quantum computing preethika kumar. “classical” computing: mosfet
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Quantum ComputingPreethika 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
2 21 00 1 ; 1
0 1
Probability of measuring|1
Probability of measuring|0
IJunction
I
0 1
Schrödinger EquationNewton’s Law of the Little World
( )( )
ti t
t
H
2( ) e (0)i t
Gate
t H
U
Hamiltonian:2n 2n non-diagonal matrix
Typical Quantum Circuit
X
H
Z
H
S
0 1
1 0
0 1
1 0
U
1 11
1 12
0 10
2
0 11
2
U1 0 0 0
0 1 0 0
0 0 0 1
0 0 1 0
0 0
1 1
x x
x x
U
Single Qubit Hamiltonian
1H
bias tunneling
ti
tti
ti
ti
t
22
22
2222
22
22
22
22
22
22
sincossin
sinsincos
U
cos 2 sin 2
sin 2 cos 2
t i t
i t t
U
2
2
cos 2 sin 2 0 0
0 cos 2 sin 2 0
i t
i t
t i t e
t i t e
U
Single Qubit Hamiltonian
1H
bias tunneling
cos 2 sin 2 0 cos 2 0 sin 2 1;
sin 2 cos 2 1 sin 2 0 cos 2 1
t i t t i t
i t t i t t
U
22 2
2
0; 0 0 ; 1 1
0
i ti t i t
i t
ee e
e
U
2
0| ; 0 1 ; 1 0
0t
iNOT X i i
i
Two Qubit System
IBA2 HHHH A B
0
0
0
0
A B B A
B A B A
A A B B
A B A B
2H
|00 |01 |10 |11
00|
01|
10|
11|
2( ) e (0)i t
Gate
t H
U
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
IBA2 HHHH A B
0
0
0
0
A B B A
B A B A
A A B B
A B A B
2H
|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: Quantum Gates(Reducing the Hamiltonian)
Research: “Controlled” Gates(Reducing the Hamiltonian)
Fix A’s state – large A – can neglect effect of A.
BAB
BBA
BAB
BBA
H
00
00
00
00
|00 |01 |10 |11
00|
01|
10|
11|
BB
BBBH 1
BB
BBBH 2
Similar to
H
BABA
BBAA
ABAB
ABBA
H
0
0
0
0
|00 |01 |10 |11
00|
01|
10|
11|
Controlled- Hadamard Gate
11
11
2
1H
Barenco, et al., PRA 52, 3457 (1995)
Bias Pulse on Target
Time
T
emax
emin
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)
Want to do gate operations on qubit B
A B1 11 2 2
C
|0 B1 11 2 2
Method 1: Fix adjacent qubits (A and C) in the |0 state
|0
Method 2: Shut off the couplings (of qubit B with A and C)
A B11 2
C
A
B
C
A
B
C
=
Pulse 1 Pulse 2
A
B
C
U U U U
A
B
C
U U
A
B
C
U
2cos
2exp
2sin
2exp
2sin
2exp
2cos
2exp
ii
ii
U
Research: Gates in LNNA
1 2
1 2
1 2
1 2
1 2
1 2
1 2
1 2
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
B B
B B
B B
B B
B B
B B
B B
B B
Research: Gates in LNNAA B
1 2C
A = 0 A
= B = ?B =
C = 0 C
=
Approach will be used to implement controlled-unitary operations
000 001 010 011 100 101 110 111
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