1. State Tomography using Statistical Learning
Belinda Pang

2. Quantum Errors Quantum Channel
general map from initial to final quantum state
“reversible”

3. Quantum Errors Unitary Decohering
can recover original state if error is known
require encoding for error correction

4. Unitary Error Correction
Predictive error correction
Systematic errors
Slowly time varying unitary errors
Mavadia, 2016

5. Characterizing unitary error – state tomography
Single qubit
two parameters
Measure along
Outcome

6. State Tomography Prepare identical qubit states k qubits
Choose set of measurement axes
Measurement outcomes
analysis
Guess true state

7. Improving state tomography
Comparing different strategies
Choice of measurement axes
Analysis techniques
Statistical learning
Using past outcomes to find better axes for future measurement
Use learning for faster data analysis

8. Preliminary Strategy 1 Fixed Axes
Outcome = 0
Outcome = 1
Permute measurements along z, x, y axes

9. Preliminary Strategy 1 Fixed Axes
Outcome = 0
Outcome = 1
Permute measurements along z, x, y axes

10. Preliminary Strategy 1 Fixed Axes
Outcome = 0
Outcome = 1
Permute measurements along z, x, y axes

11. Fixed Axes – Analysis
True State

12. Fixed Axes – Analysis Estimate Fidelity Issue
Angle may not be well defined if
Calculate instead
Choose between

13. Fixed Axes – Results

14. Preliminary Strategy 2 Uniformly Distributed Axes
Outcome = 0
Outcome = 1
Uniformly Distributed Axes
Measurement axes randomly distributed over Bloch sphere
Outcomes of 100 measurements plotted over Bloch sphere

15. Uniformly Distributed Axes – Analysis
Basic Idea
Quantify how likely a hypothesis state could have the generated measurement data
Outcome = 0
Outcome = 1
generates
Probability that outcome=0 when measuring true state along axes n over whole Bloch sphere

16. Uniformly Distributed Axes – Analysis
Basic Idea
Quantify how likely a hypothesis state could have the generated measurement data
Outcome = 0
Outcome = 1
compare

17. Uniformly Distributed Axes – Analysis
probability
outcome
sum over data
function argument
Define Error Function
Best Guess
Fidelity

18. Uniformly Distributed Axes – Results

19. Comparison of Strategies

20. Future Work Short Term Long Term
Generate set of random future measurement axes from prior distribution, updated using past measurements
Long Term
Characterize general quantum channel (12 parameters as opposed to 2)