Sensing the insensible using optical schemes: converting the maze problem into a quantum search problem

2020 ◽  
Author(s):  
Debabrata Goswami
Keyword(s):  
Search Problem ◽  
Quantum Search ◽  
Maze Problem

scholarly journals Implementation of Grover’s Quantum Search Algorithm using Rigetti Forest

2019 ◽  
Vol 8 (6S3) ◽  
pp. 110-114
Keyword(s):  
Quantum Computing ◽  
Search Algorithm ◽  
Search Problem ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Search Result ◽  
Amplitude Amplification ◽  
Testing And Evaluation

Grover’s quantum search algorithm allows quadratic speedup in unsorted search problem by utilizing amplitude amplification trick in quantum computing. In this paper, an approach to implement Grover’s quantum search algorithm is proposed. The implementation is done using Rigetti Forest and Python. The testing and evaluation processes are carried on in two computers with different hardware specifications to derive more information from the result. The results are measured in user time and compared with implementation from Quantum Computing Playground. The user time of this implementation for 10 qubits and 1024 data is slower compared to Quantum Computing Playground’s implementation. The proposed implementation can be improved by calculating the probability of Grover’s quantum search algorithm in finding the appropriate search result.

On the General Class of Models of Adiabatic Evolution

2016 ◽  
Vol 23 (03) ◽  
pp. 1650016 ◽  
Author(s):  
Jie Sun ◽  
Songfeng Lu ◽  
Fang Liu
Keyword(s):  
Ground State ◽  
General Class ◽  
Time Complexity ◽  
State Energy ◽  
Search Problem ◽  
Quantum Search ◽  
Final States ◽  
Adiabatic Evolution ◽  
Speed Up ◽  
Effective Use

The general class of models of adiabatic evolution was proposed to speed up the usual adiabatic computation in the case of quantum search problem. It was shown [8] that, by temporarily increasing the ground state energy of a time-dependent Hamiltonian to a suitable quantity, the quantum computation can perform the calculation in time complexity O(1). But it is also known that if the overlap between the initial and final states of the system is zero, then the computation based on the generalized models of adiabatic evolution can break down completely. In this paper, we find another severe limitation for this class of adiabatic evolution-based algorithms, which should be taken into account in applications. That is, it is still possible that this kind of evolution designed to deal with the quantum search problem fails completely if the interpolating paths in the system Hamiltonian are chosen inappropriately, while the usual adiabatic evolutions can do the same job relatively effectively. This implies that it is not always recommendable to use nonlinear paths in adiabatic computation. On the contrary, the usual simple adiabatic evolution may be sufficient for effective use.

QUANTUM SEARCH ALGORITHM CAN BE IMPROVED

2005 ◽  
Vol 03 (01) ◽  
pp. 23-30
Author(s):  
LOV K. GROVER
Keyword(s):  
Search Algorithm ◽  
Exhaustive Search ◽  
Quantum Mechanical ◽  
Search Problem ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Query Operations

Quantum search is a quantum mechanical technique for searching N possibilities in only [Formula: see text] steps. This has been proved to be the best possible algorithm for the exhaustive search problem in the sense that the number of queries it requires cannot be reduced. However, as this paper shows, the number of non-query operations can be reduced by a third without a single increase in the number of queries.

scholarly journals FORMULATION OF A FAMILY OF SURE-SUCCESS QUANTUM SEARCH ALGORITHMS

2004 ◽  
Vol 02 (03) ◽  
pp. 285-293
Author(s):  
JIN-YUAN HSIEH ◽  
CHE-MING LI ◽  
JENN-SEN LIN ◽  
DER-SAN CHUU
Keyword(s):  
Quantum Algorithms ◽  
Search Algorithms ◽  
Search Problem ◽  
Quantum Search ◽  
Matching Conditions ◽  
Quantum Search Algorithms ◽  
Grover Search ◽  
Phase Angles

In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding formulae for evaluating the iterations or oracle calls required in the search computation. We also present how to adjust the phase angles in the generalized Grover operator to ensure the sure-success if minimal oracle calls are demanded in the search.

scholarly journals Spatial quantum search in a triangular network

2012 ◽  
Vol 22 (3) ◽  
pp. 521-531 ◽  
Author(s):  
G. ABAL ◽  
R. DONANGELO ◽  
M. FORETS ◽  
R. PORTUGAL
Keyword(s):  
Triangular Lattice ◽  
Time Complexity ◽  
General Framework ◽  
Quantum Algorithm ◽  
Search Problem ◽  
Quantum Search ◽  
Spatial Search ◽  
Oracle Query ◽  
Triangular Network ◽  
Special Case

