Tight Bounds on Pauli Channel Learning without Entanglement.

Quantum entanglement is a crucial resource for learning properties from nature, but a precise characterization of its advantage can be challenging. In this Letter, we consider learning algorithms without entanglement to be those that only utilize states, measurements, and operations that are separable between the main system of interest and an ancillary system. Interestingly, we show that these algorithms are equivalent to those that apply quantum circuits on the main system interleaved with mid-circuit measurements and classical feedforward. Within this setting, we prove a tight lower bound for Pauli channel learning without entanglement that closes the gap between the best-known upper and lower bound. In particular, we show that Θ(2^{n}ϵ^{-2}) rounds of measurements are required to estimate each eigenvalue of an n-qubit Pauli channel to ϵ error with high probability when learning without entanglement. In contrast, a learning algorithm with entanglement only needs Θ(ϵ^{-2}) copies of the Pauli channel. The tight lower bound strengthens the foundation for an experimental demonstration of entanglement-enhanced advantages for Pauli noise characterization.

Exciplex-forming cohost systems with 2,7-dicyanofluorene acceptors for high efficiency red and deep-red OLEDs.

Two 2,7-dicyaonfluorene-based molecules 27-DCN and 27-tDCN are utilized as acceptors (A) to combine with hexaphenylbenzene-centered donors (D) TATT and DDT-HPB for probing the exciplex formation. The photophysical characteristics reveal that the steric hindered 27-tDCN not only can increase the distance of D and A, resulting in a hypsochromic emission, but also dilute the concentration of triplet excitons to suppress non-radiative process. The 27-tDCN-based exciplex-forming blends exhibit better photoluminescence quantum yield (PLQY) as compared to those of 27-DCN-based pairs. In consequence, among these D:A blends, the device employing DDT-HPB:27-tDCN blend as the emissiom layer (EML) exhibits the best EQE of 3.0% with electroluminescence (EL) λmax of 542 nm. To further utilize the exciton electrically generated in exciplex-forming system, two D-A-D-configurated fluorescence emitter DTPNT and DTPNBT are doped into the DDT-HPB:27-tDCN blend. The nice spectral overlap ensures fast and efficient Förster energy transfer (FRET) process between the exciplex-forming host and the fluorescent quests. The red device adopting DDT-HPB:27-tDCN:10 wt% DTPNT as the EML gives EL λmax of 660 nm and maximum external quantum efficiency (EQEmax) of 5.8%, while EL λmax of 685 nm and EQE of 5.0% for the EML of DDT-HPB:27-tDCN:10 wt% DTPNBT. This work manifests a potential strategy to achieve high efficiency red and deep red OLED devices by incorporating the highly fluorescent emitters to extract the excitons generated by the exciplex-forming blend with bulky acceptor for suppressing non-radiative process.

Improved machine learning algorithm for predicting ground state properties.

Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an n-qubit gapped local Hamiltonian after learning from only [Formula: see text] data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require [Formula: see text] data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as [Formula: see text] in the number of qubits n. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.

The complexity of NISQ.

The recent proliferation of NISQ devices has made it imperative to understand their power. In this work, we define and study the complexity class NISQ, which encapsulates problems that can be efficiently solved by a classical computer with access to noisy quantum circuits. We establish super-polynomial separations in the complexity among classical computation, NISQ, and fault-tolerant quantum computation to solve some problems based on modifications of Simon's problems. We then consider the power of NISQ for three well-studied problems. For unstructured search, we prove that NISQ cannot achieve a Grover-like quadratic speedup over classical computers. For the Bernstein-Vazirani problem, we show that NISQ only needs a number of queries logarithmic in what is required for classical computers. Finally, for a quantum state learning problem, we prove that NISQ is exponentially weaker than classical computers with access to noiseless constant-depth quantum circuits.

Out-of-distribution generalization for learning quantum dynamics.

Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits.

Learning Many-Body Hamiltonians with Heisenberg-Limited Scaling.

