State Tomography using Statistical Learning Belinda Pang

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

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

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

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

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

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

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

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

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

Fixed Axes – Analysis True State

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

Fixed Axes – Results

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

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

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

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

Uniformly Distributed Axes – Results

Comparison of Strategies

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)