Reduction of the circuit depth of quantum circuits is a crucial bottleneck to enabling quantum technology. This depth is inversely proportional to the number of available quantum gates that have been synthesized. Moreover, quantum gate-synthesis and control problems exhibit a vast range of external parameter dependencies, both physical and application specific. In this paper, we address the possibility of learning families of optimal-control pulses that depend adaptively on various parameters, in order to obtain a global optimal mapping from the space of potential parameter values to the control space and hence to produce continuous classes of gates. Our proposed method is tested on different experimentally relevant quantum gates and proves capable of producing high-fidelity pulses even in the presence of multiple variables or uncertain parameters with wide ranges.

Quantum computers solve ever more complex tasks using steadily growing system sizes. Characterizing these quantum systems is vital, yet becoming increasingly challenging. The gold-standard method for this task is quantum state tomography (QST), capable of fully reconstructing a quantum state without prior knowledge. The measurement and classical computing costs, however, increase exponentially with the number of constituents (e.g., qubits)—a daunting bottleneck given the scale of existing and near-term quantum devices. Here, we demonstrate a scalable and practical QST approach that only uses a single measurement setting, namely symmetric informationally complete (SIC) positive operator-valued measures (POVMs). We implement these nonorthogonal measurements on an ion trap quantum processor by utilizing additional energy levels within each ion—without requiring ancillary ions to assist in measurements. More precisely, we locally map the SIC POVM to orthogonal states embedded in a higher-dimensional system, which we read out using repeated in-sequence detections, thereby providing full tomographic information in every shot. Combining this SIC tomography with the recently developed randomized measurement toolbox (“classical shadows”) proves to be a powerful combination. SIC tomography alleviates the need for choosing measurement settings at random (“derandomization”), while classical shadows enable the estimation of arbitrary polynomial functions of the density matrix orders of magnitudes faster than standard methods. The latter enables in-depth entanglement characterization, which we experimentally showcase on a five-qubit absolutely maximally entangled state. Moreover, the fact that the full tomography information is available in every shot enables online QST in real time (i.e., while the experiment is running). We demonstrate this on an eight-qubit entangled state (which has $2^8\cdot 2^8-1=65535$ degrees of freedom), as well as for fast state identification. All in all, these features single out SIC-based classical shadow estimation as a highly scalable and convenient tool for quantum state characterization.

The study of confinement in quantum spin chains has seen a large surge of interest in recent years. It is not only important for understanding a range of effective one-dimensional condensed-matter realizations but it also shares some of the nonperturbative physics with quantum chromodynamics (QCD), which makes it a prime target for current quantum simulation efforts. In analogy to QCD, the confinement-induced two-particle bound states that appear in these models are dubbed mesons. Here, we study scattering events due to meson collisions in a quantum spin chain with long-range interactions such that two mesons have an extended interaction. We show how novel hadronic bound states, e.g., with four constituent particles akin to tetraquarks, may form dynamically in fusion events. In a natural collision their signal is weak, as elastic meson scattering dominates. However, we propose two controllable protocols that allow for a clear observation of dynamical hadron formation. We discuss how this physics can be simulated in trapped-ion or Rydberg-atom setups.

We introduce a general setup for the analog quantum simulation of the dynamics of open quantum systems based on semiconductor quantum dots electrically connected to an array of quantum $RLC$ electronic circuits. The dots are chosen to be in the regime of spin-charge hybridization to enhance their sensitivity to the $RLC$ circuits while mitigating the detrimental effects of unwanted noise. In this context, we establish an experimentally realizable map between the hybrid system and a qubit coupled to thermal harmonic environments of arbitrary complexity that enables the analog quantum simulation of open quantum systems. We assess the utility of the simulator by numerically exact emulations that indicate that the experimental setup can faithfully mimic the intended target even in the presence of its natural inherent noise. We further provide a detailed analysis of the physical requirements on the quantum dots and the $RLC$ circuits needed to experimentally realize this proposal that indicates that the simulator can be created with existing technology. The approach can exactly capture the effects of highly structured non-Markovian quantum environments typical of photosynthesis and chemical dynamics and it offers clear potential advantages over conventional and even quantum computation. The proposal opens up a general path for effective quantum dynamics simulations based on semiconductor quantum dots.

