Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations

Abhishek Setty, Rasul Abdusalamov, Felix Motzoi. Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson's equation, second-order differential equation, system of…

Tensor Train Multiplication (TTM)

Alexios A Michailidis, Christian Fenton, Martin Kiffner. We present the Tensor Train Multiplication (TTM) algorithm for the elementwise multiplication of two tensor trains with bond dimension χ. The computational complexity and memory requirements of the TTM algorithm scale as χ3 and χ2, respectively. This represents a significant improvement compared with the conventional approach, where the computational complexity scales as χ4 and memory requirements scale as χ3.We benchmark…

Quantum Algorithm for the Advection-Diffusion Equation with Optimal Success Probability

Paul Over, Sergio Bengoechea, Peter Brearley, Sylvain Laizet, Thomas Rung. A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. After discretization, the explicit time-marching operator is separated into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation problem and is combined with the shift operator through…

Tensor networks enable the calculation of turbulence probability distributions

Nikita Gourianov, Peyman Givi, Dieter Jaksch, Stephen Pope. Predicting the dynamics of turbulent fluid flows has long been a central goal of science and engineering. Yet, even with modern computing technology, accurate simulation of all but the simplest turbulent flow-fields remains impossible: the fields are too chaotic and multi-scaled to directly store them in memory and perform time-evolution. An alternative…

A Quantum Information Perspective on Many-Body Dispersive Forces

Christopher Willby, Martin Kiffner, Joseph Tindall, Jason Crain, and Dieter Jaksch. Despite its ubiquity, many-body dispersion remains poorly understood. Here we investigate the distribution of entanglement in quantum Drude oscillator assemblies, minimal models for dispersion bound systems. We analytically determine a relation between entanglement and energy, showing how the entanglement distribution governs dispersive bonding. This suggests that the monogamy of…

Dispersive Qubit Readout with Intrinsic Resonator Reset

M. Jerger, F. Motzoi, Y. Gao, C. Dickel, L. Buchmann, A. Bengtsson, G. Tancredi, Ch. Warren, J. Bylander, D. DiVincenzo, R. Barends, P. A. Bushev. A key challenge in quantum computing is speeding up measurement and initialization. Here, we experimentally demonstrate a dispersive measurement method for superconducting qubits that simultaneously measures the qubit and returns the readout resonator to its…

Correction formulas for the two-qubit Mølmer-Sørensen gate

Susanna Kirchhoff, Frank K. Wilhelm, Felix Motzoi. The Mølmer-Sørensen gate is a widely used entangling gate for ion platforms with inherent robustness to trap heating. The gate performance is limited by coherent errors, arising from the Lamb-Dicke (LD) approximation and sideband errors. Here, we provide explicit analytical formulas for errors up to fourth order in the LD parameter, by using…

Gate-set evaluation metrics for closed-loop optimal control on nitrogen-vacancy center ensembles in diamond

Philipp J. Vetter, Thomas Reisser, Maximilian G. Hirsch, Tommaso Calarco, Felix Motzoi, Fedor Jelezko and Matthias M. Muller. A recurring challenge in quantum science and technology is the precise control of their underlying dynamics that lead to the desired quantum operations, often described by a set of quantum gates. These gates can be subject to application-specific errors, leading to a…

Reinforcement learning pulses for transmon qubit entangling gates

Ho Nam Nguyen, Felix Motzoi, Mekena Metcalf, K. Birgitta Whaley, Marin Bukov, Markus Schmitt. The utility of a quantum computer depends heavily on the ability to reliably perform accurate quantum logic operations. For finding optimal control solutions, it is of particular interest to explore model-free approaches, since their quality is not constrained by the limited accuracy of theoretical models for…

Experimental error suppression in Cross-Resonance gates via multi-derivative pulse shaping

Boxi Li, Tommaso Calarco and Felix Motzoi. While quantum circuits are reaching impressive widths in the hundreds of qubits, their depths have not been able to keep pace. In particular, cloud computing gates based on fixed-frequency superconducting architectures have stalled, hovering on average around the 1% error range for half a decade, considerably underutilizing the potential offered by their coherence…
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The QCFD (Quantum Computational Fluid Dynamics) project is funded under the European Union’s Horizon Programme (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10), Grant Agreement 101080085 QCFD.