DeepAI AI Chat
Log In Sign Up

Quantum communication complexity of linear regression

by   Ashley Montanaro, et al.

Dequantized algorithms show that quantum computers do not have exponential speedups for many linear algebra problems in terms of time and query complexity. In this work, we show that quantum computers can have exponential speedups in terms of communication complexity for some fundamental linear algebra problems. We mainly focus on solving linear regression and Hamiltonian simulation. In the quantum case, the task is to prepare the quantum state of the result. To allow for a fair comparison, in the classical case the task is to sample from the result. We investigate these two problems in two-party and multiparty models, propose near-optimal quantum protocols and prove quantum/classical lower bounds. In this process, we propose an efficient quantum protocol for quantum singular value transformation, which is a powerful technique for designing quantum algorithms. As a result, for many linear algebra problems where quantum computers lose exponential speedups in terms of time and query complexity, it is possible to have exponential speedups in terms of communication complexity.


page 1

page 2

page 3

page 4


Linear combination of Hamiltonian simulation for non-unitary dynamics with optimal state preparation cost

We propose a simple method for simulating a general class of non-unitary...

Realizing quantum linear regression with auxiliary qumodes

In order to exploit quantum advantages, quantum algorithms are indispens...

Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints

Lasso and Ridge are important minimization problems in machine learning ...

Quantum query complexity with matrix-vector products

We study quantum algorithms that learn properties of a matrix using quer...

Quantum Regularized Least Squares

Linear regression is a widely used technique to fit linear models and fi...

Random circuit block-encoded matrix and a proposal of quantum LINPACK benchmark

The LINPACK benchmark reports the performance of a computer for solving ...

Communication Complexity of One-Shot Remote State Preparation

Quantum teleportation uses prior shared entanglement and classical commu...