Quantum Computing

INTRODUCTION• Energy consumption• Speed• Qubit• 0&1• Superposition state

The world's first quantum computer?• Orion-2007• based on superconducting electronics• Superconductors can be used to build large structures that behave

according to the rules of quantum mechanics• Less energy consumption• High performance• E.g. search for phone number in world phonebook

2 Theory of QC• 2.1 The power of quantum computers

• Clock speed• Number of steps to calculate a problem.• Comparison between QC & CC

• Complexity theory• Time• Space• Energy

• Factoring number in to its prime numbers• O(e^n1/3) for normal algorithms.• O(n3) for quantum algorithms.

• Searching unsorted database, Communication tasks etc.

• 2.2 Quantum parallelism

• Reversibility• Heat generation• superposition states

• 0 & 1• 0+1 written as a|0 + b|1 ,⟩ ⟩• where a and b are complex numbers satisfying |a|^2 + |b|^2 = 1.• In some sense, this means that a qubit can be in |0 and |1 at the same time⟩ ⟩• An “equal” superposition of |0 and |1 . ⟩ ⟩

• The output state is now a superposition of the two output values. In this sense, function f is evaluated for both possible input values in one step.

• Two qubits with in a superposition of |0 and |1⟩ ⟩• c0|00 + c1|01 + c2|10 + c3|11 ⟩ ⟩ ⟩ ⟩

• A 2-qubit logic gate g will transform this state to• c0|g(00) + c1|g(01) + c2|g(10) + c3|g(11) (4)⟩ ⟩ ⟩ ⟩

• So in a sense g has been evaluated for four input values in parallel. For every extra qubit involved in the computation, the number of parallel function evaluations doubles. This exponential parallelism became known as quantum parallelism.

2.4 Requirements and challenges

• Requirements• a system of qubits.• the qubits must be individually addressable and must interact with each other • it must be possible to initialize them to a known state because the result of a

computation generally depends on its input state.• we must be able to extract a computation result from the qubits by some

measurement.

• Challenges• Decoherence: This property states that if a coherent state (state with

superposition) interacts with the environment, it will fall into a classical physics state without superposition

• Zeno effect: States that an unstable particle, if constantly observed, will never decay into a superpositioned state

• Entanglement: two or more particles can be linked, and if linked, you can change properties of one particle changing the linked one.

3. FUTURE OF QUANTUM COMPUTING• Artificial Intelligence • High performance will allow us in development of complex compression

algorithms• voice and image recognition• molecular simulations• true randomness• Molecular simulations are important for developing simulation applications

for chemistry and biology• Cryptography

• Peter Shor’s Algorithm

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