Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We prove a bound on this approximation error, exponentially improving a recent result of Burgarth, Facchi, Gramegna, and Pascazio. We apply the symmetry-protection technique to the simulations of the $XXZ$ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory. For both systems, the technique can reduce the simulation error by several orders of magnitude over the unprotected simulation. Finally, we provide numerical evidence suggesting that the technique can also protect simulation against other types of coherent, temporally correlated errors, such as the $1/f$ noise commonly found in solid-state experiments.

As quantum computers approach the fault-tolerance threshold, diagnosing and characterizing the noise on large-scale quantum devices is increasingly important. One of the most important classes of noise channels is the class of Pauli channels, for reasons of both theoretical tractability and experimental relevance. Here we present a practical algorithm for estimating the $s$ nonzero Pauli error rates in an $s$-sparse, $n$-qubit Pauli noise channel, or more generally the $s$ largest Pauli error rates. The algorithm comes with rigorous recovery guarantees and uses only $O(n^2)$ measurements, $O(s{n}^2)$ classical processing time, and Clifford quantum circuits. We experimentally validate a heuristic version of the algorithm that uses simplified Clifford circuits on data from an IBM 14-qubit superconducting device and our open-source implementation. These data show that accurate and precise estimation of the probability of arbitrary-weight Pauli errors is possible even when the signal is 2 orders of magnitude below the measurement noise floor.

Most proof-of-principle experiments for spin qubits have been performed with $\mathrm{Ga}\mathrm{As}$-based quantum dots because of the excellent control they offer over tunneling barriers and the orbital and spin degrees of freedom. Here we present the first realization of high-quality single and double quantum dots hosted in an $\mathrm{In}\mathrm{As}$ two-dimensional electron gas, demonstrating accurate control down to the few-electron regime, where we observe a clear Kondo effect and singlet-triplet spin blockade. We measure an electronic $g$ factor of 16 and a typical magnitude of the random hyperfine fields on the quantum dots of approximately $0.6\mathrm{mT}$. We estimate the spin-orbit length in the system to be approximately $5-10\mu \mathrm{m}$ (which is almost 2 orders of magnitude longer than typically measured in $\mathrm{In}\mathrm{As}$ nanostructures), achieved by a very symmetric design of the quantum well. These favorable properties put the $\mathrm{In}\mathrm{As}$ two-dimensional electron gas on the map as a compelling host for studying fundamental aspects of spin qubits. Furthermore, having weak spin-orbit coupling in a material with a large Rashba coefficient potentially opens up avenues for engineering structures with spin-orbit coupling that can be controlled locally in space and/or time.

Models for quantum computation with circuit connections subject to the quantum superposition principle have recently been proposed. In them, a control quantum system can coherently determine the order in which a target quantum system undergoes $N$ gate operations. This process, known as the quantum $N$-switch, is a resource for several information-processing tasks. In particular, it provides a computational advantage—over fixed-gate-order quantum circuits—for phase-estimation problems involving $N$ unknown unitary gates. However, the corresponding algorithm requires an experimentally unfeasible target-system dimension (super)exponential in $N$. Here, we introduce a promise problem for which the quantum $N$-switch gives an equivalent computational speedup with target-system dimension as small as 2 regardless of $N$. We use state-of-the-art multicore optical-fiber technology to experimentally demonstrate the quantum $N$-switch with $N=4$ gates acting on a photonic-polarization qubit. This is the first observation of a quantum superposition of more than $N=2$ temporal orders, demonstrating its usefulness for efficient phase estimation.

Methods for modeling large driven-dissipative quantum systems are becoming increasingly urgent due to recent experimental progress in a number of photonic platforms. We demonstrate the positive-$P$ method to be ideal for this purpose across a wide range of parameters, focusing on the archetypal driven-dissipative Bose-Hubbard model. Notably, these parameters include intermediate regimes where interactions and dissipation are comparable, and especially cases with low occupations for which common semiclassical approximations can break down. The presence of dissipation can alleviate instabilities in the method that are known to occur for closed systems, allowing the simulation of dynamics up to and including the steady state. Throughout the parameter space of the model, we determine the magnitude of dissipation that is sufficient to make the method useful and stable, finding its region of applicability to be complementary to that of the truncated Wigner method. We then demonstrate its use in a number of examples with nontrivial quantum correlations, including a demonstration of solving the urgent open problem of large and highly nonuniform systems with tens of thousands of sites.

