Hamiltonian. The TPE Hamiltonian is similar to Kerr nonlinearity, but unlike the Kerr it induces only a bounded distinction between even- and odd-photon eigenstates, a highly beneficial feature for protecting the cat qubits with dissipative mechanisms. Using this combined confinement scheme, we demonstrate fast and bias-preserving gates with drastically improved performance compared to dissipative or Hamiltonian schemes. In addition, this combined scheme can be implemented experimentally with only minor modifications of existing dissipative cat-qubit experiments.

Quantum channels breaking entanglement, incompatibility, or nonlocality are defined as such because they are not useful for entanglement-based, one-sided device-independent, or device-independent quantum-information processing, respectively. Here, we show that such breaking channels are related to complementary tests of macrorealism, i.e., temporal separability, channel unsteerability, temporal unsteerability, and the temporal Bell inequality. To demonstrate this we first define a steerability-breaking channel, which is conceptually similar to entanglement and nonlocality-breaking channels and prove that it is identical to an incompatibility-breaking channel. A hierarchy of quantum nonbreaking channels is derived, akin to the existing hierarchy relations for temporal and spatial quantum correlations. We then introduce the concept of channels that break temporal correlations, explain how they are related to the standard breaking channels, and prove the following results. (1) A robustness-based measure for non-entanglement-breaking channels can be probed by temporal nonseparability. (2) A non-steerability-breaking channel can be quantified by channel steering. (3) Temporal steerability and nonmacrorealism can be used for, respectively, distinguishing unital steerability-breaking channels and nonlocality-breaking channels for a maximally entangled state. Finally, a two-dimensional depolarizing channel is experimentally implemented as a proof-of-principle example to demonstrate the hierarchy relation of nonbreaking channels using temporal quantum correlations.

Current superconducting quantum processors require strategies for coping with material defects and imperfect parameter targeting in order to scale up while maintaining high performance. To that end, in situ control of qubit frequencies with magnetic flux can be used to avoid spurious resonances. However, increased dephasing due to $1/f$ flux noise limits performance at all of these operating points except for noise-protected sweet spots, which are sparse under dc flux bias and monochromatic flux modulation. Here we experimentally demonstrate that two-tone flux modulation can be used to create a continuum of dynamical sweet spots, greatly expanding the range of qubit frequencies achievable while first-order insensitive to slow flux noise. To illustrate some advantages of this flexibility, we use bichromatic flux control to reduce the error rates and gate times of parametric entangling operations between transmons. Independent of the gate scheme, the ability to use flux control to freely select qubit frequencies while maintaining qubit coherence represents an important step forward in the robustness and scalability of near-term superconducting qubit devices.

Gaussian boson sampling (GBS) is a quantum sampling task in which one has to draw samples from the photon-number distribution of a large-dimensional nonclassical squeezed state of light. In an effort to make this task intractable for a classical computer, experiments building GBS machines have mainly focused on increasing the dimensionality and squeezing strength of the nonclassical light. However, no experiment has yet demonstrated the ability to displace the squeezed state in phase space, which is generally required for practical applications of GBS. In this work, we build a GBS machine that achieves the displacement by injecting a laser beam alongside a two-mode squeezed vacuum state into a 15-mode interferometer. We focus on two new capabilities. Firstly, we use the displacement to reconstruct the multimode Gaussian state at the output of the interferometer. Our reconstruction technique is in situ and requires only three measurement settings regardless of the state dimension. Secondly, we study how the addition of classical laser light in our GBS machine affects the complexity of sampling its output photon statistics. We introduce and validate approximate semiclassical models that reduce the computational cost when a significant fraction of the detected light is classical.

We show that a common language can be used to unify the description of parametrically coupled circuits—parametric amplifiers, frequency converters, and parametric nonreciprocal devices—with that of band-pass filter and impedance matching networks. This enables one to readily adapt network synthesis methods from microwave engineering in the design of parametrically coupled devices having prescribed transfer characteristics, e.g., gain, bandwidth, return loss, and isolation. We review basic practical aspects of coupled-mode theory and filter synthesis, and then show how to apply both, on an equal footing, to the design of multipole, broadband parametric and nonreciprocal networks. We supplement the discussion with a range of examples and reference designs.

Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque and unwieldy. We show how to transform the process matrix of a gate into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generators, classify them, and show how to represent the error generator of any gate as a mixture of elementary error generators with various rates. Finally, we show how to build a large variety of reduced models for gate errors by combining elementary error generators and/or entire subsectors of generator space. We conclude with a few examples of reduced models, including one with just $9N^2$ parameters that describes almost all commonly predicted errors on an $N$-qubit processor.

Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware overhead required for fault-tolerant quantum information processing. A broad class of bosonic codes, namely rotation-symmetric codes, can be characterized by their phase-space rotation symmetry. However, their performance has been examined to date only within an idealistic noise model. Here, we further analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. To this end, we numerically compute the average gate fidelity, including measurement errors into the noise model of the data qubit. Focusing on physical measurement models, we assess the performance of heterodyne and adaptive homodyne detection in comparison to the previously studied canonical phase measurement. This setting allows us to shed light on the role of different currently available measurement schemes when decoding the encoded information. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential. In addition, we perform a detailed analysis of Gottesman-Kitaev-Preskill (GKP) codes using a similar error-correction circuit that allows us to analyze the effect of realistic measurement models on different codes. In comparison to RSB codes, we find for GKP codes an even greater reduction in performance together with a vulnerability to photon-number dephasing. Our results show that highly efficient measurement protocols constitute a crucial building block towards error-corrected quantum information processing with bosonic continuous-variable systems.

