### Presentation

There are different sources of decoherence^{[1]} depending on the quantum device technology, but the decoherence mechanism can be distinguished in two parts : the relaxation time and the dephasing time. This module implements both relaxation and dephasing time measurement.

### Languages & Frameworks

- PyQuil
- Qiskit
- Q#

### Method

The relaxation time *T1* is the decay of a qubit from its excited state to its ground state |1〉 → |0〉. The relaxation time can be measured simply by preparing a qubit in |1〉 state, then measuring it after a Δ*t* delay.

The dephasing time *T2** is a longitudinal phase fluctuation wich occurs on coherent supperposed state. The dephasing time measurement can be performed with Ramsey Fringes experiment, wich consists on applying a first Rx(π/2) rotation, then a second Rx(π/2) rotation followed by a measure after a Δ*t* delay.

This module implements both relaxation and dephasing time measurement, the delay is simulated by applying N times (settable) the identity gate, as shown on the following circuits :

### Parameters

The python module is made of two functions * <Language>*RelaxationTime and

*DephasingTime taking as parameters :*

*<Language>*- QubitCount : the qubit count to run the benchmark on
- Shots : the shot count of each Δ
*t*delay circuit - UseNoise : use noise in case of simulation
- StepCount : the count of step of the measurement
- StepDepth : identity gate count between each step

Additional parameters are possible depending on the language allowing to run the measurement on a real quantum device.

#### Results

A measurement returns an array of qubit count rows and step count + 1 cols (an initial run is made with 0 identity gate count), and a .csv file is generated to allow generating a graph.

As an exemple, a relaxation time measurement has been made using Qiskit, giving the following graph :

In yellow you can see the extrapolated theorical relaxation time, it is given as *e ^{-t/T1}* , here T1=2400 in unit of time, where 1 unit of time is the identity gate execution time.

#### References

[1] G. Ithier et al., Phys. Rev. B 72, 134519 (2005)