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Francisca Vasconcelos and Megan Yamoah
FPGA Qubit Package6.111 Final Project Proposal
equs.mit.eduEngineering Quantum Systems
Engineering Quantum Systems (EQuS) GroupMassachusetts Institute of Technology6 November 2018
Vasconcelos & Yamoah - 26.111 Final Project - Fall 2018
• Implement useful pre-processing for superconducting quantum devices
• Involves:– Processing microwave signals from devices at ~20 mK– Classifying state– Outputting data in a meaningful format
• Why FPGA?– Feedback– Quantum algorithms
Introduction
50 µm
J. Yoder, D. Kim, et al., (2016)
Vasconcelos & Yamoah - 36.111 Final Project - Fall 2018
• Qubit state represented in 2D Hilbert space– Complex number space– Superpositions
• Measurement– Single basis– Wave function collapse– Statistical
• State discrimination
Background
Vasconcelos & Yamoah - 46.111 Final Project - Fall 2018
Lab Equipment
AWG Cryogenic Fridges with Qubit Packages
Lab Measurement RacksKeysight PXI Enclosure
Xilinx Kintex-7with Keysight compatibility
Vasconcelos & Yamoah - 56.111 Final Project - Fall 2018
Broad Block Diagram
Vasconcelos & Yamoah - 66.111 Final Project - Fall 2018
Pre-processing Diagram
Integration
2 x ~100 16 bit values
Counter-rotation
CORDIC Implementation~1096 LUTs, ~1050 FFs
Timing ModuleDetermine when to start taking data
trigger
start
ADC Input:10 x 16 bit
NUM_SAMPLESSAMPLE_FREQ
raw I-Q values2 x 16 bit
Vasconcelos & Yamoah - 76.111 Final Project - Fall 2018
Initial Processing - Background
Qubit output
I-Q mixer output
Complex number representation
Vasconcelos & Yamoah - 86.111 Final Project - Fall 2018
• Iterative algorithm• Represent rotation matrix as multiplication by a power of 2 or adding
operations
CORDIC
COordinate Rotation DIgital Computer
https://www.xilinx.com/support/documentation/ip_documentation/cordic/v6_0/pg105-cordic.pdf
Vector rotation
CORDIC
Vasconcelos & Yamoah - 96.111 Final Project - Fall 2018
Binning / Classification Diagram
Vasconcelos & Yamoah - 106.111 Final Project - Fall 2018
Binner
• Divide I-Q plane into squares (user defines resolution)• Continuously bin values into this 2D histogram• Once measurement is over, report count for each bin • Decreased resolution reduces amount of data sent to computer &
increases processing speed
Actual Data Binned Data(Specifiable # Bins & Bin Width)
Vasconcelos & Yamoah - 116.111 Final Project - Fall 2018
Classification
• Easier: Horizontal (assume I-Q mapping has been rotated) • Harder: Linear with Proposed approach: Geometric Method
(No need to use arctan, sqrt, or any other complicated functions!)
Excited State
Ground State
ae
g
(0,0)
(iE-iL,qE-qL)
I
Q
(iG-iL,qG-qL)
Excited State
Ground State
ae
g
(iL,qL)
(iE,qE)
(iG,qG)
I
QExcited State
Ground State
I
Q
1) Get values to be classified 2) Create vector representation 3) Map vectors to origin
4) Compute dot products and accordingly bin values:
Vasconcelos & Yamoah - 126.111 Final Project - Fall 2018
Megan’s Goals• Baseline
– Receive and output digitized signal values
– Output random I-Q values• Expected
– CORDIC rotation– Integration / Averaging
• Stretch– De-noising– Integrate in lab measurement chain
Goals & Timeline
Fran’s Goals• Baseline
– Data dump– Data read
• Expected– Horizontal classifier– Configuration parameters– Binner– Basic Labber integration
• Stretch– Linear classification – Report classifier distances– Full integration in lab measurement
chain (run QST)
Now 12/12Thanksgiving
Baseline Completed
Work on ExpectedWork on Baseline
Complete Expected
Begin Stretch Work on Stretch Wiggle/Debug Room