Quantum computation has been growing rapidly in both theory and experiments. In particular, quantum computing devices with a large number of qubits have been developed by IBM, Google, IonQ, and others. The current quantum computing devices are noisy intermediate-scale quantum devices, and so approaches to validate quantum processing on these quantum devices are needed. One of the most common ways of validation for an n-qubit quantum system is quantum tomography, which tries to reconstruct a quantum system’s density matrix by a complete set of observables. However, the inherent noise in the quantum systems and the intrinsic limitations pose a critical challenge to precisely know the actual measurement operators that make quantum tomography impractical in experiments. Here, we propose an alternative approach to quantum tomography, based on the maximal information entropy, that can predict the values of unknown observables based on the available mean measurement data. This can then be used to reconstruct the density matrix with high fidelity even though the results for some observables are missing. Of additional contexts, a practical approach to the inference of the quantum mechanical state using only partial information is also needed.

Developing scalable quantum algorithms to study finite-temperature physics of quantum many-body systems has attracted considerable interest due to recent advancements in quantum hardware. However, such algorithms in their present form require resources that exceed the capabilities of current quantum computers except for a limited range of system sizes and observables. Here, we report calculations of finite-temperature properties, including energy, static and dynamical correlation functions, and excitation spectra of spin systems with up to four sites on five-qubit IBM Quantum devices. These calculations are performed using the quantum imaginary time evolution (QITE) algorithm and made possible by several algorithmic improvements, including a method to exploit symmetries that reduces the quantum resources required by QITE, circuit optimization procedures to reduce circuit depth, and error-mitigation techniques to improve the quality of raw hardware data. Our work demonstrates that the ansatz-independent QITE algorithm is capable of computing diverse finite-temperature observables on near-term quantum devices.

The precise control of complex quantum systems promises numerous technological applications including digital quantum computing. The complexity of such devices renders the certification of their correct functioning a challenge. To address this challenge, numerous methods were developed in the last decade. In this tutorial, we explain prominent protocols for certifying the physical layer of quantum devices described by quantum states and processes. Such protocols are particularly important in the development of near-term devices. Specifically, we discuss methods of direct quantum-state certification, direct-fidelity estimation, shadow-fidelity estimation, direct quantum-process certification, randomized benchmarking, and cross-entropy benchmarking. Moreover, we provide an introduction to powerful mathematical methods, which are widely used in quantum-information theory, in order to derive theoretical guarantees for the protocols.

Understanding the spectrum of noise acting on a qubit can yield valuable information about its environment, and crucially underpins the optimization of dynamical decoupling protocols that can mitigate such noise. However, extracting accurate noise spectra from typical time-dynamics measurements on qubits is intractable using standard methods. Here, we propose to address this challenge using deep-learning algorithms, leveraging the remarkable progress made in the field of image recognition, natural language processing, and more recently, structured data. We demonstrate a neural-network-based methodology that allows for extraction of the noise spectrum associated with any qubit surrounded by an arbitrary bath, with significantly greater accuracy than the current methods of choice. The technique requires only a two-pulse echo decay curve as input data and can further be extended either for constructing customized optimal dynamical decoupling protocols or for obtaining critical qubit attributes such as its proximity to the sample surface. Our results can be applied to a wide range of qubit platforms, and provide a framework for improving qubit performance with applications not only in quantum computing and nanoscale sensing but also in material characterization techniques such as magnetic resonance.

We analyze the complexity of quantum state verification in the context of solving systems of linear equations of the form $A\overrightarrow{x}=\overrightarrow{b}$. We show that any quantum operation that verifies whether a given quantum state is within a constant distance from the solution of the quantum linear systems problem requires $q=\mathrm{\Omega }(\kappa )$ uses of a unitary that prepares a quantum state $|b⟩$, proportional to $\overrightarrow{b}$, and its inverse in the worst case. Here, $\kappa$ is the condition number of matrix $A$. For typical instances, we show that $q=\mathrm{\Omega }(\sqrt{\kappa })$ with high probability. These lower bounds are almost achieved if quantum state verification is performed using known quantum algorithms for the quantum linear systems problem. We also analyze the number of copies of $|b⟩$ required by verification procedures of the prepare-and-measure type. In this case, the lower bounds are quadratically worse, being $\mathrm{\Omega }({\kappa }^2)$ in the worst case and $\mathrm{\Omega }(\kappa )$ in typical instances with high probability. We discuss the implications of our results to known variational and related approaches to this problem, where state preparation, gate, and measurement errors will need to decrease rapidly with $\kappa$ for worst-case and typical instances if error correction is not used, and present some open problems.

