# A unified picture of Balance puzzles and Group testing: Some lessons from quantum mechanics for the pandemic

@inproceedings{Waghela2021AUP, title={A unified picture of Balance puzzles and Group testing: Some lessons from quantum mechanics for the pandemic}, author={Chetan Waghela}, year={2021} }

Balance (Counterfeit coin) puzzles have been part of recreational mathematics for a few decades. A particular type of Counterfeit coin puzzle is known in the literature as the ”Beam balance puzzle”. An abstract solution to it is provided by Iwama et.al as a modification of the Bernstein-Vazirani algorithm, making use of quantum parallelism and entanglement. Moreover, during this pandemic, group testing has proved to be an efficient algorithm to save time and cost of testing specimens for the… Expand

#### References

SHOWING 1-10 OF 41 REFERENCES

Quantum complexity theory

- Computer Science
- STOC '93
- 1993

This dissertation proves that relative to an oracle chosen uniformly at random, the class NP cannot be solved on a quantum Turing machine in time $o(2\sp{n/2}).$ and gives evidence suggesting that quantum Turing Machines cannot efficiently solve all of NP. Expand

Classical realization of the quantum Deutsch algorithm

- Physics, Computer Science
- 2018

The aim of this work is to introduce the basic concepts of quantum computation for readers with just a minimum knowledge of quantum mechanics and to present a novel and entirely accessible implementation of a classical analogue of the quantum Deutsch algorithm. Expand

Upper bounds on the multiplicative complexity of symmetric Boolean functions

- Medicine, Computer Science
- Cryptography and Communications
- 2019

New techniques that yield circuits with fewer AND gates than upper bounded are introduced, and upper bounds for the maximum MC in the class of n-variable symmetric Boolean functions, for each n up to 132 are shown. Expand

Single quantum querying of a database

- Computer Science, Physics
- 1997

This work presents a class of fast quantum algorithms, based on Bernstein and Vazirani's parity problem, that retrieves the entire contents of a quantum database in a single query and compares the efficiency of these quantum algorithms with the classical algorithms that are bounded by the classical information-theoretic bound. Expand

Implementation of a quantum algorithm to solve the Bernstein-Vazirani parity problem without entanglement on an ensemble quantum computer

- Physics
- 2001

Bernstein and Varizani have given the first quantum algorithm to solve the parity problem in which a strong violation of the classical information theoretic bound comes about. In this paper we refine… Expand

A scheme for efficient quantum computation with linear optics

- Physics, Medicine
- Nature
- 2001

It is shown that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors and are robust against errors from photon loss and detector inefficiency. Expand

Optical implementations, oracle equivalence, and the Bernstein-Vazirani algorithm

- Computer Science, Physics
- 2007

A new implementation of the Bernstein-Vazirani algorithm that relies on the fact that the polarization states of classical light beams can be cloned and is capable of computing f(x) for a given x, which is not possible with earlier versions used in recent NMR and optics implementations of the algorithm. Expand

The Counterfeit Coin Problem Revisited

- Mathematics, Computer Science
- SIAM J. Comput.
- 1982

This work finds the optimal algorithm in the sense of average run time for the counterfeit coin problem: Given n coins, one of which is heavier or lighter than the rest, and whether it is heavy or light. Expand

Quantum mechanics and classical light

- Physics
- 2019

ABSTRACT The similarities between quantum mechanics and paraxial optics were already well-known to the founding fathers of quantum mechanics; indeed knowledge of paraxial optics partly informed… Expand

A Predetermined Algorithm for Detecting a Counterfeit Coin with a Multi-arms Balance

- Computer Science, Mathematics
- Discret. Appl. Math.
- 1998

A predetermined algorithm is given that requires the minimum possible average number of weighings for almost all values of n in the classical problem of searching a light coin in a set of n coins. Expand