Interconnection Networks for Scalable Quantum Computers

1
Interconnection Networks for Scalable Quantum
Computers
Nemanja Isailovic, Yatish Patel, Mark Whitney,
John Kubiatowicz U.C. Berkeley June 21,
2006 ISCA 33
2
Motivation

• Varied Algorithms and Communication Patterns

• All-to-All Communication

? Routers

• Goal Design a generalized NW for a Quantum
  Datapath

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Ion Trap Quantum Computer

• Major Components

Two-Qubit Gate
- Qubit an ion
Q1
- Gate a location

• Ballistic Movement

- Apply pulse sequences to electrodes
- Electrostatic forces move ion
Q2
- Intersections similar, but more complicated
pulse sequences
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Ballistic Movement Network
One-Qubit Gate
Two-Qubit Gate
Q2
Q3
Two-Qubit Gate
One-Qubit Gate
Q4
Q5
Memory Cell
Memory Cell
Q1

• Problem Noise accumulation!

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Noise Accumulation from Movement
Qubit Error
Distance Moved in Gates

• Noise may increase error by factor of 100

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Movement Option 2 Teleportation
3. Transmit two classical bits
Source Location
Target Location
D
4. Local Ops
Entanglement
2. Local Ops
D?
D
E2
E1
1. Generate EPR pair

• Goal Transfer the state, not the data ion

• Problem EPR pairs become noisy

• Teleportation Benefits

- Error Correction of data (arbitrary state)
100 ms Purification of EPR pair (known
state) 120 µs
- Pre-distribution of EPR pairs
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EPR Pair Distribution Network
One-Qubit Gate
Two-Qubit Gate
Q2
Q3
EPR Pair Generators
Two-Qubit Gate
One-Qubit Gate
Q4
Q5
Memory Cell
Memory Cell
Q1
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Setting Up a Teleportation Link

• Purification Amplification of EPR pair link

- Two EPR pairs ? One purer pair, one junk
pair
- Chance of failure

• Need to send multiple pairs

STRONGER
Entanglement
G
P
P
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Chained Teleportation
Teleportation
Teleportation
G
T
T

• Adjacent T nodes linked for teleportation

• Positive Features
• - T node linking not on critical path
• - Pre-purification (Link Amplification) part
  of link setup

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Pre-Purification
T
Long-Distance EPR Pairs Per Data Communication
G
T
Error Rate Per Operation

• Benefit decreased congestion at T Nodes

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Studied Architecture Mesh Grid

• Grid of T nodes

, linked by G nodes

• Packet-switched network
• - Dimension-order routing

• Each qubit has associated message

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Classical Control

• Quantum Datapath Layer
• - T Nodes and G Nodes (P Nodes and Gates not
  shown)
• Classical Control Layers
• - Messages Associated with Qubits
• - Teleportation and Purification Bits

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Simulation

• Goal Communication Area v. Computation Area
• - Simulates communication pattern
• - Tracks resource use
• Benchmark Quantum Fourier Transform
• - Subroutine of Shors factorization algorithm
• Architecture
• - 16x16 mesh grid
• - Dimension-order routing
• Variables
• - Area dedicated to Communication Network
• - Relative resource allocation
• - t teleporters per T Node
• - p purifiers per P Node
• - g generators per G Node (saturate T
  Nodes)

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Simulation Results
Computation Area Estimate
Normalized Execution Time
Communication Network Area (in Ion Traps)

• Communication Setup Latency v. Computation Time
• - Computation time may overwhelm
• - But Setup Latency increases rapidly

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Conclusion

• Communication Infrastructure Complex Enough to
  Require Engineering
• - Varied communication ? Router framework
• - Ballistic Movement noise ? Teleportation

• EPR Pair Distribution Network
• - Chained Teleportation with Purification at
  endpoints
• - Pre-purified (Amplified) links between
  Routers
• - Classical Network(s) linked to Quantum
  Network

• Simulation Study of QFT
• - Mesh grid
• - Dimension-order routing
• - Suggests Good Design Point
• - Communication Area Computation Area