Predicting Expressibility of Parameterized Quantum Circuits using Graph Neural Network

Parameterized Quantum Circuits (PQCs) are essential to quantum machine learning and optimization algorithms. The expressibility of PQCs, which measures their ability to represent a wide range of quantum states, is a critical factor influencing their efficacy in solving quantum problems. However, the existing technique for computing expressibility relies on statistically estimating it through classical simulations, which requires many samples. In this work, we propose a novel method based on Graph Neural Networks (GNNs) for predicting the expressibility of PQCs. By leveraging the graph-based representation of PQCs, our GNN-based model captures intricate relationships between circuit parameters and their resulting expressibility. We train the GNN model on a comprehensive dataset of PQCs annotated with their expressibility values. Experimental evaluation on a four thousand random PQC dataset and IBM Qiskit's hardware efficient ansatz sets demonstrates the superior performance of our approach, achieving a root mean square error (RMSE) of 0.03 and 0.06, respectively

Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum Coprocessor

Adiabatic quantum computing enables the preparation of many-body ground states. This is key for applications in chemistry, materials science, and beyond. Realisation poses major experimental challenges: Direct analog implementation requires complex Hamiltonian engineering, while the digitised version needs deep quantum gate circuits. To bypass these obstacles, we suggest an adiabatic variational hybrid algorithm, which employs short quantum circuits and provides a systematic quantum adiabatic optimisation of the circuit parameters. The quantum adiabatic theorem promises not only the ground state but also that the excited eigenstates can be found. We report the first experimental demonstration that many-body eigenstates can be efficiently prepared by an adiabatic variational algorithm assisted with a multi-qubit superconducting coprocessor. We track the real-time evolution of the ground and exited states of transverse-field Ising spins with a fidelity up that can reach about 99%.Comment: 12 pages, 4 figure

High Fidelity Noise-Tolerant State Preparation of a Heisenberg spin-1/2 Hamiltonian for the Kagome Lattice on a 16 Qubit Quantum Computer

This work describes a method to prepare the quantum state of the Heisenberg spin-1/2 Hamiltonian for the Kagome Lattice in an IBM 16 qubit quantum computer with a fidelity below 1% of the ground state computed via a classical Eigen-solver. Furthermore, this solution has a very high noise tolerance (or overall success rate above 98%). With industrious care taken to deal with the persistent noise inherent to current quantum computers; we show that our solution, when run, multiple times achieves a very high probability of success and high fidelity. We take this work a step further by including efficient scalability or the ability to run on any qubit size quantum computer. The platform of choice for this experiment: The IBM 16 qubit transmon processor ibmq_guadalupe using the Variational Quantum Eigensolver (VQE).Comment: 10 pages, 11 figure

Quantum Data Compression and Quantum Cross Entropy

Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. A central quantity for the theoretical foundation of quantum machine learning is the quantum cross entropy. In this paper, we present one operational interpretation of this quantity, that the quantum cross entropy is the compression rate for sub-optimal quantum source coding. To do so, we give a simple, universal quantum data compression protocol, which is developed based on quantum generalization of variable-length coding, as well as quantum strong typicality.Comment: 8 page

Application of deep quantum neural networks to finance

Use of the deep quantum neural network proposed by Beer et al. (2020) could grant new perspectives on solving numerical problems arising in the field of finance. We discuss this potential in the context of simple experiments such as learning implied volatilites and differential machine proposed by Huge and Savine (2020). The deep quantum neural network is considered to be a promising candidate for developing highly powerful methods in finance

Solving Partial Differential Equations using a Quantum Computer

The simulation of quantum systems currently constitutes one of the most promising applications of quantum computers. However, the integration of more general partial differential equations (PDEs) for models of classical systems that are not governed by the laws of quantum mechanics remains a fundamental challenge. Current approaches such as the Variational Quantum Linear Solver (VQLS) method can accumulate large errors and the associated quantum circuits are difficult to optimize. A recent method based on the Feynmann-Kitaev formalism of quantum dynamics has been put forth, where the full evolution of the system can be retrieved after a single optimization of an appropriate cost function. This spacetime formulation alleviates the accumulation of errors, but its application is restricted to quantum systems only. In this work, we introduce an extension of this formalism applicable to the non-unitary dynamics of classical systems including for example, the modeling of diffusive transport or heat transfer. In addition, we demonstrate how PDEs with non-linear elements can also be integrated to incorporate turbulent phenomena