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)
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
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
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