Journal of Global Research in Computer Sciences
MenuISSN: 2229-371X
ISSN: 2229-371X
| Shaktikanta Nayak, Sitakanta Nayak, J.P.Singh Department of Management Studies, Indian Institute of Technology, Roorkee, Uttarakhand (India)-247667 |
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Quantum computation exploits the inherent parallelism due to the principle of superposition of quantum states and hence it has the potential to increase the solution speed for many computational problems. In recent years Grover’s search algorithm, Sore’s factorization algorithm and Deutsch’s algorithm have proven to solve some of the problems exponentially faster than their classical counter parts. The study of financial market is highly sensitive, uncertain and complex in nature. However the traditional classical computers have limited computational capacity with respect to complexity of the problem. In this paper a possible application of Deutsch’s algorithm for market price prediction has been discussed.
Keywords |
| Quantum computing, Quantum algorithm, Computational Finance |
INTRODUCTION |
| The study of financial market is highly sensitive, uncertain and unpredictable and depends upon many external factors. There is no well defined analytical procedure to predict the financial market. Since there is no well-defined mathematical or analytical solution for financial market predictions, people generally apply numerical methods and computer simulation to get better results. The introduction of computer science to solve the financial problems is known as computational finance, where computer simulation tries to find out the most approximate result of a given problem. But the traditional classical computers have limited computational capacity with respect to complexity of the problem. Hence the processing time depends upon the speed of the processor and the speed of processor depends upon the number of instructions executed in each clock period. |
| Therefore if we want to increase the proceeding capacity of the classical computer we have to add more and more computational components to the physical system which ultimately increases the hard ware components of a system. According to the prediction of Moore’s Law, if we will increase the number of transistors in a fixed size integrated circuit, a day will come the size of transistors will tend to atomic. Hence, naturally we are coming to a point where quantum theory is entering to the field of computation known as quantum computation. Quantum computation exploits the inherent parallelism due to the principle of superposition of quantum states and hence it has the potential to increase the solution speed for many computational problems. In recent years for some cases the quantum algorithms, like Grover’s algorithm for unstructured data base search [4, 5, 13], Sore’s factorization algorithm [11] and Deutsch’s algorithm, solve the problems exponentially faster than their classical counter parts. Hence it is worth to introduce quantum algorithms in context of computational finance. So introducing quantum concepts in financial domain may lead better approximation to make a good decision in a stipulated time period. In this paper a theoretical method has been discussed that predicts the market price of a financial instrument using Deutsch algorithm. The organization of the paper is as follows: section-2 introduces quantum concepts in computation, section-3 working principle of quantum algorithm, section-4 definition of Deutsch’s algorithm, section-5 Statement of the financial problem and solution, section-6 Conclusion and references. |
QUANTUM CONCEPTS IN COMPUTATION |
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| Two types of operations under go in a quantum system: measurement and quantum state transformations. In classical computing set of universal gates are used for computational purpose, where as in quantum computation most algorithms follow a sequence of quantum state transformations followed by measurement. Actual quantum computation processes are very different from that of classical counterpart. In classical computer we give input data through the input devices .The input signal is stored in computer memory ,then fed into the microprocessor and the result is stored in memory before it is displayed in the screen .Thus the information travels around the circuit .In contrast , information in quantum computation is first stored in a register and then external fields , such as oscillating magnetic fields , electric fields or laser beams are applied to produce gate operations on the register. These external fields are designed so that they produce desired gate operation, i.e. unitary matrix acting on a particular set of qubits .Hence information sits in the register and they are updated each time the gate operation acts on the register. In order to understand the manipulation of quantum registers we must know how quantum systems evolve. For better understanding refer [8-11]. |
Working Principle Of Quantum Computer: |
| Consider a classical register with 3 bits, then possible outcome will be 238 (it would be possible to use this register to represent any one of the numbers from 0 to 7 at any instance of time).If we will consider a register of 3 qubits, then the register can represent all the numbers from 0 to 7 simultaneously. A single processor having qubit registers will be able to perform calculations using all possible values of the input registers simultaneously. This phenomenon is called quantum parallelism. Quantum parallelism is possible due to the superposition principle of quantum states. Unlike classical bits qubits can exist simultaneously as 0 and 1, with probability for each state given by numerical coefficients. The basic components of a quantum computer [3, 8, 12] are as follows: |
| a. A register or a set of registers. |
| b. A unitary matrix, which is used to execute the quantum algorithms. |
| c. Measurements to extract information. |
WORKING PRINCIPLE OF QUANTUM ALGORITHM |
| The idea to implement quantum mechanics for algorithmic tasks was introduced by Feynman [1, 2].The most important quantum algorithms discovered to date all perform tasks for which there are no classical equivalents .Deutsch’s algorithm [3] is designed to solve the problem of identifying whether a binary function is constant or balanced. Its running time is while classical method requires. Simon’s algorithm [11] is designed for finding the periodicity in a 2-1 binary function that is guaranteed to possess a periodic element. Here exponential speed up is also achieved. Another famous algorithm called Grover’s algorithm is meant for searching an unsorted database in time, where classical search algorithm has running time. This is an example of a real world problem for which quantum algorithm provides the performance that is classically impossible. Finally the most important quantum algorithm is Shor’s algorithm [6] for prime factorization. This algorithm finds the prime factors of very large numbers in polynomial time for which the best classical algorithm requires exponential time. The basic steps used in the quantum algorithms [2, 5, 11] are as follows: |
| a. Initialize the quantum registers. |
| b. Put the registers in superposition of states. |
| c. Evolve the registers using unitary operators. |
| d. Measure the states to get the result. |
Quantum Oracle: |
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CONCLUSION |
| In this paper we have discussed working principle of quantum computer, quantum algorithm and a possible application of Deutsch’s algorithm to financial market price prediction. Here we have discussed an example that will predict the market price of a financial instrument evaluating the function only once using Deutsch’s algorithm. Thus it is computationally much faster than the classical approach. This algorithm solves our problem efficiently but the drawback is in the implementation of the algorithm using quantum computer. |
References |
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