scholarly journals AN OBSERVER-BASED DE-QUANTISATION OF DEUTSCH'S ALGORITHM

2011 ◽  
Vol 22 (01) ◽  
pp. 191-201
Author(s):  
CRISTIAN S. CALUDE ◽  
MATTEO CAVALIERE ◽  
RADU MARDARE
Keyword(s):  
Quantum Computing ◽  
Quantum Measurement ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Classical Solutions ◽  
Finite State Automata ◽  
Computational Problem ◽  
Classical Simulation ◽  
Finite State ◽  
Classical Computing

Deutsch's problem is the simplest and most frequently examined example of computational problem used to demonstrate the superiority of quantum computing over classical computing. Deutsch's quantum algorithm has been claimed to be faster than any classical ones solving the same problem, only to be discovered later that this was not the case. Various de-quantised solutions for Deutsch's quantum algorithm—classical solutions which are as efficient as the quantum one—have been proposed in the literature. These solutions are based on the possibility of classically simulating "superpositions", a key ingredient of quantum algorithms, in particular, Deutsch's algorithm. The de-quantisation proposed in this note is based on a classical simulation of the quantum measurement achieved with a model of observed system. As in some previous de-quantisations of Deutsch's quantum algorithm, the resulting de-quantised algorithm is deterministic. Finally, we classify observers (as finite state automata) that can solve the problem in terms of their "observational power".

Can Quantum Computers Solve Linear Algebra Problems to Advance Engineering Applications?

2018 ◽  
Author(s):  
Guanglei Xu ◽  
William S. Oates
Keyword(s):  
Quantum Computing ◽  
Linear Algebra ◽  
Quantum Algorithms ◽  
Finite Difference Methods ◽  
Engineering Application ◽  
Quantum Circuit ◽  
Quantum Computers ◽  
Measurement Methodology ◽  
Classical Computing ◽  
Richard Feynman

Since its inception by Richard Feynman in 1982, quantum computing has provided an intriguing opportunity to advance computational capabilities over classical computing. Classical computers use bits to process information in terms of zeros and ones. Quantum computers use the complex world of quantum mechanics to carry out calculations using qubits (the quantum analog of a classical bit). The qubit can be in a superposition of the zero and one state simultaneously unlike a classical bit. The true power of quantum computing comes from the complexity of entanglement between many qubits. When entanglement is realized, quantum algorithms for problems such as factoring numbers and solving linear algebra problems show exponential speed-up relative to any known classical algorithm. Linear algebra problems are of particular interest in engineering application for solving problems that use finite element and finite difference methods. Here, we explore quantum linear algebra problems where we design and implement a quantum circuit that can be tested on IBM’s quantum computing hardware. A set of quantum gates are assimilated into a circuit and implemented on the IBM Q system to demonstrate its algorithm capabilities and its measurement methodology.

scholarly journals Variational Quantum Optimization with Multi-Basis Encodings

2021 ◽  
Author(s):  
Taylor Patti ◽  
Jean Kossaifi ◽  
Anima Anandkumar ◽  
Susanne Yelin
Keyword(s):  
Nonconvex Optimization ◽  
Quantum Algorithms ◽  
Optimization Algorithms ◽  
Quantum Algorithm ◽  
Activation Functions ◽  
Quantum Formalism ◽  
Classical Simulation ◽  
Circuit Depth ◽  
Quantum Optimization ◽  
Classical Optimization

Abstract Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization landscapes. We tackle these challenges by introducing a new variational quantum algorithm that utilizes multi-basis graph encodings and nonlinear activation functions. Our technique results in increased optimization performance, a factor of two increase in effective quantum resources, and a quadratic reduction in measurement complexity. While the classical simulation of many qubits with traditional quantum formalism is impossible due to its exponential scaling, we mitigate this limitation with exact circuit representations using factorized tensor rings. In particular, the shallow circuits permitted by our technique, combined with efficient factorized tensor-based simulation, enable us to successfully optimize the MaxCut of the nonlocal 512-vertex DIMACS library graphs on a single GPU. By improving the performance of quantum optimization algorithms while requiring fewer quantum resources and utilizing shallower, more error-resistant circuits, we offer tangible progress for variational quantum optimization.

scholarly journals Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 481
Author(s):  
Dong An ◽  
Noah Linden ◽  
Jin-Peng Liu ◽  
Ashley Montanaro ◽  
Changpeng Shao ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Monte Carlo Methods ◽  
Quantum Algorithms ◽  
General Setting ◽  
Quantum Algorithm ◽  
Mathematical Finance ◽  
Classical Solutions ◽  
Multilevel Monte Carlo

Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic speed-up for multilevel Monte Carlo methods in a general setting. As applications, we apply it to compute expectation values determined by classical solutions of SDEs, with improved dependence on precision. We demonstrate the use of this algorithm in a variety of applications arising in mathematical finance, such as the Black-Scholes and Local Volatility models, and Greeks. We also provide a quantum algorithm based on sublinear binomial sampling for the binomial option pricing model with the same improvement.

