Leon Camenzind 11/08/17

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

Setup and Charge stability Diagram Q2 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, 046802 (2016)

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)

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%

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

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

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

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

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

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 ∗ 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

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 0.3% due to charge readout

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

Thank you for your attention

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

𝑇 1

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

Delbecq, Fig1