A well-protected and characterized source in a quantum key distribution system is needed for its security. Unfortunately, the source is vulnerable to light-injection attacks, such as Trojan-horse, laser-seeding, and laser-damage attacks, in which an eavesdropper actively injects bright light to hack the source unit. The hacking laser could be a high-power one that can modify properties of components via the laser-damage attack and also further help the Trojan-horse and other light-injection attacks. Here we propose a countermeasure against the light-injection attacks, consisting of an additional sacrificial component placed at the exit of the source. This component should either withstand high-power incoming light while attenuating it to a safe level that cannot modify the rest of the source, or get destroyed into a permanent high-attenuation state that breaks up the line. We demonstrate experimentally that off-the-shelf fiber-optic isolators and circulators have these desired properties, at least under attack by a continuous-wave high-power laser.

Users of quantum networks can securely communicate via so-called (quantum) conference key agreement—making their identities publicly known. In certain circumstances, however, communicating users demand anonymity. Here, we introduce a security framework for anonymous conference key agreement with different levels of anonymity, which is inspired by the $\epsilon$-security of quantum key distribution. We present efficient and noise-tolerant protocols exploiting multipartite Greenberger-Horne-Zeilinger (GHZ) states and prove their security in the finite-key regime. We analyze the performance of our protocols in noisy and lossy quantum networks and compare with protocols that only use bipartite entanglement to achieve the same functionalities. Our simulations show that GHZ-based protocols can outperform protocols based on bipartite entanglement and that the advantage increases for protocols with stronger anonymity requirements. Our results strongly advocate the use of multipartite entanglement for cryptographic tasks involving several users.

Under suitable assumptions, some recently developed quantum algorithms can estimate the ground-state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block-encoding input model of the Hamiltonian, the implementation of which is known to require a large resource overhead. We develop a tool called quantum eigenvalue transformation of unitary matrices with real polynomials (QETU), which uses a controlled Hamiltonian evolution as the input model, a single ancilla qubit, and no multiqubit control operations and is thus suitable for early fault-tolerant quantum devices. This leads to a simple quantum algorithm that outperforms all previous algorithms with a comparable circuit structure for estimating the ground-state energy. For a class of quantum spin Hamiltonians, we propose a new method that exploits certain anticommutation relations and further removes the need to implement the controlled Hamiltonian evolution. Coupled with a Trotter-based approximation of the Hamiltonian evolution, the resulting algorithm can be very suitable for early fault-tolerant quantum devices. We demonstrate the performance of the algorithm using IBM qiskit for the transverse-field Ising model. If we are further allowed to use multiqubit Toffoli gates, we can then implement amplitude amplification and a new binary amplitude-estimation algorithm, which increases the circuit depth but decreases the total query complexity. The resulting algorithm saturates the near-optimal complexity for ground-state preparation and energy estimation using a constant number of ancilla qubits (no more than three).

Single-charge tunneling is a decoherence mechanism affecting superconducting qubits, yet the origin of excess quasiparticle excitations (QPs) responsible for this tunneling in superconducting devices is not fully understood. We measure the flux dependence of charge-parity (or, simply, “parity”) switching in an offset-charge-sensitive transmon qubit to identify the contributions of photon-assisted parity switching and QP generation to the overall parity-switching rate. The parity-switching rate exhibits a qubit-state-dependent peak in the flux dependence, indicating a cold distribution of excess QPs that are predominantly trapped in the low-gap film of the device. Moreover, we find that the photon-assisted process contributes significantly to both parity switching and the generation of excess QPs by fitting to a model that self-consistently incorporates photon-assisted parity switching as well as interfilm QP dynamics.

Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches have enabled near-linear scaling in the condition number $\kappa$ of the linear system, without requiring a complicated variable-time amplitude amplification procedure. However, the most efficient of those procedures is still asymptotically suboptimal by a factor of $\log (\kappa )$. Here, we prove a rigorous form of the adiabatic theorem that bounds the error in terms of the spectral gap for intrinsically discrete-time evolutions. In combination with the qubitized quantum walk, our discrete adiabatic theorem gives a speed-up for all adiabatic algorithms. Here, we use this combination to develop a quantum algorithm for solving linear systems that is asymptotically optimal, in the sense that the complexity is strictly linear in $\kappa$, matching a known lower bound on the complexity. Our $\mathcal{O}[\kappa \log (1/ϵ)]$ complexity is also optimal in terms of the combined scaling in $\kappa$ and the precision $ϵ$. Compared to existing suboptimal methods, our algorithm is simpler and easier to implement. Moreover, we determine the constant factors in the algorithm, which would be suitable for determining the complexity in terms of gate counts for specific applications.

