Quantum Computing Hakem Alazmi Jhilakshi Sharma Linda Vu

Outline Fundamentals of Quantum Computing Principles of Quantum Computing: Qubits Superposition Entanglement Classification Classical vs. Quantum Computing Types of Quantum Computing Time Complexity Advantages & Disadvantages Present & Future Applications

Quantum Computing Timeline 1980’s Richard Feynman: “ We can leverage quantum properties for computation and solve problems unsolvable by classical computing” 1985 David Deutsch: called as “ Father” of quantum computing. 1994 Petre Shor’s algorithms for quantum code breaking. 2007 D wave, announced the first quantum computing chip.

Why Quantum Computing? Slowing down of Moore’s law. Size of transistors. Classical computers lag in solving many kinds of numerical problems. For example: Factorization.

What is Quantum Computing? Fundamental Theories of Quantum Computing Quantum computing is the intersection of math, physics, and computer science. Modern physics explains the behavior of matter and energy at an atomic and subatomic level. Quantum bits Superposition Entanglement

Quantum Bit

Quantum Superposition Possible states Spin up and spin down What happens when a qubit is observed or measured? Depends on the probability Benefits of quantum superposition Calculations Parallelism What about multiple quantum bits?

Quantum Entanglement System of qubits Quantum entanglement is a physical phenomenon that occurs when pairs or groups of qubits generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s). System of qubits System of qubits

Classical Computers vs Quantum Computers Data storage: Based on voltage vs electron spin. Speed: Measured in gigahertz vs. teraflops Information Processing: Logic gates vs quantum logic gates Circuit: Macroscopic technologies vs microscopic technologies.

Types of Quantum Computing Quantum Annealers: It performs specific functions. Analogue Quantum: It contains 50 to 100 qubits. Universal Quantum: It contains 100,000 qubits.

Quantum Computing Hardware Implementation Methods Qubits Most renowned way of building quantum computing is by Qubits. Quantum dots: It is also known as Ion Trap. Nuclear Magnetic Resonance: It uses the spin states of molecules as qubits.

Time Complexity Time complexity of Quantum Computers is explained by the Quantum Complexity Theory Computational complex theory in theoretical computer science Quantum Query Complexity Grover’s Algorithm Has O√N complexity, that is, uses just O√N evaluations of the function, where N is the size of the domain The quantum complexity classes BQP and QMA are the bounded-error quantum analogues of computational classes P and NP BQP Class of decision problems solvable by a quantum computer in polynomial time QMA The proofs have to be verifiable in polynomial time on a quantum computer

Advantages of Quantum Computers Information Storage Pattern - Flexibility on storage Speed - Perform multiple task simultaneously Security - Provides unbreakable security features Power Efficient - Quantum computers reduces power consumption by 100 up to 1000 times because of quantum tunneling AI - Making exponentially fast connections for machine learning operations Problem solving - Can solve unsolvable problems such as the traveling salesman problem and bounded-error quantum polynomial time (BQP) which are decision based problems

Disadvantages to Quantum Computing Difficult to build - Quantum Computers need stability because of the atoms, any interference will cause the computer to be disrupted and cause the quantum particles to behave in a strange behavior Temperature - Quantum Computers need to be in a cold environment (-460 degrees Fahrenheit) Incompatibility - Quantum algorithms do not apply to most classical computing applications Sensitivity - Quantum Computers are sensitive Security - Quantum Computers will be able to decrypt and encrypt security that is much more difficult to break and/or encode.

Challenges in Implementation Evaluating Time Complexity Evaluating the complexity/power of various quantum models of computation, proof systems, games (sometimes suggested by theoretical physicists), reducing some of them to others Information Processing Quantum information processing with new particles and physical systems New quantum models of computations and new types of quantum error-correction Decoherence Effective quantum control in reproducible quantum systems (including the control of quantum decoherence) Quantum Error Correction Consumer Friendly Implementation

Present and future applications Present Applications: Bristlecone, by Google Boasts of 72 qubits Q System, by IBM Uses 49 qubits D - Wave 2000Q, Goldman Sachs a quantum annealing system with 2000 qubits and advanced feature controls Hybrid Quantum/Classical Computing Applications Future Applications: Artificial Intelligence Optimising search through gigantic datasets Cybersecurity Breaking Encryption Quantum Enabled Discoveries

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