A comprehensive description of molecular electron-transfer reactions is essential for our understanding of fundamental phenomena in bioenergetics and molecular electronics. However, experimental studies of molecular systems in condensed-phase environments face difficulties in independently controlling the parameters that govern the transfer mechanism with high precision. We show that, instead, trapped-ion experiments allow us to reproduce and continuously connect vastly different regimes of molecular charge transfer through precise tuning of, e.g., the phonon temperature, electron-phonon interaction, and electronic coupling. Such a setting does not only allow us to reproduce widely used transport models, such as Marcus theory. It also provides access to transfer regimes that are unattainable for molecular experiments, while controlling and measuring the relevant observables on the level of individual quanta. Our numerical simulations predict an unconventional quantum transfer regime, featuring a transition from quantum adiabatic to resonance-assisted transfer as a function of the donor-acceptor energy gap, which can be reached by increasing the electronic coupling at low temperatures. Trapped-ion-based quantum simulations thus promise to enhance our microscopic understanding of molecular electron-transfer processes and may help to reveal efficient design principles for synthetic devices.

We introduce an axiomatic approach for channel divergences and channel relative entropies that is based on three information-theoretic axioms of monotonicity under superchannels, i.e., generalized data processing inequality, additivity under tensor products, and normalization, similar to the approach given for the state domain in Gour and Tomamichel [arXiv:2006.11164v1 (2020), arXiv:2006.12408v2 (2020)]. We show that these axioms are sufficient to give enough structure in the channel domain as well, leading to numerous properties that are applicable to all channel divergences. These include faithfulness, continuity, a type of triangle inequality, and boundedness between the min and max channel relative entropies. In addition, we prove a uniqueness theorem showing that the Kullback-Leibler divergence has only one extension to classical channels. For quantum channels, with the exception of the max relative entropy, this uniqueness does not hold. Instead, we prove the optimality of the amortized channel extension of the Umegaki relative entropy, by showing that it provides a lower bound on all channel relative entropies that reduce to the Kullback-Leibler divergence on classical states. We also introduce the maximal channel extension of a given classical state divergence and study its properties.

We propose a scheme for universal quantum computing based on Kramers rare-earth ions. Their nuclear spins in the presence of a Zeeman-split electronic crystal field ground state act as “passive” qubits that store quantum information. The “active” qubits are switched on optically by fast coherent transitions to excited crystal field states with a magnetic moment, and the magnetic dipole interaction between these states is used to implement controlled not (cnot) gates. We compare our proposal with others, noting particularly the much improved cnot gate time as compared with a $\mathrm{Si}$:$\mathrm{P}$ proposal, also relying on magnetic dipole interactions between active qubits, and rare-earth schemes depending on the dipole blockade for qubits spaced by more than of the order of $1\mathrm{nm}$.

Optically addressable paramagnetic defects in wide-band-gap semiconductors are promising platforms for quantum communications and sensing. The presence of avoided crossings between the electronic levels of these defects can substantially alter their quantum dynamics and be both detrimental and beneficial for quantum information applications. Here we present a joint theoretical and experimental study of the quantum dynamics of paramagnetic defects interacting with a nuclear spin bath at avoided crossings. We find that we can condition the clock transition of the divacancies in $\mathrm{Si}\mathrm{C}$ on multiple adjacent nuclear spins states. We suppress the effects of fluctuating charge impurities and demonstrate an increased coherence time at clock transition, which is limited purely by magnetic noise. Our results pave the way to designing single defect quantum devices operating at avoided crossings.

Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The two-dimensional quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which control parameters play the role of extra, synthetic dimensions. However, so far, a very limited number of implementations of higher-dimensional topological systems have been proposed, a notable example being the so-called four-dimensional quantum Hall effect. Here we show that mesoscopic superconducting systems can implement higher-dimensional topology and represent a formidable platform to study a quantum system with a purely nontrivial second Chern number. We demonstrate that the integrated absorption intensity in designed microwave spectroscopy is quantized and the integer is directly related to the second Chern number. Finally, we show that these systems also admit a non-Abelian Berry phase. Hence, they also realize an enlightening paradigm of topological non-Abelian systems in higher dimensions.

Recently, there has been much interest in the efficient preparation of complex quantum states using low-depth quantum circuits, such as the quantum approximate optimization algorithm (QAOA). While it has been numerically shown that such algorithms prepare certain correlated states of quantum spins with surprising accuracy, a systematic way of quantifying the efficiency of the QAOA in general classes of models has been lacking. Here, we propose that the success of the QAOA in preparing ordered states is related to the interaction distance of the target state, which measures how close that state is to the manifold of all Gaussian states in an arbitrary basis of single-particle modes. We numerically verify this for several examples of nonintegrable quantum models, including Ising models with two- and three-spin interactions and the cluster model in an external field. Our results suggest that the structure of the entanglement spectrum, as witnessed by the interaction distance, correlates with the success of QAOA state preparation, and that this correlation also contains information about different phases present in the model. We conclude that the QAOA typically finds a solution that perturbs around the closest free-fermion state.

Multiparty quantum cryptography based on distributed entanglement will find its natural application in the upcoming quantum networks. The security of many multipartite device-independent (DI) protocols, such as DI conference-key agreement, relies on bounding the von Neumann entropy of the parties’ outcomes conditioned on the eavesdropper’s information, given the violation of a multipartite Bell inequality. We consider three parties testing the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality and certify the privacy of their outcomes by bounding the conditional entropy of a single party’s outcome and the joint conditional entropy of two parties’ outcomes. From the former bound, we show that genuine multipartite entanglement is necessary to certify the privacy of a party’s outcome, while the latter significantly improves previous results. We obtain the entropy bounds thanks to two general results of independent interest. The first one drastically simplifies the quantum setup of an $N$-partite Bell scenario. The second one provides an upper bound on the violation of the MABK inequality by an arbitrary $N$-qubit state, as a function of the state’s parameters.

Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas have been proposed recently for predicting the limited number of features for these states, or estimating the expectation values of operators, without the need for full state reconstruction. These ideas go under the general name of shadow tomography. Here, we provide an experimental demonstration of property estimation based on classical shadows proposed in Huang et al. [Nat. Phys. 16, 1050 (2020)] and study its performance in a quantum-optical experiment with high-dimensional spatial states of photons. We show by means of experimental data how this procedure outperforms conventional state reconstruction in fidelity estimation from a limited number of measurements.

A possible solution of the information paradox can be sought in quantum information scrambling. In this paradigm, it is postulated that all information entering a black hole is rapidly and chaotically distributed across the event horizon, making it impossible to reconstruct the information by means of any local measurement. However, in this scenario, the effects of decoherence are typically ignored, which may render information scrambling moot in cosmological settings. In this work, we develop key steps toward a thermodynamic description of information scrambling in open quantum systems. In particular, we separate the entropy change into contributions arising from scrambling and decoherence, for which we derive statements of the second law. This is complemented with a numerical study of the Sachdev-Ye-Kitaev, Maldacena-Qi, XXX, mixed-field Ising, and Lipkin-Meshkov-Glick models in the presence of decoherence in the energy or in the computational basis.

The last decade has witnessed remarkable progress in the development of quantum technologies. Although fault-tolerant devices likely remain years away, the noisy intermediate-scale quantum devices of today may be leveraged for other purposes. Leading candidates are variational quantum algorithms (VQAs), which have been developed for applications including chemistry, optimization, and machine learning, but whose implementations on quantum devices have yet to demonstrate improvements over classical capabilities. In this Perspective, we propose a variety of ways that the performance of VQAs could be informed by quantum optimal control theory. A major theme throughout is the need for sufficient control resources in VQA implementations; we discuss different ways this need can manifest, outline a variety of open questions, and look to the future.