Published on:

11 September 2023

Primary Category:

Quantum Physics

Paper Authors:

Alejandro Mata Ali,

Iñigo Perez Delgado,

Marina Ristol Roura,

Aitor Moreno Fdez. de Leceta,

Sebastián V. Romero

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Proposes new algorithm for solving linear systems using qudits and tensor networks

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Avoids issues in HHL like gate errors and post-selection through classical simulation

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Can obtain full solution vector directly, unlike HHL's expected values

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Demonstrates by solving differential equations related to oscillators and heat

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Shows promising scaling, though not yet as fast as optimized classical techniques

Solving Linear Equations with Qudits and Tensor Networks

This paper proposes a novel algorithm for solving systems of linear equations using qudits (generalized qubits) and tensor networks. The algorithm is inspired by the quantum HHL algorithm, but avoids issues like gate errors and post-selection by using a classical tensor network simulation. Compared to HHL, this approach can obtain the full solution vector directly, rather than just expected values. The authors demonstrate the algorithm by numerically solving example differential equations related to the harmonic oscillator, damped oscillator, and 2D heat equation. While not as efficient as optimized classical methods, this algorithm offers promising scaling in solving large systems of equations. It also provides insight into the potential capabilities of quantum algorithms without quantum noise.

Fast numerical method for generalized two-level quantum systems

Efficient quantum simulation of systems with multiple energy scales

A quantum algorithm for quadratic optimization

Differentiable solver for quantum dot characterization

A Beginner's Guide to Quantum Optimization

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