# Augmented Index and Quantum Streaming Algorithms for DYCK(2)

@article{Nayak2017AugmentedIA, title={Augmented Index and Quantum Streaming Algorithms for DYCK(2)}, author={Ashwin Nayak and Dave Touchette}, journal={ArXiv}, year={2017}, volume={abs/1610.04937} }

We show how two recently developed quantum information theoretic tools can be applied to obtain lower bounds on quantum information complexity. We also develop new tools with potential for broader applicability, and use them to establish a lower bound on the quantum information complexity for the Augmented Index function on an easy distribution. This approach allows us to handle superpositions rather than distributions over inputs, the main technical challenge faced previously. By providing a…

## 9 Citations

Augmented index and quantum streaming algorithms for DYCK(2)

- Computer Science
- 2017

By providing a quantum generalization of the argument of Jain and Nayak, this work leverages this to obtain a lower bound on the space complexity of multi-pass, unidirectional quantum streaming algorithms for the Dyck(2) language.

23 : 2 Quantum Chebyshev ’ s Inequality and Applications

- 2019

In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the…

Separating Quantum Communication and Approximate Rank

- Mathematics, Computer ScienceComputational Complexity Conference
- 2017

This work exhibits a total function H with quantum communication complexity almost quadratically larger than the logarithm of its approximate rank, and shows the upper bound on the approximate rank of F_G by relating it to the Boolean circuit size of the starting function F.

N ov 2 01 6 Separating quantum communication and approximate rank

- 2016

One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix…

Exponential separation of quantum communication and classical information

- Computer Science, PhysicsSTOC
- 2017

A simple proof for an optimal trade-off between Alice's and Bob's communication is given, even when allowing pre-shared entanglement, while computing the related Greater-Than function on n bits.

Quantum Log-Approximate-Rank Conjecture is Also False

- Mathematics, Physics2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

This work derives a polynomially-related quantum communication complexity lower bound using the quantum information complexity approach, thus providing an exponential separation between the log approximate rank and quantum communication complex of f.

Quantum Chebyshev's Inequality and Applications

- Mathematics, PhysicsICALP
- 2019

A new quantum paradigm that is based on a refinement of the Amplitude Estimation algorithm of Brassard et al. is developed, and it is demonstrated that, in a certain model of quantum sampling, one can approximate with relative error the mean of any random variable with a number of quantum samples that is linear in the ratio of the square root of the variance to the mean.

The Flow of Information in Interactive Quantum Protocols: the Cost of Forgetting

- Mathematics, Computer ScienceITCS
- 2017

This work provides a specific sense in which forgetting information is a necessary feature of interactive quantum protocols, and proves that any quantum protocol that does not forget information solves Disjointness on n-bits in Omega (n) communication, completely losing the quadratic quantum speedup.

A Quantum Advantage for a Natural Streaming Problem

- Physics, Computer ScienceArXiv
- 2021

This work gives a one-pass quantum streaming algorithm for one of the best-studied problems in classical graph streaming—the triangle counting problem; the algorithm uses polynomially less space in certain regions of the parameter space.

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