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Lecture : Dariush Moridi Quantum Computer Lecture : Dariush Moridi

Overview Data Representation Operations on Data Features and uses Introduction and History Data Representation Operations on Data Features and uses Conclusion

Introduction A quantum computer is a computation device that use of quantum mechanical phenomena, such as superposition , to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), quantum computation uses quantum properties to represent data and perform operations on these data. A current computer has bits which represent 0 and 1 based on electrical signals. But in Quantum computer works with Qbits. In a Quantum Computer could be replicated by atoms in the excited or grounded state. However, given the multiple properties of quantum mechanics it would allow that other states to be inferred at the same time.

History 1982 - Feynman proposed the idea of creating machines based on the laws of quantum mechanics instead of the laws of classical physics. 1985 - David Deutsch of the University of Oxford, describes the first universal quantum computer. 1994 - Peter Shor came up with a quantum algorithm to factor very large numbers in polynomial time. 1998 - First working 2-qubit NMR computer demonstrated at University of California, Berkeley. Dwave announced a 128 Qubit system on December 2008

Data Representation Operations on Data Features and uses Conclusion Introduction and History Data Representation Operations on Data Features and uses Conclusion

Qbit “Quantum” + “Bit” = Qubit Data Representation The basic building part of a Quantum Computer is the Qubit The data about the spin position is referred to as a Qubit In classic computer a bit must be only 0 or 1, but a qubit can be 0,1 or superposition of 0 and 1 When multiple Qubits are combined it gives exceptional increase in there ability to represent data

A Classical Bit: Two Possible States

A Classical Bit: Two Possible States 1

Single Bit Operation: NOT x y 0 1 1 0 y x

Single Bit Operation: NOT x y 0 1 1 0 y x 1

A Quantum Bit or “Qubit” |  is pronounced “ket” and denotes the state of the computer

A Quantum Bit or “Qubit” 1

A Quantum Bit or “Qubit” 1

A Quantum Bit or “Qubit” Superposition : Ability of a particle to be in two different states at the same time Quantum superposition of 0 and 1 The qubit may be in a superposition x|0> + y|1> of the two states. The complex amplitudes x and y determine which state we will see if we make a measurement. When an observer measures a qubit in this superposition, the probability that the observer will see state |0> is |x|2 and the probability of seeing |1> is |y|2. 1

A Quantum Bit or “Qubit” 1

A Quantum Bit: A Continuum of States 1 cos q sin q +

A Quantum Bit: A Continuum of States Actually, qubit states live on the surface of a sphere. 1 2 sin cos f q i e - +

A Quantum NOT Gate X

A Quantum NOT Gate X X

A Quantum NOT Gate X

A Quantum NOT Gate X X

Hadamard Gate H H

Hadamard Gate H H

Hadamard Gate H H

Hadamard Gate H H

Hadamard Gate H H is its own inverse H

Hadamard Gate H H is its own inverse H

Hadamard Gate H H is its own inverse H

Hadamard Gate H H is its own inverse H

One qubit H The significant point being that by performing the single operation on the qubit, we have performed the operation on two different values

H H Two qubits Counting in binary 1 2 3 1 2 Counting in binary 3 Likewise, two-qubit system would perform the operation on 4 values

Three qubits H H H

Three qubits H H H 1 2 3 4 5 6 7 three-qubit system on eight

N qubits H H N H H Increasing the number of qubits therefore exponentially increases the 'quantum parallelism' we can obtain with the system … 1 2 3 2N-1

N qubits H H H H Quantum superposition of all possible input states!

Data Representation Operations on Data Features and uses Conclusion Introduction and History Data Representation Operations on Data Features and uses Conclusion

Quantum Gates - Hadamard Simplest gate involves one qubit and is called a Hadamard Gate (also known as a square-root of NOT gate.) Used to put qubits into superposition. H H State |0> State |0> + |1> State |1> Note: Two Hadamard gates used in succession can be used as a NOT gate

Quantum Gates - Controlled NOT A gate which operates on two qubits is called a Controlled-NOT (CN) Gate. If the bit on the control line is 1, invert the bit on the target line. Input Output A - Target A’ A B A’ B’ 1 B - Control B’ Note: The CN gate has a similar behavior to the XOR gate

Quantum Gates - Controlled Controlled NOT (CCN) A gate which operates on three qubits is called a Controlled Controlled NOT (CCN) Gate. If the bits on both of the control lines is 1,then the target bit is inverted. Input Output A B C A’ B’ C’ 1 A - Target A’ B - Control 1 B’ C - Control 2 C’

A Universal Quantum Computer The CCN gate has been shown to be a universal reversible logic gate as it can be used as a NAND gate. Output A - Target A’ Input A B C A’ B’ C’ 1 B - Control 1 B’ C - Control 2 C’ When our target input is 1, our target output is a result of a NAND of B and C.

Data Representation Operations on Data Features and uses Conclusion Introduction and History Data Representation Operations on Data Features and uses Conclusion

Features and uses Quantum computer is much faster than classical computer. This computer can solve very complex calculations and simulations. Quantum computer can be used in area of finance. It can be used to solving complex Mathematical problems. Military uses of quantum computer. Google image search. Example: To search the entire Library of Congress for one’s name given an unsorted database... Classical Computer – 100 years Quantum Computer – ½ second

Introduction and History Data Representation Operations on Data Features and uses Conclusion

conclusion The field of quantum computing is growing rapidly as many of today's leading computing groups, universities, colleges, and all the leading IT vendors are researching the topic. This is an exciting field with many open questions and extremely diverse problematics. The quantum computers power to perform calculations across a multitude of parallel universes gives it the ability to quickly perform tasks that classical computers will never be able to practically achieve. 

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