Learning a many-body Hamiltonian from its dynamics is a fundamental problem in physics. In this Letter, we propose the first algorithm to achieve the Heisenberg limit for learning an interacting N-qubit local Hamiltonian. After a total evolution time of O(ε^{-1}), the proposed algorithm can efficiently estimate any parameter in the N-qubit Hamiltonian to ε error with high probability. Our algorithm uses ideas from quantum simulation to decouple the unknown N-qubit Hamiltonian H into noninteracting patches and learns H using a quantum-enhanced divide-and-conquer approach. The proposed algorithm is robust against state preparation and measurement error, does not require eigenstates or thermal states, and only uses polylog(ε^{-1}) experiments. In contrast, the best existing algorithms require O(ε^{-2}) experiments and total evolution time. We prove a matching lower bound to establish the asymptotic optimality of our algorithm.

Preparing random states and benchmarking with many-body quantum chaos.

Producing quantum states at random has become increasingly important in modern quantum science, with applications being both theoretical and practical. In particular, ensembles of such randomly distributed, but pure, quantum states underlie our understanding of complexity in quantum circuits1 and black holes2, and have been used for benchmarking quantum devices3,4 in tests of quantum advantage5,6. However, creating random ensembles has necessitated a high degree of spatio-temporal control7-12 placing such studies out of reach for a wide class of quantum systems. Here we solve this problem by predicting and experimentally observing the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics, which we use to implement an efficient, widely applicable benchmarking protocol. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system, offering new insights into quantum thermalization13. Predicated on this discovery, we develop a fidelity estimation scheme, which we demonstrate for a Rydberg quantum simulator with up to 25 atoms using fewer than 104 experimental samples. This method has broad applicability, as we demonstrate for Hamiltonian parameter estimation, target-state generation benchmarking, and comparison of analogue and digital quantum devices. Our work has implications for understanding randomness in quantum dynamics14 and enables applications of this concept in a much wider context4,5,9,10,15-20.

Provably efficient machine learning for quantum many-body problems.

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

Generalization in quantum machine learning from few training data.

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as [Formula: see text]. When only K ≪ T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to [Formula: see text]. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

Quantum advantage in learning from experiments.

Quantum technology promises to revolutionize how we learn about the physical world. An experiment that processes quantum data with a quantum computer could have substantial advantages over conventional experiments in which quantum states are measured and outcomes are processed with a classical computer. We proved that quantum machines could learn from exponentially fewer experiments than the number required by conventional experiments. This exponential advantage is shown for predicting properties of physical systems, performing quantum principal component analysis, and learning about physical dynamics. Furthermore, the quantum resources needed for achieving an exponential advantage are quite modest in some cases. Conducting experiments with 40 superconducting qubits and 1300 quantum gates, we demonstrated that a substantial quantum advantage is possible with today's quantum processors.

Challenges and opportunities in quantum machine learning.

At the intersection of machine learning and quantum computing, quantum machine learning has the potential of accelerating data analysis, especially for quantum data, with applications for quantum materials, biochemistry and high-energy physics. Nevertheless, challenges remain regarding the trainability of quantum machine learning models. Here we review current methods and applications for quantum machine learning. We highlight differences between quantum and classical machine learning, with a focus on quantum neural networks and quantum deep learning. Finally, we discuss opportunities for quantum advantage with quantum machine learning.

What the foundations of quantum computer science teach us about chemistry.

With the rapid development of quantum technology, one of the leading applications that has been identified is the simulation of chemistry. Interestingly, even before full scale quantum computers are available, quantum computer science has exhibited a remarkable string of results that directly impact what is possible in a chemical simulation with any computer. Some of these results even impact our understanding of chemistry in the real world. In this Perspective, we take the position that direct chemical simulation is best understood as a digital experiment. While on the one hand, this clarifies the power of quantum computers to extend our reach, it also shows us the limitations of taking such an approach too directly. Leveraging results that quantum computers cannot outpace the physical world, we build to the controversial stance that some chemical problems are best viewed as problems for which no algorithm can deliver their solution, in general, known in computer science as undecidable problems. This has implications for the predictive power of thermodynamic models and topics such as the ergodic hypothesis. However, we argue that this Perspective is not defeatist but rather helps shed light on the success of existing chemical models such as transition state theory, molecular orbital theory, and thermodynamics as models that benefit from data. We contextualize recent results, showing that data-augmented models are a more powerful rote simulation. These results help us appreciate the success of traditional chemical theory and anticipate new models learned from experimental data. Not only can quantum computers provide data for such models, but they can also extend the class and power of models that utilize data in fundamental ways. These discussions culminate in speculation on new ways for quantum computing and chemistry to interact and our perspective on the eventual roles of quantum computers in the future of chemistry.

