Table 1 Simulated probability of incorrectly transferring either a single-spin eigenstate (1 − f1) or a singlet state (1 − f23) in a chain of three spins starting from the initial state \(\left|{S}_{12}{\uparrow }_{3}\right\rangle\) 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

1 × 10−2

3 × 10−2

1 × 10−3

2 × 10−3

6 × 10−5

1 × 10−4

S12S23

3 × 10−2

1 × 10−1

7 × 10−3

1 × 10−2

5 × 10−3

7 × 10−3

  1. The sequence of SWAP gates that replicates the AQT is S12S23, where Sij indicates a SWAP between spins i and j. The single-spin \({T}_{2}^{* }\) and exchange quality factors Q are listed for three different cases. The case of \({T}_{2}^{* }=18\) ns and Q = 20 approximately corresponds to the experimental parameters studied here. \({T}_{2}^{* }=1000\) ns and Q = 20 correspond to what could likely be obtained in isotopically purified Si spin qubits. \({T}_{2}^{* }=1000\) ns and Q = 100 correspond to a significant reduction in both magnetic-field and charge noise over the experimental parameters studied here. In all cases, the errors associated with the AQT process are lower than the errors associated with the SWAP process. All values are rounded to one significant figure.
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