1. Leon Camenzind
11/08/17

2. Improve read-out fidelity
Motivation
Improve read-out fidelity
Charge state measurement
Spin-to-charge
For fault-tolerant quantum computing
More time for spin read-out

3. Setup and Charge stability DiagramQ2 Q1
(101) Q3
[1], same device
Q1 decoupled
Q2 / Q3 build 𝑆− 𝑇 0 qubit
MM  Δ 𝐵 23
𝐵 𝑒𝑥𝑡 =0.7𝑇
[1] Delbecq et al, PRL 116, (2016)

4. Standart single-shot measurement
(111)
Detuning 𝜖
(111)
Procedure:
1. R (reset) wait until system relaxes into GS (102)
2. Pulse adiabatically to O: 𝑆− 𝑇 0 precessions
3. Pulse back to R
4. 𝑆 goes adiabatically to (102)
5. 𝑇 0 remains in (111) and decays in (102) with 𝑇 1 (nearest neighbor hoping with change in s)

5. Charge state detection fidelity
Sensor signal in R
Decay of mean sensor signal
𝑡 𝑚 =4𝜇𝑠
No 𝑇 1
With 𝑇 1
𝑉 𝑡ℎ
Longer integration: better electrical signal but loss of fidelity ( 𝑇 1 !) 𝑡 𝑚 ~ 𝑇 1
Optimal 𝑡 𝑚 and 𝑉 𝑡ℎ  charge state detection fidelity of 84%

6. Single-shot measurement using metastable state
(111)
Procedure:
1. R (reset) wait until system relaxes into GS
2. Pulse to O: 𝑆− 𝑇 0 precessions
3. Pulse back to M
4. 𝑆 goes adiabatically to (102)
5. 𝑇 0 remains in (111) and
7. then loads an additional electron into Q3 (112) with rate 𝜏 𝑟 ≫10 𝑀𝐻𝑧
8. (112) decays to (102) in time 𝑇 112

7. Boost in fidelity Decay of mean sensor signal Sensor signal in M 𝑉 𝑡ℎ
𝑡 𝑚 =4𝜇𝑠
𝑉 𝑡ℎ
No 𝑇 1
With 𝑇 1
Improvements
¨Change of total amount of electrons in system → charge detection fidelity
𝑇 112 protected by next nearest neighbor hoping (1𝟏2 → 102)
Optimal 𝑡 𝑚 and 𝑉 𝑡ℎ → Charge state detection fidelity of 99.7% limited by 𝑻 𝟏𝟏𝟐 (*)
(*) «Battle of timescales»: 𝑇 112 ≫ 𝑇 1 ≫ 𝜏 𝑟
𝜏 𝑟 / 𝑇 1 < 10 −3 vs 𝒕 𝑴 / 𝑻 𝟏𝟏𝟐 ~𝟓⋅ 𝟏𝟎 −𝟑

8. Optimization of read-out fidelities
𝑉 𝑡ℎ 𝜎
𝑡 𝑑
𝑡 𝑑 : delay before read-out
𝐹 112 ( 𝑡 𝑑 )= 𝑒 − 𝑡 𝑑 / 𝑇 𝐹 112 ( 𝑡 𝑑 =0)
Idea: QD array with subsequental read-out
𝑉 𝑆 − 𝑉 𝑇 0
Sensor noise

9. < Qubit initialization
Problem: 𝑇 112 ≫ 𝑇 1 , so how to initialize from (112)?
(111)
<
(111) degenerated with (112)

10. Initialziation (idea)
Johnson et al., Nature 435 (2005)

11. Fidelity of spin-measurement
Main source of errors: non-adiabatic passage for O  M ( singlet-singlet anticrossing)
Idea: measure «nonadiabiacity» in initialzing (102) instead of (111)
(102)
Non-adiabatic passage
Landau-Zener:
𝑝 𝑛 ~1/ exp 2𝜋 𝑡 𝑐 2 ℏ Δ𝑡 Δ𝜖
𝑝 𝑛 →0 for Δ𝑡→∞
For I → O → M cycle, from rate equations: 𝑃 𝑠 𝑡 =𝑎+ 𝑣 2 𝑒 − 𝑡/ 𝑇 2 ∗ cos 𝜔𝑡+𝜙 +𝑐𝑒 −Γ𝑡
𝟐 𝒕 𝒄
(111)
(102)
adiabatic passage
𝑆− 𝑇 0 precession
Imperfect initialization
𝑐∝ 𝑝 𝑛
Γ=14 𝑀𝐻𝑧

12. Pulse ramp time Δt dependence
𝑝 𝑛 ~1/ exp 2𝜋 𝑡 𝑐 2 ℏ Δ𝑡 Δ𝜖
0.2% «spin-to-charge transfer error»
Spin measurement fidelity of 99.5% whereas
0.2% due to spin to charge transfer % due to charge readout

13. Conclusions
99.5% single-shot spin fidelity..
..using a metastable state for charge readout
..also enabling faster Qubit initialization
Improved S2N & increased state lifetime
Spin fidelity limited by charge readout

14. Thank you for your attention

15. Q1 decoupled
Q2 / Q3 build 𝑆− 𝑇 0 qubit
𝐵 𝑒𝑥𝑡 =0.7𝑇 Q2

16. 𝑇 1

17. 𝑃 𝑠 𝑡 =𝑎+ 𝑣 2 𝑒 𝑡 𝑇 2 ∗ 2 cos 𝜔𝑡+𝜙 +𝑐 𝑒 −Γ𝑡

19. Delbecq, Fig1