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Quantum Computing Ambarish Roy 16.508

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Presentation Flow

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Introduction

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Two basic directions First MOSFETs to Single-Electron Devices Second Quantum Computation

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Objective Not intended to accelerate digital computation Use new algorithm’s approachTheory Hilbert space Qubits - a quantum object Superposition of states - Quantum parallelism Constructive and Destructive interference technique

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Hilbert Space A quantum state, describing all we know about a system, can be thought of as a vector in some abstract space called Hilbert space.

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Classical Computational Science

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Entire process flow 1847 – Ideas for logical operations like AND, OR, and NOT on binary numbers 1936 – Turing Machine Bits and Gates Small to Huge Logic Design

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reversible gate Reversible gates contains information about the Input Quantum mechanics describes only reversible processes. Example: CNOT gate, reversible gate used in Quantum Computation (Fredkin Gate)

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CNOT Two inputs ‘a’ and ‘b’ ‘b’ complements, if a=1 Output is ‘b’, if a=0 Therefore a C(ontrolled)NOT gate Truth table:

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Quantum Qubits and Gates

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Forming Qubits Semiconductor materials provides the richest set of tools for constructing qubits. III-V materials preferred Possible basis for qubits are Quantum Dots The confinement of the electrons in the Quantum Dots makes the energy levels discrete, thus offering the possibility of using them for encoding quantum information.

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Quantum Logic Gates Unlike digital logic gates, quantum logic gates generally act on a superposition of digital states Concept on Adjoint and Hermitian matrices Example: state describing two states c 0 and c 1 :

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Example: 3 Bit register = 8 states Example: CNOT Gate Therefore, Parallelism

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Errors and Decoherence

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Sources of Error The gate operations are not perfect The isolation between the QM system and environment is not perfect The system itself differs from the idealized model system considered while designing Therefore, deviation from the ideal result

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Counter-strategy options Optimize the apparatus that controls Quantum system Design gate operations in such a way that errors in experimental parameters tend to cancel than amplify Store information in areas of the Hilbert space that are least affected by the interaction between the system and its environment

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Tasks for Quantum Computers

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Why Quantum During repetition of some tasks on a large no. of input values, Quantum algorithms are more efficient that classical algorithms. Example, Searching the database-the steps required for evaluation is decreased Advantages of quantum parallelism can be exploited in cases where one is not interested in all answers to all possible inputs Classes of Algorithms Quantum Fourier transform based algorithms Quantum searching algorithms Algorithms available Shor’s 1994, Grover’s 1997, and Deutsch & Jozsa 1992

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Potential limitations to generate a time evolution that is identical to that of the digital system In comparison with the rich theoretical work, relatively little experimental work has been published Keeping the track of all degrees of freedom is a computationally expensive problem

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Building a Quantum computer

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The network Model First step is to define how the information is to be stored Once qubits are defined the architecture must provide means of operating on this quantum register Algorithm required to initialize the quantum register The result of the computation must be read out

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Requirements for quantum hardware Qubits: Not to form a large register and confine to a smaller required states Initialization: System must be put in a well defined state while initializing Decoherence time: The computation must be completed before the decay has significantly degraded the information Quantum gates: Building up a universal set of quantum gates like in digital computers

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Liquid state NMR quantum Comp. NMR is mainly a spectroscopic tool that is used for the analysis of almost any type of molecule. In the form of MRI it also has become an important tool in clinical medicine It encodes the quantum information in the nuclear spin degrees of freedom of molecules placed in a glass tube We study NMR systems to show how quantum computers can be implemented

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uses Quantum Computers to replace classical computers Quantum Teleportation Quantum Cryptography

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Today at Present The most advanced quantum computers have not gone beyond manipulating more than 7 qubits, meaning that they are still at the "1 + 1" stage 5-qubit, august 2000, IBM-Almaden Research Center 7-qubit, march 2000, Los Alamos National Lab. “Practical Quantum computer is years away”

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