Quantum Computing Approach for Alignment-Free Sequence Search and Classification

2012 ◽  
pp. 279-300
Author(s):  
Rao M. Kotamarti ◽  
Mitchell A. Thornton ◽  
Margaret H. Dunham
Keyword(s):  
Quantum Computing ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Search Space ◽  
Classification Problem ◽  
Sequence Classification ◽  
Sequence Search ◽  
Quantum Version ◽  
Computing Approach ◽  
Candidate Set

Many classes of algorithms that suffer from large complexities when implemented on conventional computers may be reformulated resulting in greatly reduced complexity when implemented on quantum computers. The dramatic reductions in complexity for certain types of quantum algorithms coupled with the computationally challenging problems in some bioinformatics problems motivates researchers to devise efficient quantum algorithms for sequence (DNA, RNA, protein) analysis. This chapter shows that the important sequence classification problem in bioinformatics is suitable for formulation as a quantum algorithm. This chapter leverages earlier research for sequence classification based on Extensible Markov Model (EMM) and proposes a quantum computing alternative. The authors utilize sequence family profiles built using EMM methodology which is based on using pre-counted word data for each sequence. Then a new method termed quantum seeding is proposed for generating a key based on high frequency words. The key is applied in a quantum search based on Grover algorithm to determine a candidate set of models resulting in a significantly reduced search space. Given Z as a function of M models of size N, the quantum version of the seeding algorithm has a time complexity in the order of as opposed to O(Z) for the standard classic version for large values of Z.

QUANTUM COMPUTING, GROVER'S SEARCH ALGORITHM AND ITS APPLICATIONS IN BIOINFORMATICS

COSMOS ◽  
2006 ◽  
Vol 02 (01) ◽  
pp. 71-80
Author(s):  
K. W. CHOO
Keyword(s):  
Quantum Computing ◽  
Mass Spectra ◽  
Search Algorithm ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Protein Mass ◽  
Quantum Counting ◽  
Grover’S Search Algorithm ◽  
Counting Algorithm

This article reviews quantum computing and quantum algorithms. Some insights into its potential in speeding up computations are covered, with emphasis on the use of Grover's Search. In the last section, we discuss applications of quantum algorithm to bioinformatics. In particular, the extension of quantum counting algorithm to protein mass spectra counting is proposed.

Quantum Computing Approach for Alignment-Free Sequence Search and Classification

2013 ◽  
pp. 1705-1726
Author(s):  
Rao M. Kotamarti ◽  
Mitchell A. Thornton ◽  
Margaret H. Dunham
Keyword(s):  
Quantum Computing ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Search Space ◽  
Classification Problem ◽  
Sequence Classification ◽  
Sequence Search ◽  
Quantum Version ◽  
Computing Approach ◽  
Candidate Set

Many classes of algorithms that suffer from large complexities when implemented on conventional computers may be reformulated resulting in greatly reduced complexity when implemented on quantum computers. The dramatic reductions in complexity for certain types of quantum algorithms coupled with the computationally challenging problems in some bioinformatics problems motivates researchers to devise efficient quantum algorithms for sequence (DNA, RNA, protein) analysis. This chapter shows that the important sequence classification problem in bioinformatics is suitable for formulation as a quantum algorithm. This chapter leverages earlier research for sequence classification based on Extensible Markov Model (EMM) and proposes a quantum computing alternative. The authors utilize sequence family profiles built using EMM methodology which is based on using pre-counted word data for each sequence. Then a new method termed quantum seeding is proposed for generating a key based on high frequency words. The key is applied in a quantum search based on Grover algorithm to determine a candidate set of models resulting in a significantly reduced search space. Given Z as a function of M models of size N, the quantum version of the seeding algorithm has a time complexity in the order of as opposed to O(Z) for the standard classic version for large values of Z.

scholarly journals Vibration Analysis of Cyclic Symmetrical Systems by Quantum Algorithms

