We propose a novel quantum technique to search for unmodelled anomalies in multi-dimensional binned collider data.We propose associating an Ising lattice spin site with each bin, with the Ising Hamiltonian suitably constructed from the observed data and a corresponding theoretical expectation.In order to capture spatially correlated anomalies in the data, we introduce spin-spin interactions between neighboring sites, as well as self-interactions.The ground state energy of the resulting Ising Hamiltonian can be used as a new test statistic, which can be computed either classically or via adiabatic quantum optimization.We demonstrate that our test statistic outperforms some of the most commonly used goodness-of-fit tests.The new approach greatly reduces the look-elsewhere effect by exploiting the typical differences between statistical noise and genuine new physics signals.
We propose a novel quantum technique to search for unmodelled anomalies in multi-dimensional binned collider data.We propose associating an Ising lattice spin site with each bin, with the Ising Hamiltonian suitably constructed from the observed data and a corresponding theoretical expectation.In order to capture spatially correlated anomalies in the data, we introduce spin-spin interactions between neighboring sites, as well as self-interactions.The ground state energy of the resulting Ising Hamiltonian can be used as a new test statistic, which can be computed either classically or via adiabatic quantum optimization.We demonstrate that our test statistic outperforms some of the most commonly used goodness-of-fit tests.The new approach greatly reduces the look-elsewhere effect by exploiting the typical differences between statistical noise and genuine new physics signals.
A bstract Due to the success of the Standard Model (SM), it is reasonable to anticipate that the signal of new physics (NP) beyond the SM is small. Consequently, future searches for NP and precision tests of the SM will require high luminosity collider experiments. Moreover, as precision tests advance, rare processes with many final-state particles require consideration which demands the analysis of a vast number of observables. The high luminosity produces a large amount of experimental data spanning a large observable space, posing a significant data-processing challenge. In recent years, quantum machine learning has emerged as a promising approach for processing large amounts of complex data on a quantum computer. In this study, we propose quantum searching neighbor (QSN) and variational QSN (VQSN) algorithms to search for NP. The QSN is a classification algorithm. The VQSN introduces variation to the QSN to process classical data. As applications, we apply the (V) QSN in the phenomenological study of the NP at the Large Hadron Collider and muon colliders. Examples are implemented on a real quantum hardware, which confirms reliable performance under noisy conditions. The results indicate that the VQSN demonstrates superior efficiency in the sense of computational complexity to a classical counterpart k-nearest neighbor algorithm, even when dealing with classical data.
We develop a quantum-inspired numerical procedure for searching low-energy states of a classical Hamiltonian composed of two-body fully-connected random Ising interactions and a random local longitudinal magnetic field. In this method, we introduce infinitesimal quantum interactions that do not commute with the original Ising Hamiltonian, and repeatedly generate and truncate direct product states, inspired by the Krylov subspace method, to obtain the low-energy states of the original classical Ising Hamiltonian. The computational cost is controlled by the form of infinitesimal quantum interactions (e.g., one-body or two-body interactions) and the numbers of infinitesimal interaction terms introduced, different initial states considered, and low-energy states kept during the iteration. For a demonstrate of the method, here we introduce as the infinitesimal quantum interactions pair products of Pauli X operators acting on different sites and on-site Pauli X operators into the random Ising Hamiltonian, in which the numerical cost is O(N3) per iteration with the system size N. We consider 120 instances of the random coupling realizations for the random Ising Hamiltonian with N up to 600 and search the 120 lowest-energy states for each instance. We find that the time-to-solution by the quantum-inspired method proposed here, with parallelization in terms of the different initial states, for searching the ground state of the random Ising Hamiltonian scales approximately as N5 for N up to 600. We also examine the basic physical properties such as the ensemble-averaged ground-state and first-excited energies and the ensemble-averaged number of states in the low-energy region of the random Ising Hamiltonian.
We use a recently developed quantum simulation approach to study the properties of a three-dimensional Ising model consisting of S = 1/2 quantum spins localized at the sites of a simple cubic lattice. We assume nearest-neighbor interaction between spins with an exchange interaction that can be either ferromagnetic or antiferromagnetic. It is found that the computational method quickly converges towards the expected equilibrium spin configurations. The resulting spontaneous magnetization curves corresponding to the two types of magnetic interactions under consideration were found to be almost identical to the ones obtained via quantum mean field theory at all temperatures. The derived total energies, total free energies, magnetic entropies and specific heats per mole of spins show no sizeable differences from known theoretical values. Furthermore, the results of the simulations for two different 3D Ising systems containing 4×4×4 and 20×20×20 spins localized at the sites of a simple cubic lattice were found to be almost identical to each other. This finding suggests that the self-consistent algorithm approach of the current simulation method allows one to obtain the physical bulk properties of a large magnetic system by relying on simulations of a much smaller spin system sample. Therefore, the method presently considered appears to be not only very accurate as gauged by comparison to mean field theory, but also able to greatly increase the speed of simulations.
We propose a strategy for modeling the behavior of an adiabatic quantum computer described by an Ising Hamiltonian with N sites and the coordination number Z. The method is based on the 1/Z expansion for the density matrix of the system. In each order, the ground state energy is found neglecting the higher-order correlations between the sites, as long as the set of equations remains non-singular. The conditions of the appearance of a singularity, equivalent to the disappearance of energy gap in the given approximation, can be directly obtained from the equations. Then the next order in the expansion must be used, at the price of an N-fold increase in computational resources. This "martingale" strategy allows reducing the computational costs to a power of N rather than 2N, with a finite probability of success. The strategy is illustrated by the case of a two-spin system and extended to a large number of qubits. Comparing the predictions to the experimental results obtained by using an adiabatic quantum computer would help quantify the importance of multi-site correlations, and the influence of decoherence, on its operation.
Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not efficiently computable on classical devices. However, there is no straightforward method to engineer the optimal quantum kernel for each specific use case. We present an approach to this problem, which employs optimization techniques, similar to those used in neural architecture search and AutoML, to automatically find an optimal kernel in a heuristic manner. To this purpose we define an algorithm for constructing a quantum circuit implementing the similarity measure as a combinatorial object, which is evaluated based on a cost function and then iteratively modified using a meta-heuristic optimization technique. The cost function can encode many criteria ensuring favorable statistical properties of the candidate solution, such as the rank of the Dynamical Lie Algebra. Importantly, our approach is independent of the optimization technique employed. The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach, showing the potential of our technique to deliver superior results with reduced effort.
The lack of evidence for new interactions and particles at the Large Hadron Collider (LHC) has motivated the high-energy physics community to explore model-agnostic data-analysis approaches to search for new physics. Autoencoders are unsupervised machine learning models based on artificial neural networks, capable of learning background distributions. We study quantum autoencoders based on variational quantum circuits for the problem of anomaly detection at the LHC. For a QCD tt background and resonant heavy-Higgs signals, we find that a simple quantum autoencoder outperforms classical autoencoders for the same inputs and trains very efficiently. Moreover, this performance is reproducible on present quantum devices. This shows that quantum autoencoders are good candidates for analysing high-energy physics data in future LHC runs.