# Process Tomography

## Functionality Description

Quantum process tomography is a method used to characterize a physical process in an open quantum system. A quantum process is a linear super operator which acts on a quantum state to produce another output quantum state. This method deals with identifying this unknown quantum dynamical process. This is similar to State Tomography but the goal here is to characterize a quantum gate instead of a state. The figure of merit here is the density matrix of the quantum dynamic process. This method is extremely resource-intensive.

## Protocols

## Properties

- This method is a certification technique which has a really high sample and resource complexity.
- The figure of merit in this method is the density matrix of the process
- All of the protocols under this technique broadly have two methods of state estimation from measurements: Linear inversion and Maximum Likelihood estimation. Linear inversion process is mathematically simpler but sometimes the computed solution of the density matrix is not valid. Hence Maximum Likelihood estimation is preferred as it constructs the states which has a higher probability of being valid.

## Related Papers

- Chuang et al arXiv:quant-ph/9610001v1: Prescription for experimental determination of the dynamics of a quantum black box
- J. F. Poyatos, J. I. Cirac, and P. Zoller, PhysRevLett.78.390: Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate
- M.W. Mitchell, et al., Phys. Rev. Lett. 91, 120402 (2003)
- J. L. O’Brien et al arXiv:quant-ph/0402166v2: Quantum process tomography of a controlled-not gate
- S. T. Merkel, J. M. Gambetta, J. A. Smolin, S. Poletto, A. D. Corcoles, B. R.
- Johnson, C. A. Ryan, and M. Steffen, Phys. Rev. A 87, 062119 (2013).
- Daniel Greenbaum (2015) arXiv:1509.02921v1: Introduction to Quantum Gate Set Tomography

**contributed by Rhea Parekh*