[1909.03898] Variational algorithms for linear algebra

Quantum algorithms have been developed for efficiently solving linear algebra tasks. However they generally require deep circuits and therefore universal fault-tolerant quantum computers. In this work, we propose variational algorithms for linear algebra tasks that are compatible with Noisy Intermediate Scaled Quantum devices. We show that the solutions of linear systems of equations and matrix-vector multiplications can be translated as the ground states of the constructed Hamiltonians. Based on recently proposed variational quantum algorithms, we introduce Hamiltonian morphing together with an adaptive ansatz for efficiently finding the ground state. As the ground state always has zero energy, it also enables us to verify the solution. Our algorithms have wide applications in machine learning and optimisation problems, and the algorithm for matrix multiplications can be also used for variational Hamiltonian simulation. Finally, we conduct numerical simulations of the algorithm for so

5 mentions: @kenjikun__@kenjikun__@PatrickColes314@dempacat
Date: 2019/09/10 06:49

Referring Tweets

@kenjikun__ ベクトルに対する行列積がある固有値方程式の最小固有状態に対応することを利用してVQEによって行列積を実現した.逆行列の演算に対しても同様に求められるので線型方程式系を解くことも可能.最小固有値は常に0になるので得られた解を検証することもできる. t.co/yl8bDHOmJZ
@PatrickColes314 @charl_bp @ryanmlarose @rigetti Coincidentally, two related papers just appeared on Arxiv, one on Tuesday (t.co/9a24HD7VKB) and one today (t.co/vWxWGEcq5u). It’s been an exciting week for quantum linear systems!
@dempacat この論文、ちゃんと読めてないんですが。64x64の線形方程式を求めるのに、128個のパラメータを(Nelder-Mead法か何かで)調整してるって言ってます? / [1909.03898] Variational algorithms for linear algebra t.co/XA1NLct2kf

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