Quantum counterfeit coin problems

@inproceedings{Iwama2010QuantumCC,
  title={Quantum counterfeit coin problems},
  author={Kazuo Iwama and Harumichi Nishimura and Raymond H. Putra and Junichi Teruyama},
  booktitle={Theor. Comput. Sci.},
  year={2010}
}
Quantum algorithms for search with wildcards and combinatorial group testing
TLDR
A nearly optimal O(√n log n) quantum query algorithm is given for search with wildcards, beating the classical lower bound of Ω(n) queries.
Reconstructing Strings from Substrings with Quantum Queries
TLDR
This paper investigates the number of quantum queries made to solve the problem of reconstructing an unknown string from its substrings in a certain query model and shows a quantum algorithm that exactly identifies the string S with at most $\frac{3}{4}N + o(N)$ queries, where N is the length of S.
Recovering Strings in Oracles: Quantum and Classic
TLDR
This paper presents a simple way to study algorithms that run in significantly less than N steps by sacrificing the exactness of the computation by using an oracle.
Efficient Quantum Algorithms for (Gapped) Group Testing and Junta Testing
TLDR
This tester is based on a new quantum algorithm for a gapped version of the combinatorial group testing problem, with an up to quartic improvement over the query complexity of the best classical algorithm.
Quantum Algorithms for Learning Symmetric Juntas via the Adversary Bound
  • Aleksandrs Belovs
  • Computer Science, Mathematics
    2014 IEEE 29th Conference on Computational Complexity (CCC)
  • 2014
TLDR
This paper constructs optimal quantum query algorithms for the cases when h is the XOR or the OR function, or the exact-half function or the majority function, and proves an upper bound of $${O(k^{1/4})}$$O (k 1/4).
Quantum algorithm for learning secret strings and its experimental demonstration
TLDR
It is proved that any classical deterministic algorithm needs at least n queries to the oracle fs to learn the n-bit secret string s in both the worst case and the average case, and an optimal classical Deterministic algorithm learning any s using n queries is presented.
Quantum Algorithm for Monotonicity Testing on the Hypercube
TLDR
A bounded-error quantum algorithm is developed that makes $\tilde O(n^{1/4}\varepsilon^{-1/2})$ queries to a Boolean function $f$, accepts a monotone function, and rejects a function that is $\varpsilon$-far from being monotones.
QLib: Quantum module library
TLDR
QLib is proposed, a quantum module library, which contains scripts to generate quantum modules of different sizes and specifications for well-known quantum algorithms, which can also serve as a suite of benchmarks for quantum logic and physical synthesis.
QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation
TLDR
This work proposes a low-level, easy-to-use benchmark suite called QASMBench based on the OpenQASM assembly representation, which consolidates commonly used quantum routines and kernels from a variety of domains including chemistry, simulation, linear algebra, searching, optimization, arithmetic, machine learning, fault tolerance, cryptography, etc., trading-off between generality and usability.
Efficient Hierarchical State Vector Simulation of Quantum Circuits via Acyclic Graph Partitioning
TLDR
This paper presents three partitioning strategies and observes that acyclic graph partitioning typically results in the best time-to-solution, in contrast, other strategies reduce the partitioning time at the expense of potentially increased simulation times.

References

SHOWING 1-10 OF 32 REFERENCES
Searching for two counterfeit coins with two-arms balance
Lower bounds for randomized and quantum query complexity using Kolmogorov arguments
  • Sophie Laplante, F. Magniez
  • Computer Science, Mathematics
    Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.
  • 2004
TLDR
A very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply, and derives a general form of the ad hoc weighted method used by Hoyer, Neerbek and Shi to give a quantum lower bound on ordered search and sorting.
Reflections for quantum query algorithms
We show that any boolean function can be evaluated optimally by a quantum query algorithm that alternates a certain fixed, input-independent reflection with a second reflection that coherently
Symmetry-Assisted Adversaries for Quantum State Generation
TLDR
A new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem and answer an open question due to Spalek by showing that the multiplicative version of the adversary method is stronger than the additive one for any problem.
Negative weights make adversaries stronger
TLDR
A stronger version of the adversary method which goes beyond this principle to make explicit use of the stronger condition that the algorithm actually computes the function, and which is a lower bound on bounded-error quantum query complexity.
Quantum query complexity and semi-definite programming
TLDR
A general lower bound for quantum query complexity is derived that encompasses a lower bound method of Ambainis and its generalizations and an interpretation of a generalized form of branching in quantum computation.
Span Programs and Quantum Query Complexity: The General Adversary Bound Is Nearly Tight for Every Boolean Function
  • B. Reichardt
  • Computer Science
    2009 50th Annual IEEE Symposium on Foundations of Computer Science
  • 2009
TLDR
It is generally that properties of eigenvalue-zero eigenvectors in fact imply an "effective" spectral gap around zero, and a strong universality result for span programs follows.
Quantum Query Complexity of State Conversion
TLDR
It is obtained that the general adversary bound characterizes the quantum query complexity of any function whatsoever, implying that discrete and continuous-time query models are equivalent in the bounded-error setting, even for the general state-conversion problem.
Quantum complexity theory
TLDR
This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation.
A fast quantum mechanical algorithm for database search
TLDR
In early 1994, it was demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) .
...
...