Magic (nonstabilizerness) is a necessary but “expensive” kind of “fuel” to drive universal fault-tolerant quantum computation. To properly study and characterize the origin of quantum “complexity” in computation as well as physics, it is crucial to develop a rigorous understanding of the quantification of magic. Previous studies of magic mostly focused on small systems and largely relied on the discrete Wigner formalism (which is only well behaved in odd prime power dimensions). Here we present an initiatory study of the magic of genuinely many-body quantum states that may be strongly entangled, with focus on the important case of many qubits, at a quantitative level. We first address the basic question of how “magical” a many-body state can be, and show that the maximum magic of an $n$-qubit state is essentially $n$, simultaneously for a range of “good” magic measures. As a corollary, the resource theory of magic has asymptotic golden currency states. We then show that, in fact, almost all $n$-qubit pure states have magic of nearly $n$. In the quest for explicit, scalable cases of highly entangled states whose magic can be understood, we connect the magic of hypergraph states with the second-order nonlinearity of their underlying Boolean functions. Next, we go on and investigate many-body magic in practical and physical contexts. We first consider a variant of measurement-based quantum computation where the client is restricted to Pauli measurements, in which magic is a necessary feature of the initial “resource” state. We show that $n$-qubit states with nearly $n$ magic, or indeed almost all states, cannot supply nontrivial speedups over classical computers. We then present an example of analyzing the magic of “natural” condensed matter systems of physical interest. We apply the Boolean function techniques to derive explicit bounds on the magic of certain representative two-dimensional symmetry-protected topological states, and comment on possible further connections between magic and the quantum complexity of phases of matter.

We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or states in a modular fashion. Using a set of local moves known as operator pushing, one can derive properties of the more complex codes, such as transversal non-Clifford gates, by tracing the flow of operators in the network. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes as well as nonstabilizer codes over qubits and qudits. For a contractible tensor network, the sequence of contractions also constructs a decoding or encoding circuit. To highlight the framework’s range of capabilities and to provide a tutorial, we lay out some examples where we glue together simple stabilizer codes to construct nontrivial codes. These examples include the toric code and its variants, a holographic code with transversal non-Clifford operators, a three-dimensional stabilizer code, and other stabilizer codes with interesting properties. Surprisingly, we find that the surface code is equivalent to the two-dimensional Bacon-Shor code after “dualizing” its tensor-network encoding map.

Tensor processing units (TPUs) are specialized hardware accelerators developed by Google to support large-scale machine-learning tasks but they can also be leveraged to accelerate and scale other linear-algebra-intensive computations. In this paper, we demonstrate the usage of TPUs for massively parallel classical simulations of quantum many-body dynamics on long time scales. We apply our methods to study the phenomenon of Floquet prethermalization, i.e., exponentially slow heating in quantum spin chains subject to high-frequency periodic driving. We simulate the dynamics of $L=34$ qubits for over ${10}^5$ Floquet periods, corresponding to circuits with $4\times {10}^6$ nearest-neighbor two-qubit gates. The circuits simulated have no additional symmetries and represent a pure-state evolution in the full $2^L$-dimensional Hilbert space. This is achieved by distributing the computation over 128 TPU cores. On that size TPU cluster, we find speed-ups in wall-clock run time of 230 times and 15 times when compared to reference CPU and single-graphics-processing-unit (GPU) simulations, respectively, for shorter-time 30-qubit simulations that can be handled by all three platforms. We study the computational cost of the simulations, as a function of both the number of qubits and the number of TPU cores used, up to our maximum capacity of $L=40$ qubits, which requires a “full pod” of 2048 TPU cores with tens of terabytes of memory in total. For these simulations, an eight-TPU-core machine is comparable to a single A100 GPU and thus the full TPU pod is comparable to a machine with hundreds of top-of-the-line GPUs. However, the TPU pod is more energy and cost efficient and readily accessible (via Google Cloud), unlike such large many-GPU configurations. We also study the accumulation of numerical error as a function of circuit depth in very deep circuits. Our work demonstrates that TPUs can offer significant advantages for state-of-the-art simulations of quantum many-body dynamics.

We study a mechanism whereby quantum information present in the initial state of a quantum many-body system can be protected for arbitrary times due to a combination of symmetry and spatial locality. Remarkably, the mechanism is sufficiently generic that the dynamics can be fully ergodic upon resolving the protecting symmetry and fixing the encoded quantum state, resulting in a quantum memory that persists up to infinite temperature. After exemplifying the mechanism in a strongly nonintegrable two-dimensional (2D) spin model inspired by the surface code, we find it has a natural interpretation in the language of noiseless subsystems and stabilizer subsystem codes. This interpretation yields a number of further examples, including a nonintegrable Hamiltonian with quantum memory based on the Bacon-Shor code. The lifetime of the encoded quantum information in these models is infinite provided that the dynamics respect the stabilizer symmetry of the underlying subsystem code. In the presence of symmetry-violating perturbations, we make contact with previous work leveraging the concept of prethermalization to show that the encoded quantum information can acquire a parametrically long lifetime under dynamics with an enlarged continuous symmetry group. The prethermalization mechanism hinges on the application of external fields that are much larger than the perturbations themselves. We identify conditions on the underlying subsystem code that enable such a prethermal enhancement of the memory lifetime.