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spin up (we know it after done a measurement). Then without have to measure it, we can |
directly know that the other qubit has spin down. Because of this ability, communication in |
quantum computation can reach a very high speed because information can be transferred |
instantly, very fast like it overmatch the speed of light. |
As quantum computing is on its way to becoming an established discipline of computing |
science, much effort is being put into the development of new quantum algorithms. One |
of quantum algorithms is Grover algorithm, which is used for searching an element in an |
unstructured list of N elements with quadratic speed-up over classical algorithms. Today, |
there are some quantum programming languages which can be used to simulate quantum |
mechanical and quantum algorithm without having a real quantum computer. In this work, |
Quantum Computer Language (QCL) will be used to make a Grover’s quantum search |
simulation in a classical computer. |
B. Position of the Research |
This research is related to an invention of a quantum search algorithm by Lov K. Grover |
[1]. His invention presents an algorithm, which is known as Grover algorithm, that is signifi- |
2 |
cantly faster than any classical algorithm can be. This quantum search algorithm can search |
for an element in an unsorted database containing N elements only in O(√N) steps, while |
in the models of classical computation, searching an unsorted database cannot be done in |
less than linear time (so merely searching through every item is optimal), which will be done |
in O(N) steps. Also, this research is related with Paramita et al work, where their paper |
presented a pseudo code for better understanding about Grover algorithm, and Freddy P. |
Zen et al work [2], who provide an example simulation of Grover algorithm in their paper. |
This research will also try to simulate Grover algorithm in a classical computer using one of |
quantum programming languages, Quantum Computer Language (QCL)[3, 4]. |
C. Significance of the Research |
Inpractice, thisresearchcanbeusedasthefastestknownmethodorsolutionforsearching |
an element in an unsorted database containing N elements. By using the method in this |
research, the searching process can speed-up quadratically over classical algorithms. |
D. Problem |
Considered points in this work are: |
1. Is it possible to simulate Grover algorithm in a classical computer? |
2. How many qubits and iterations the program needed to search an element? |
3. How minimum and maximum the size of elements in the database that the program |
can hold? |
E. Objective |
The objective of this work is to to make a simulation of Grover algorithm using Quantum |
Computer Language (QCL), to know how many qubits and iterations needed for the search- |
ing process, and to know how minimum and maximum the size of elements in the database |
that can be hold by the program. |
3 |
F. Scope |
This thesis concern on simulating Grover algorithm in a classical computer using Quan- |
tum Computer Language (QCL). The program can search a desired element in an unsorted |
database of N elements. |
G. Working Methodology |
This work begins with designing pseudo code and flowchart for Grover algorithm. Then, |
the design will be implemented by using Quantum Computer Language. After that, there |
will be several test to know how many qubits and iterations needed forthe searching process, |
also to know how minimum and maximum the size of elements in the database that can be |
hold by the program. |
II. LITERATURE REVIEW |
Computer science has grown faster, made an evolution in computation. Research has |
already begun on what comes after our current computing revolution. This research has |
discovered the possibility for an entirely new type of computer, one that operates according |
to the laws of quantum physics - a quantum computer. |
1. Way to Quantum Computation |
Quantum computers were first proposed in the 1970s and 1980s by theorists such as |
Richard Feynman, Paul Benioff, and David Deutsch. At that times, many scientists doubted |
that they could ever be made practical. Richard Feynman was the first to suggest, in a talk |
in1981,thatquantum-mechanical systems might bemorepowerfulthanclassical computers. |
In this lecture [5], reproduced in the International Journal of Theoretical Physics in 1982, |
Feynman asked what kind of computer could simulate physics and then argued that only |
a quantum computer could simulate quantum physics efficiently. He focused on quantum |
physics rather than classical physics. He said that nature isn’t classical, and if we want |
to make a simulation of nature, we’d better make it quantum mechanical, because it does |
not look so easy. Around the same time, in a paper titled "Quantum mechanical models |
4 |
of Turing machines that dissipate no energy" [6] and related articles, Paul Benioff demon- |
strated that quantum-mechanical systems could model Turing machines. In other words, he |
proved that quantum computation is at least as powerful as classical computation. But is |
quantum computation more powerful than classical computation? David Deutsch explored |
this question and more in his 1985 paper "Quantum theory, the Church-Turing principle and |
the universal quantum computer" [7]. First, he introduced quantum counterparts to both |
the Turing machine and the universal Turing machine. He then demonstrated that the uni- |
versal quantum computer can do things that the universal Turing machine cannot, including |
generate genuinely random numbers, perform some parallel calculations in a single register, |
and perfectly simulate physical systems with finite dimensional state spaces. In 1989, in |
"Quantum computational networks" [8], Deutsch described a second model for quantum |
computation: quantum circuits. He demonstrated that quantum gates can be combined |
to achieve quantum computation in the same way that Boolean gates can be combined to |
achieve classical computation. He then showed that quantum circuits can compute anything |
that the universal quantum computer can compute, and vice versa. |
A. Quantum Computers Development |
Quantum computers could one day replace silicon chips, just like the transistor once |
replaced the vacuum tube. But for now, the technology required to develop such a quantum |
computer is beyond our reach. Most research in quantum computing is still very theoretical. |
Themostadvancedquantumcomputershavenotgonebeyondmanipulatingmorethan16 |
qubits, meaning that they are a far cry from practical application. However, the potential |
remains that quantum computers one day could perform, quickly and easily, calculations |
that are incredibly time-consuming on conventional computers. Several key advancements |
have been made in quantum computing in the last few years. Let’s look at a few of the |
quantum computers that have been developed. |
In 1998, Los Alamos and MIT researchers managed to spread a single qubit across |
• |
three nuclear spins in each molecule of a liquid solution of alanine (an amino acid used |
to analyze quantum state decay) or trichloroethylene (a chlorinated hydrocarbon used |
for quantum error correction) molecules. Spreading out the qubit made it harder to |
5 |
corrupt, allowing researchers to use entanglement to study interactions between states |
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