Quantum Computing is the future?? Eric Welch 4 April 2021 Texas State University Department of Physics Zakhidov Optoelectronics Group https://zakhidov.wp.txstate.edu 1

Texas State University Department of Physics What is Quantum Computing The use of quantum mechanics to perform computation | ⟩ 𝜓 = 𝛼| ⟩ 0 + 𝛽| ⟩ 1 𝛼 ! + 𝛽 ! = 1

Texas State University Department of Physics

Texas State University Department of Physics Why quantum?? Classical Quantum N S

Texas State University Department of Physics How Quantum states are created Annealing 1. Requires ultracold environment 2. Use magnetic fields to mirror an energy minimization problem 3. Couplers used to modify probability of measurements 4. Large number of qubits (𝑛 > 2000) 5. Solves somewhat hard problems (class NP) Gate 1. Requires ultracold environment/atoms 2. Gates are used in succession for computing 3. Small number of qubits (𝑛 < 50) 4. Solves very hard problems (class P)

Texas State University Department of Physics Quantum architecture Dwave – quantum annealing 1. Niobium SQUID device 2. Superconducting couplers 3. Gates are formed by Josephson junctions 4. Individual qubit memory Ionq – gate-based ion 1. Ytterbium ions 2. Linear chain gate model 3. Complete connectivity Rigetti – gate based 1. Si SQUID device 2. Outer casing for supercooling 3. Optical wires 4. Liquid He-3 and He-4 5. Swap gates to link outer qubits

Texas State University Department of Physics What can quantum computing do?? ?? ✅ Encryption/Cryptography ✅ Grover’s Algorithm – find an item in a database ✅ Simulation of quantum systems – quantum chemistry, physics and material science ✅ Adiabatic optimization – energy minimization problems ✅ Machine learning ✅ Genomics – computational biology

Texas State University Department of Physics The reality of quantum computing Pros ✅ Speed (quantum advantage) ✅ Exponentially larger storage capacity ✅ Potential use in solving some of the most advanced problems in maths and science Cons ❌ Currently, there are no room temperature superconductors ❌ Qubit entanglement and coupling is challenging and prone to errors ❌ Noise is hard to account for ❌ Cosmic rays may interfere and cause decoherence, losing all data

Texas State University Department of Physics Quantum Computing Tools SIMULATORS MACHINES

Texas State University Department of Physics Quantum Simulations - TSP TSP Problem: Imagine, a traveling salesman needs to visit N cities traversing the shortest path, and only visiting each city once Brute force: try every possible path until the minimum is found Greedy: only test nearest neighbors Python library: dynamic programming (subsystem optimization) AWS classical simulator: brute force type method using simulated annealing AWS quantum simulators: QUBO method (similar to Ising model) AWS machines: can utilize numerous methods both in gate and annealing architectures

Texas State University Department of Physics Quantum Simulations - QFT Like classical DFT, QFT applies DFT to the amplitudes of a quantum state Shor’s algorithm – factor large numbers Computing the discrete logarithm Quantum phase estimation algorithm Estimate eigenvalues of a unitary operator

Texas State University Department of Physics HUMAN QUANTUM COMPUTERS?? Thank you!! Questions??