The spatial search problem consists of minimising the number of steps required to find a given site in a network, with the restriction that only an oracle query or a translation to a neighbouring site is allowed at each step. We propose a quantum algorithm for the spatial search problem on a triangular lattice with N sites and torus-like boundary conditions. The proposed algorithm is a special case of the general framework for abstract search proposed by Ambainis, Kempe and Rivosh (AKR) in Ambainis et al. (2005) and Tulsi in Tulsi (2008) applied to a triangular network. The AKR–Tulsi formalism was employed to show that the time complexity of the quantum search on the triangular lattice is $O(\sqrt{N \log N})$.

scholarly journals Spatial search on a honeycomb network

2010 ◽  
Vol 20 (6) ◽  
pp. 999-1009 ◽  
Author(s):  
G. ABAL ◽  
R. DONANGELO ◽  
F. L. MARQUEZINO ◽  
R. PORTUGAL
Keyword(s):  
Time Complexity ◽  
Search Algorithm ◽  
Hexagonal Lattice ◽  
Quantum Algorithm ◽  
Quantum Walk ◽  
Honeycomb Lattice ◽  
Search Problem ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Spatial Search

The spatial search problem consists of minimising the number of steps required to find a given site in a network under the restriction that only oracle queries or translations to neighbouring sites are allowed. We propose a quantum algorithm for the spatial search problem on a honeycomb lattice with N sites and torus-like boundary conditions. The search algorithm is based on a modified quantum walk on an hexagonal lattice and the general framework proposed by Ambainis, Kempe and Rivosh (Ambainis et al. 2005) is employed to show that the time complexity of this quantum search algorithm is $O(\sqrt{N \log N})$.

scholarly journals Transition probabilities in generalized quantum search Hamiltonian evolutions

2019 ◽  
Vol 17 (01) ◽  
pp. 2050006 ◽  
Author(s):  
Steven Gassner ◽  
Carlo Cafaro ◽  
Salvatore Capozziello
Keyword(s):  
Transition Probability ◽  
Success Probability ◽  
Search Time ◽  
Search Algorithms ◽  
Search Problem ◽  
Quantum Search ◽  
Optimal Search ◽  
Target State ◽  
Special Cases ◽  
Source State

A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schrödinger’s quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in detail the computational aspects necessary to calculate the transition probability from a source state to a target state in a continuous time quantum search problem defined by a multiparameter generalized time-independent Hamiltonian. In particular, quantifying the performance of a quantum search in terms of speed (minimum search time) and fidelity (maximum success probability), we consider a variety of special cases that emerge from the generalized Hamiltonian. In the context of optimal quantum search, we find it is possible to outperform, in terms of minimum search time, the well-known Farhi–Gutmann analog quantum search algorithm. In the context of nearly optimal quantum search, instead, we show it is possible to identify sub-optimal search algorithms capable of outperforming optimal search algorithms if only a sufficiently high success probability is sought. Finally, we briefly discuss the relevance of a tradeoff between speed and fidelity with emphasis on issues of both theoretical and practical importance to quantum information processing.

scholarly journals Test-state approach to the quantum search problem

2011 ◽  
Vol 83 (5) ◽  
Author(s):  
Arun Sehrawat ◽  
Le Huy Nguyen ◽  
Berthold-Georg Englert
Keyword(s):  
Search Problem ◽  
Quantum Search

scholarly journals Parallel Simulation of Quantum Search

2010 ◽  
Vol 5 (5) ◽  
pp. 634 ◽  
Author(s):  
Simona Caraiman ◽  
Vasile Manta
Keyword(s):  
High Performance ◽  
Quantum Computer ◽  
Parallel Implementation ◽  
Quantum Computers ◽  
Search Problem ◽  
Quantum Search ◽  
Grid Systems ◽  
Specific Scheme ◽  
And Storage ◽  
Efficient Parallelization

Simulation of quantum computers using classical computers is a computationally hard problem, requiring a huge amount of operations and storage. Parallelization can alleviate this problem, allowing the simulation of more qubits at the same time or the same number of qubits to be simulated in less time. A promising approach is represented by executing these simulators in Grid systems that can provide access to high performance resources. In this paper we present a parallel implementation of the QC-lib quantum computer simulator deployed as a Grid service. Using a specific scheme for partitioning the terms describing quantum states and efficient parallelization of the general singe qubit operator and of the controlled operators, very good speed-ups were obtained for the simulation of the quantum search problem.

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