## 11 Citations

Quantum algorithm for multivariate polynomial interpolation

- Mathematics, Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2018

This work presents and analyzes quantum algorithms for this multivariate polynomial interpolation problem over the fields Fq, R and C and finds a much larger gap between classical and quantum algorithms than the univariate case, where the speedup is by a factor of 2.

Optimal Quantum Algorithm for Polynomial Interpolation

- Computer Science, MathematicsICALP
- 2016

It is shown that the lower bound is achievable: d/2+1/2 quantum queries suffice to determine the polynomial with bounded error, and the algorithm's success probability as a function of the number of queries is precisely optimal.

Quantum Algorithms for Learning a Hidden Graph

- Computer ScienceTQC
- 2022

This work studies the problem of learning an unknown graph provided via an oracle using a quantum algorithm, and gives quantum algorithms in the graph state model whose complexity is similar to the parity query model.

Quantum algorithms for learning graphs and beyond

- Computer ScienceArXiv
- 2020

We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a…

Quantum learning Boolean linear functions w.r.t. product distributions

- Computer ScienceQuantum Inf. Process.
- 2020

The biased quantum Fourier transform introduced in Kanade et al. (2018) is employed to develop efficient quantum algorithms for learning Boolean linear functions on n bits from quantum examples w.r.t. and proves lower bounds on the classical and quantum sample complexities of the learning problem.

Binary classification with classical instances and quantum labels

- Computer ScienceQuantum Mach. Intell.
- 2021

This work proposes a novel quantum version of the classical binary classification task by considering maps with classical input and quantum output and corresponding classical-quantum training data and provides sample complexity lower bounds which show that the upper bounds are essentially tight for pure output states.

Optimal Quantum Sample Complexity of Learning Algorithms

- Computer ScienceComputational Complexity Conference
- 2017

The main result is that quantum and classical sample complexity are in fact equal up to constant factors in both the PAC and agnostic models.

Identifying Generalized Reed-Muller Codewords by Quantum Queries

- Computer ScienceInt. J. Found. Comput. Sci.
- 2017

We provide an exact quantum query algorithm that identifies uncorrupted codewords from a degree-d generalized Reed-Muller code of length qn over the finite field of size q. When d is constant, the…

Preliminaries and notations ( a ) Notation and definitions

- 2018

A quantum algorithm for Viterbi decoding of classical convolutional codes

- Computer ScienceQuantum Inf. Process.
- 2015

A quantum Viterbi algorithm (QVA) with better than classical performance under certain conditions is applied to decoding classical convolutional codes, for instance, large constraint length $$Q$$Q and short decode frames $$N$$N.

## References

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Sharp Quantum versus Classical Query Complexity Separations

- Computer ScienceAlgorithmica
- 2002

A black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved exactly in the quantum case with a single query (and a polynomial number of auxiliary operations).

Bound on the number of functions that can be distinguished with k quantum queries

- Mathematics, Computer Science
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A bound for how many functions can be distinguished with k quantum queries is derived.

Quantum versus classical learnability

- Computer ScienceProceedings 16th Annual IEEE Conference on Computational Complexity
- 2001

This work considers quantum versions of two well-studied models of learning Boolean functions: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples to establish a polynomial relationship between the number of quantum versus classical queries required for learning.

Quantum Algorithms to Solve the Hidden Shift Problem for Quadratics and for Functions of Large Gowers Norm

- Computer Science, MathematicsMFCS
- 2009

Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used…

Quantum algorithms for some hidden shift problems

- Computer ScienceSODA '03
- 2003

The hidden coset problem is defined, which generalizes the hidden shift problem and the hidden subgroup problem and provides a unified way of viewing the ability of the Fourier transform to capture subgroup and shift structure.

Quantum computation beyond the circuit model

- Physics
- 2008

The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of…

Bounds for the quantity of information transmitted by a quantum communication channel

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Elements of Information Theory

- Computer Science
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The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.

Lower Bounds on Quantum Query Complexity

- Computer ScienceBull. EATCS
- 2005

This paper discusses here what quantum computers cannot do, and specifically how to prove limits on their computational power.