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Anuradha Mahasinghe
Keyword(s):  
Vibration Analysis ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Equation Of Motion ◽  
Classical Solutions ◽  
Quantum Computers ◽  
Cyclic Symmetry ◽  
Rotating System ◽  
Elastic Systems ◽  
Engineering Problems

Quantum computers have provided exponentially faster solutions to several physical and engineering problems over existing classical solutions. In this paper we present two quantum algorithms to analyze the forced vibration of a mechanical system with cyclic symmetry. Our main algorithm solves the equation of motion of an undamped and nonelastic rotating system with cyclic symmetry consisting of n sectors, by encoding the displacements of each sector at time t in a quantum state. The runtime of this algorithm is polylog in both n and t, thus exponentially faster than the analogous classical algorithm. Also we consider damped and elastic systems with cyclic symmetry and present another quantum algorithm to solve it in runtime polylog in n and polynomial in t.

scholarly journals Simulating quantum computers with probabilistic methods

2011 ◽  
Vol 11 (9&10) ◽  
pp. 784-812 ◽  
Author(s):  
Maarten Van den Nest
Keyword(s):  
Fourier Spectrum ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Probabilistic Methods ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Partition Functions ◽  
Classical Simulation ◽  
Last Stage ◽  
Standard Techniques

We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate new classes of classically simulatable quantum circuits where standard techniques relying on the exact computation of measurement probabilities fail to provide efficient simulations. For example, we show how various concatenations of matchgate, Toffoli, Clifford, bounded-depth, Fourier transform and other circuits are classically simulatable. We also prove that sparse quantum circuits as well as circuits composed of CNOT and $\exp[{i\theta X}]$ gates can be simulated classically. In a second part, we apply our results to the simulation of quantum algorithms. It is shown that a recent quantum algorithm, concerned with the estimation of Potts model partition functions, can be simulated efficiently classically. Finally, we show that the exponential speed-ups of Simon's and Shor's algorithms crucially depend on the very last stage in these algorithms, dealing with the classical postprocessing of the measurement outcomes. Specifically, we prove that both algorithms would be classically simulatable if the function classically computed in this step had a sufficiently peaked Fourier spectrum.

scholarly journals qRobot: A Quantum Computing Approach in Mobile Robot Order Picking and Batching Problem Solver Optimization

Algorithms ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 194
Author(s):  
Parfait Atchade-Adelomou ◽  
Guillermo Alonso-Linaje ◽  
Jordi Albo-Canals ◽  
Daniel Casado-Fauli
Keyword(s):  
Quantum Computing ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Order Picking ◽  
Public Access ◽  
Raspberry Pi ◽  
Problem Solver ◽  
Proof Of Concept ◽  
Distribution Centers ◽  
D Wave

This article aims to bring quantum computing to robotics. A quantum algorithm is developed to minimize the distance traveled in warehouses and distribution centers where order picking is applied. For this, a proof of concept is proposed through a Raspberry Pi 4, generating a quantum combinatorial optimization algorithm that saves the distance travelled and the batch of orders to be made. In case of computational need, the robot will be able to parallelize part of the operations in hybrid computing (quantum + classical), accessing CPUs and QPUs distributed in a public or private cloud. We developed a stable environment (ARM64) inside the robot (Raspberry) to run gradient operations and other quantum algorithms on IBMQ, Amazon Braket (D-Wave), and Pennylane locally or remotely. The proof of concept, when run in the above stated quantum environments, showed the execution time of our algorithm with different public access simulators on the market, computational results of our picking and batching algorithm, and analyze the quantum real-time execution. Our findings are that the behavior of the Amazon Braket D-Wave is better than Gate-based Quantum Computing over 20 qubits, and that AWS-Braket has better time performance than Qiskit or Pennylane.

The Essence of Quantum Computing

2018 ◽  
Author(s):  
Rajendra K. Bera
Keyword(s):  
Hilbert Space ◽  
Quantum Computing ◽  
Quantum Physics ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Turing Machines ◽  
Classical Physics ◽  
Core Set ◽  
The World ◽  
Subordinate Role

It now appears that quantum computers are poised to enter the world of computing and establish its dominance, especially, in the cloud. Turing machines (classical computers) tied to the laws of classical physics will not vanish from our lives but begin to play a subordinate role to quantum computers tied to the enigmatic laws of quantum physics that deal with such non-intuitive phenomena as superposition, entanglement, collapse of the wave function, and teleportation, all occurring in Hilbert space. The aim of this 3-part paper is to introduce the readers to a core set of quantum algorithms based on the postulates of quantum mechanics, and reveal the amazing power of quantum computing.

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