Practical distributed quantum computing requires the development of efficient compilers, able to make quantum circuits compatible with some given hardware constraints. This problem is known to be tough, even for local computing. Here, we address it on distributed architectures. As generally assumed in this scenario, telegates represent the fundamental remote (inter-processor) operations. Each telegate consists of several tasks: (i) entanglement generation and distribution, (ii) local operations, and (iii) classical communications. Entanglement generations and distribution is an expensive resource, as it is time-consuming. To mitigate its impact, we model an optimization problem that combines running-time minimization with the usage of distributed entangled states. Specifically, we formulated the distributed compilation problem as a dynamic network flow. To enhance the solution space, we extend the formulation, by introducing a predicate that manipulates the circuit given in input and parallelizes telegate tasks. To evaluate our framework, we split the problem into three sub-problems, and solve it by means of an approximation routine. Experiments demonstrate that the run-time is resistant to the problem size scaling. Moreover, we apply the proposed algorithm to compile circuits under different topologies, showing that topologies with a higher ratio between edges and nodes give rise to shallower circuits.

Loading data efficiently from classical memories to quantum computers is a key challenge of noisy intermediate-scale quantum computers. Such a problem can be addressed through quantum generative adversarial networks (qGANs), which are noise tolerant and agnostic with respect to data. Tuning a qGAN to balance accuracy and training time is a hard task that becomes paramount when target distributions are multivariate. Thanks to our tuning of the hyper-parameters and of the optimizer, the training of qGAN reduces, on average, the Kolmogorov–Smirnov statistic of 43–64% with respect to the state of the art. The ability to reach optima is non-trivially affected by the starting point of the search algorithm. A gap arises between the optimal and sub-optimal training accuracy. We also point out that the simultaneous perturbation stochastic approximation (SPSA) optimizer does not achieve the same accuracy as the Adam optimizer in our conditions, thus calling for new advancements to support the scaling capability of qGANs.

Complex quantum circuits are constituted by combinations of quantum subroutines. The computation is possible as long as the quantum data encoding is consistent throughout the circuit. Despite its fundamental importance, the formalization of quantum data encoding has never been addressed systematically so far. We formalize the concept of quantum data encoding, namely the format providing a representation of a data set through a quantum state, as a distinct abstract layer with respect to the associated data loading circuit. We survey existing encoding methods and their respective strategies for classical-to-quantum exact and approximate data loading, for the quantum-to-classical extraction of information from states, and for quantum-to-quantum encoding conversion. Next, we show how major quantum algorithms find a natural interpretation in terms of data loading. For instance, the quantum Fourier transform is described as a quantum encoding converter, while the quantum amplitude estimation as an extraction routine. The new conceptual framework is exemplified by considering its application to the simple case of the Bernstein–Vazirani algorithm, and then to quantum-based Monte Carlo simulations, thus showcasing the power of the proposed formalism for the description of complex quantum circuits. Indeed, the approach clarifies the structure of complex quantum circuits and enables their efficient design.

We generalize the Approximate Quantum Compiling algorithm into a new method for CNOT-depth reduction, which is apt to process wide target quantum circuits. Combining this method with state-of-the-art techniques for error mitigation and circuit compiling, we present a 10-qubit experimental demonstration of Iterative Amplitude Estimation on a quantum computer. The target application is a derivation of the Expected Value of contract portfolios in the energy industry. In parallel, we also introduce a new variant of the Quantum Amplitude Estimation algorithm which we call Dynamic Amplitude Estimation, as it is based on the dynamic circuit capability of quantum devices. The algorithm achieves a reduction in the circuit width in the order of the binary precision compared to the typical implementation of Quantum Amplitude Estimation, while simultaneously decreasing the number of quantum-classical iterations (again in the order of the binary precision) compared to the Iterative Amplitude Estimation. The calculation of the Expected Value, VaR and CVaR of contract portfolios on quantum hardware provides a proof of principle of the new algorithm.

Computing nonlinear functions over multilinear forms is a general problem with applications in risk analysis. For instance in the domain of energy economics, accurate and timely risk management demands for efficient simulation of millions of scenarios, largely benefiting from computational speedups. We develop a novel hybrid quantum–classical algorithm based on polynomial approximation of nonlinear functions, computed through Quantum Hadamard Products, and we rigorously assess the conditions for its end-to-end speedup for different implementation variants against classical algorithms. In our setting, a quadratic quantum speedup, up to polylogarithmic factors, can be proven only when forms are bilinear and approximating polynomials have second degree, if efficient loading unitaries are available for the input data sets. We also enhance the bidirectional encoding, that allows tuning the balance between circuit depth and width, proposing an improved version that can be exploited for the calculation of inner products. Lastly, we exploit the dynamic circuit capabilities, recently introduced on IBM Quantum devices, to reduce the average depth of the Quantum Hadamard Product circuit. A proof of principle is implemented and validated on IBM Quantum systems.