Decoherence time measurement

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 Δt 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 Δt 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 :

Figure 1 : a) the relaxation time measurement circuit. b) the dephasing time measurement circuit.

Parameters

The python module is made of two functions <Language>RelaxationTime and <Language>DephasingTime taking as parameters :

  • QubitCount : the qubit count to run the benchmark on
  • Shots : the shot count of each Δt 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 :

Figure 2 : in blue relaxation time measurement with 0 to 4000 identity gate delay, in yellow therical relaxation time

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)

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