Efficient Estimation of Pauli Observables by Derandomization.

We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements by fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any L low-weight Pauli observables, a deterministic measurement on only of order log(L) copies of a quantum state suffices. In some cases, for example, when some of the Pauli observables have high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.

Information-Theoretic Bounds on Quantum Advantage in Machine Learning.

We study the performance of classical and quantum machine learning (ML) models in predicting outcomes of physical experiments. The experiments depend on an input parameter x and involve execution of a (possibly unknown) quantum process E. Our figure of merit is the number of runs of E required to achieve a desired prediction performance. We consider classical ML models that perform a measurement and record the classical outcome after each run of E, and quantum ML models that can access E coherently to acquire quantum data; the classical or quantum data are then used to predict the outcomes of future experiments. We prove that for any input distribution D(x), a classical ML model can provide accurate predictions on average by accessing E a number of times comparable to the optimal quantum ML model. In contrast, for achieving an accurate prediction on all inputs, we prove that the exponential quantum advantage is possible. For example, to predict the expectations of all Pauli observables in an n-qubit system ρ, classical ML models require 2^{Ω(n)} copies of ρ, but we present a quantum ML model using only O(n) copies. Our results clarify where the quantum advantage is possible and highlight the potential for classical ML models to address challenging quantum problems in physics and chemistry.

Power of data in quantum machine learning.

The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits.

In Vitro Characterization of Neutralizing Hen Antibodies to Coxsackievirus A16.

Coxsackievirus A16 (CA16) is one of the major causative agents of hand, foot, and mouth disease (HFMD). Children aged <5 years are the most affected by CA16 HFMD globally. Although clinical symptoms of CA16 infections are usually mild, severe complications, such as aseptic meningitis or even death, have been recorded. Currently, no vaccine or antiviral therapy for CA16 infection exists. Single-chain variable fragment (scFv) antibodies significantly inhibit viral infection and could be a potential treatment for controlling the infection. In this study, scFv phage display libraries were constructed from splenocytes of a laying hen immunized with CA16-infected lysate. The pComb3X vector containing the scFv genes was introduced into ER2738 Escherichia coli and rescued by helper phages to express scFv molecules. After screening with five cycles of bio-panning, an effective scFv antibody showing favorable binding activity to proteins in CA16-infected lysate on ELISA plates was selected. Importantly, the selected scFv clone showed a neutralizing capability against the CA16 virus and cross-reacted with viral proteins in EV71-infected lysate. Intriguingly, polyclonal IgY antibody not only showed binding specificity against proteins in CA16-infected lysate but also showed significant neutralization activities. Nevertheless, IgY-binding protein did not cross-react with proteins in EV71-infected lysate. These results suggest that the IgY- and scFv-binding protein antibodies provide protection against CA16 viral infection in in vitro assays and may be potential candidates for treating CA16 infection in vulnerable young children.

Mixed-State Entanglement from Local Randomized Measurements.

We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state, followed by postprocessing using the classical shadows framework. Our method can be applied to any quantum system with single-qubit control. We provide a detailed analysis of the required number of experimental runs, and demonstrate the protocol using existing experimental data [Brydges et al., Science 364, 260 (2019)SCIEAS0036-807510.1126/science.aau4963].

Dissecting the human protein-protein interaction network via phylogenetic decomposition.

The protein-protein interaction (PPI) network offers a conceptual framework for better understanding the functional organization of the proteome. However, the intricacy of network complexity complicates comprehensive analysis. Here, we adopted a phylogenic grouping method combined with force-directed graph simulation to decompose the human PPI network in a multi-dimensional manner. This network model enabled us to associate the network topological properties with evolutionary and biological implications. First, we found that ancient proteins occupy the core of the network, whereas young proteins tend to reside on the periphery. Second, the presence of age homophily suggests a possible selection pressure may have acted on the duplication and divergence process during the PPI network evolution. Lastly, functional analysis revealed that each age group possesses high specificity of enriched biological processes and pathway engagements, which could correspond to their evolutionary roles in eukaryotic cells. More interestingly, the network landscape closely coincides with the subcellular localization of proteins. Together, these findings suggest the potential of using conceptual frameworks to mimic the true functional organization in a living cell.