The implementation of time-evolution operators on quantum circuits is important for quantum simulation. However, the standard method, Trotterization, requires a huge number of gates to achieve desirable accuracy. Here, we propose a local variational quantum compilation (LVQC) algorithm, which allows us to accurately and efficiently compile time-evolution operators on a large-scale quantum system by optimization with smaller-size quantum systems. LVQC utilizes a subsystem cost function, which approximates the fidelity of the whole circuit, defined for each subsystem that is as large as the approximate causal cones generated by the Lieb-Robinson (LR) bound. We rigorously derive its scaling property with respect to the subsystem size and show that the optimization conducted on the subsystem size leads to the compilation of whole-system time-evolution operators. As a result, LVQC runs with limited-size quantum computers or classical simulators that can handle such smaller quantum systems. For instance, finite-ranged and short-ranged interacting $L$-size systems can be compiled with $O(L^0)$- or $O(\log L)$-size quantum systems depending on the observables of interest. Furthermore, since this formalism relies only on the LR bound, it can efficiently construct time-evolution operators of various systems in generic dimensions involving finite-, short-, and long-ranged interactions. We also numerically demonstrate the LVQC algorithm for one-dimensional systems. Through the employment of classical simulation by time-evolving block decimation, we succeed in compressing the depth of the time-evolution operators up to $40$ qubits by the compilation for $20$ qubits. LVQC not only provides classical protocols for designing large-scale quantum circuits but also sheds light on applications of intermediate-scale quantum devices in implementing algorithms in larger-scale quantum devices.

Significant aspects of advanced quantum technology today rely on rapid control of atomic matterwaves with hyperfine Raman transitions. Unfortunately, efficient Raman excitations are usually accompanied by uncompensated dynamic phases and coherent spin leakages, preventing accurate and repetitive transfer of recoil momentum to large samples. We provide a systematic study to demonstrate that the limitations can be substantially overcome by dynamically programming an adiabatic pulse sequence. Experimentally, counterpropagating frequency-chirped pulses are programmed on an optical delay line to parallelly drive five $\mathrm{\Delta }m=0$ hyperfine Raman transitions of ${}^{85}\mathrm{Rb}$ atoms for spin-dependent kick (SDK) within $\tau =40$ ns, with an $f_{\mathrm{SDK}}\approx 97.6\mathrm{\%}$ inferred fidelity. Aided by numerical modeling, we demonstrate that by alternating the chirps of successive pulses in a balanced fashion, accumulation of nonadiabatic errors including the spin leakages can be managed, while the dynamic phases can be robustly cancelled. Operating on a phase-stable delay line, the method supports precise, fast, and flexible control of spinor matterwave with efficient Raman excitations.

Atom interferometry on optical clock transitions is being pursued for numerous long-baseline experiments both terrestrially and for future space missions. Crucial to meeting the required sensitivities of these experiments is the implementation of large momentum transfer ($>{10}^3\hslash k$). Here, we show that to sequentially apply such a large momentum via $\pi$ pulses places stringent requirements on the frequency noise of the interferometry laser and we find that the linewidth is required to be considerably lower than the previous estimate of approximately 10 Hz. This is due to imperfect pulse fidelity in the presence of noise and is apparent even for an atom at rest interacting with resonant light, making this a fundamental constraint on operational fidelity for a given laser and pulse sequence. Within this framework, we further present and analyze two high-power frequency-stabilized laser sources designed to perform interferometry on the ${}^1{S}_0{–}^3{P}_0$ clock transitions of cadmium and strontium, operating at 332 nm and 698 nm, respectively.

Quantum correlations are at the core of current developments in quantum technologies. Certification protocols of entanglement and steering, suitable for continuous-variable non-Gaussian states are scarce and generally highly demanding from an experimental point of view. We propose a protocol based on Fisher information for witnessing steering in general continuous-variable bipartite states, through homodyne detection. It proves to be relevant for the detection of non-Gaussian steering in scenarios where witnesses based on Gaussian features like the covariance matrix are shown to fail.

We investigate practical dense coding by imposing locality restrictions on decoders and symmetry restrictions on encoders within the resource theory of asymmetry framework. In this task, the sender Alice and the helper Fred preshare an entangled state. Alice encodes a classical message into the quantum state using a symmetric preserving encoder and sends the encoded state to Bob through a noiseless quantum channel. The receiver Bob and helper Fred are limited to performing quantum measurements satisfying certain locality restrictions to decode the classical message. We are interested in the ultimate dense coding capacity under these constraints. Our contributions are summarized as follows. First, we derive both one-shot and asymptotic optimal achievable transmission rates of the dense coding task under different encoder and decoder combinations. Surprisingly, our results reveal that the transmission rate cannot be improved even when the decoder is relaxed from one-way local operations and classical communication (LOCC) to two-way LOCC, separable measurements, and partial transpose positive measurements of the bipartite system. Second, depending on the class of allowed decoders with certain locality restrictions, we relax the class of encoding operations to superquantum encoders in the general probability theory framework and derive dense coding transmission rates under this setting. For example, when the decoder is fixed to a separable measurement, theoretically, a positive operation is allowed as an encoding operation. Remarkably, even under this superquantum relaxation, the transmission rate still cannot be lifted. This fact highlights the universal validity of our analysis on practical dense coding beyond quantum theory.

