Table 2 Simulated probability of incorrectly transferring a single-spin superposition state (1 − f1) and a singlet state (1 − f23) in a chain of three spins starting from the initial state \(\frac{1}{\sqrt{2}}\left|{S}_{12}{(\uparrow +\downarrow )}_{3}\right\rangle\) using AQT or SWAP gates.

From: Adiabatic quantum state transfer in a semiconductor quantum-dot spin chain

 

\({T}_{2}^{* }=18\) ns, Q = 20

\({T}_{2}^{* }=1000\) ns, Q = 20

\({T}_{2}^{* }=1000\) ns, Q = 100

 

1 − f1

1 − f23

1 − f1

1 − f23

1 − f1

1 − f23

AQT

2 × 10−1

3 × 10−2

2 × 10−3

2 × 10−3

8 × 10−4

1 × 10−4

S12S23

5 × 10−2

1 × 10−1

7 × 10−3

1 × 10−2

5 × 10−3

7 × 10−3

  1. The single-spin \({T}_{2}^{* }\) exchange quality factors Q are listed for the same three cases as above. In general, the AQT errors are lower than errors associated with SWAP gates, except when \({T}_{2}^{* }=18\) ns. In this case, the duration of the AQT significantly exceeds \({T}_{2}^{* }\). All values are rounded to one significant figure.
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