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Solving Linear Equations with Qudits and Tensor Networks

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


Key Details

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

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

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

Demonstrates by solving differential equations related to oscillators and heat

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

AI generated summary

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.

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