We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer, allowing us to learn the Hamiltonian parameters. We develop algorithms for performing this computation on both noisy near-term and future fault-tolerant quantum computers. We argue that the former is promising as an early beyond-classical quantum application since it only requires evolution of a local spin Hamiltonian. We investigate the example of a protein (ubiquitin) confined on a membrane as a benchmark of our method. We isolate small spin clusters, demonstrate the convergence of our learning algorithm on one such example, and then investigate the learnability of these clusters as we cross the ergodic to nonergodic phase transition by suppressing the dipolar interaction. We see a clear correspondence between a drop in the multifractal dimension measured across many-body eigenstates of these clusters, and a transition in the structure of the Hessian of the learning cost function (from degenerate to learnable). Our hope is that such quantum computations might enable the interpretation and development of new NMR techniques for analyzing molecular structure.

Self-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set $B_Q$ of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, $B_Q$ is difficult to characterize, so it is also difficult to prove whether or not a given matrix of quantum correlations allows for self-testing. Here, we show how some tools from graph theory can help to address this problem. We observe that $B_Q$ is strictly contained in an easy-to-characterize set associated with a graph, $\mathrm{\Theta }(G)$. Therefore, whenever the optimum over $B_Q$ and the optimum over $\mathrm{\Theta }(G)$ coincide, self-testing can be demonstrated by simply proving self-testability with $\mathrm{\Theta }(G)$. Interestingly, these maxima coincide for the quantum correlations that maximally violate many families of Bell-like inequalities. Therefore, we can apply this approach to prove the self-testability of many quantum correlations, including some that are not previously known to allow for self-testing. In addition, this approach connects self-testing to some open problems in discrete mathematics. We use this connection to prove a conjecture [M. Araújo et al., Phys. Rev. A, 88, 022118 (2013)] about the closed-form expression of the Lovász theta number for a family of graphs called the Möbius ladders. Although there are a few remaining issues (e.g., in some cases, the proof requires the assumption that measurements are of rank 1), this approach provides an alternative method to self-testing and draws interesting connections between quantum mechanics and discrete mathematics.

Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of nontrivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states (MPSs). We compare counterdiabatic and leakage minimization approaches to the so-called local steering problem that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counterdiabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally, we apply our leakage minimization approach to construct quantum scars in the periodically driven nonintegrable Ising model.

Quantum networks are the center of many of the recent advances in quantum science, not only leading to the discovery of new properties in the foundations of quantum theory but also allowing for novel communication and cryptography protocols. It is known that networks beyond that in the paradigmatic Bell’s theorem imply new and sometimes stronger forms of nonclassicality. Due to a number of practical difficulties, however, the experimental implementation of such networks remains far less explored. Going beyond what has been previously tested, here we verify the nonlocality of an experimental triangle network, consisting of three independent sources of bipartite entangled photon states interconnecting three distant parties. By performing separable measurements only and evaluating parallel chained Bell inequalities, we show that such networks can lead to a genuine form of tripartite nonlocality, where classical models are unable to mimic the quantum predictions even if some of the parties are allowed to communicate.

Quantum machine learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model) are likely to have trainability and generalization issues, especially for large problem sizes. As such, it is fundamental to develop schemes that encode as much information as available about the problem at hand. In this work we present a simple, yet powerful, framework where the underlying invariances in the data are used to build QML models that, by construction, respect those symmetries. These so-called group-invariant models produce outputs that remain invariant under the action of any element of the symmetry group $\mathfrak{G}$ associated with the dataset. We present theoretical results underpinning the design of $\mathfrak{G}$-invariant models, and exemplify their application through several paradigmatic QML classification tasks, including cases when $\mathfrak{G}$ is a continuous Lie group and also when it is a discrete symmetry group. Notably, our framework allows us to recover, in an elegant way, several well-known algorithms for the literature, as well as to discover new ones. Taken together, we expect that our results will help pave the way towards a more geometric and group-theoretic approach to QML model design.