1. Quantum Computing Preethika Kumar

2. “Classical” Computing: MOSFET

3. CMOS Limitations (Wave-Particle Duality)

4. 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

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

6. Typical Quantum CircuitX S H H Z

7. Single Qubit Hamiltonian
bias
tunneling

8. Single Qubit Hamiltonian
bias
tunneling

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

10. 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

11. 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)

12. 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|

13. 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

14. 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

15. Research: Gates in LNNAB C =
Pulse 1
Pulse 2 A B C U A B C U A B C U

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

17. Research: Mirror Inverse Operations

18. Research: Mirror Inverse Operations

19. Research: Mirror Inverse Operations

20. Research: Mirror Inverse Operations

21. 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