Quantum Computing Preethika Kumar

“Classical” Computing: MOSFET

CMOS Limitations (Wave-Particle Duality)

In the Quantum World….. Bits become qubits: “0”, “1” or “both” Unitary matrices become quantum gates: We have a universal set of gates Probability of measuring|0 Probability of measuring|1 I Junction I

Schrödinger Equation Newton’s Law of the Little World Hamiltonian: 2n  2n non-diagonal matrix

Typical Quantum Circuit X S H H Z

Single Qubit Hamiltonian bias tunneling

Single Qubit Hamiltonian bias tunneling

Two Qubit System A B  |00 |01 |10 |11 00| 01| 10| 11|

Some Potential Challenges No Cloning Theorem - moving quantum data (fan-out) - quantum error correction (redundancy) Measurements collapse quantum states - closed quantum systems (coupling with environment) - quantum error correction (syndromes) Architectural layouts: limited interactions - gate operations - moving quantum data

Research: Quantum Gates (Reducing the Hamiltonian) B  |00 |01 |10 |11 00| 01| 10| 11| Goal: Find system parameters (mathematical solution) Constraints: - Minimize control circuitry (closed system) - Fixed system parameters (design)

Research: “Controlled” Gates (Reducing the Hamiltonian) |00 |01 |10 |11 00| 01| 10| 11| Similar to Fix A’s state – large A – can neglect effect of A. |00 |01 |10 |11 00| 01| 10| 11|

Controlled- Hadamard Gate Barenco, et al., PRA 52, 3457 (1995) Bias Pulse on Target Time T e max min Parameters : T = 7 ns  = 25 MHz  = 35.9 MHz min = 60.9 MHz max = 10.0 GHz

Research: Gates in Linear Nearest Neighbor Architectures (LNNA) 1 2 C Want to do gate operations on qubit B |0 B 1 2 Method 1: Fix adjacent qubits (A and C) in the |0 state Method 2: Shut off the couplings (of qubit B with A and C) A B 1 2 C

Research: Gates in LNNA B C = Pulse 1 Pulse 2 A B C U A B C U A B C U

Research: Gates in LNNA B 1 2 C A = 0 A =  B = ? B =  C = 0 C =  Approach will be used to implement controlled-unitary operations

Research: Mirror Inverse Operations

Research: Mirror Inverse Operations

Research: Mirror Inverse Operations

Research: Mirror Inverse Operations

Current Research Adiabatic Quantum Computing - optimization problems - hardware exists (DWave Systems) Quantum Neural Networks - designing QNNs (exploit quantum phenomena) - using QNNs for different applications to calculate parameters Fault-tolerant Quantum Computing - gate design without decoding