Improving Fidelity in SiMOS Qubits through Pulse

Engineering Author: Gordon Yuheng Liang (z3459293)

Supervisor: Prof Andrew Dzurak Co-Supervisor: Dr Henry Yang

Research Theme: Fundamental and Enabling Research

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Introduction and Motivation

Aim and Objectives

Key Findings and Results

Programmable quantum computers require accurate control and readout of quantum bits

(qubits). This poses challenges for quantum devices, where device gates experience noise that

affects electron spin resonance (ESR) operations required for computation. Presented here is a

pulse engineering solution for optimising noise performance and improving fidelity of qubits in

silicon-based complementary metal-oxide semiconductor (CMOS) technologies. In addition, pulse

engineering offers improvements upon current techniques for suppressing decoherence, and

enables further lengthening of spin coherence times via dynamical decoupling.

1. To characterise the error rate of single qubit operations via Gradient Ascent Pulse

Engineering (GRAPE)1

2. To investigate the required initial conditions of GRAPE for the ESR line that optimises spin

fidelity and error rates

Figure 2: Single Qubit πx Pulse Optimisation in MATLAB

Left: Microwave Pulse Shape (Blue – CH1 X-Rotation, Red – CH2 Y-Rotation) Right: Error Rate of Qubit Gate (Yellow – Mean/100 samples)

Conclusion • Applying GRAPE control methods can greatly improve fidelity by two orders for gate

operations in single qubit systems

• Dynamical Decoupling sequences will preserve spin coherence more effectively when double

optimised from single qubit solutions, both in mean and deviation by the same factor

• Initial pulse conditions show a marked difference in deviation corrections

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(a) Unoptimised πx Rotation Initial Pulse and

Error Rate (Control)

(b) Optimised πx Rotation Pulse and Error

Rate

Single Gate Optimisation

• GRAPE Algorithm applied to initial ESR line pulse

(100MHz Sampling Frequency)

• Clear trend in noise reduction for upper bound

• Average noise level reduced by two orders of

magnitude

• Evolution of pulse envelope changes during

simulation with power limitations at 1 Unit,

normalised to the maximum microwave power

output bounded by either equipment, or heat load

of the device.

• At 40GHz carrier frequency, the magnitude of the

microwave is B0 = 1.4T

Figure 1: Device SEM and

cross-sectional schematic

Background Silicon quantum logic devices contain quantum dot structures

(labelled GC and G1-4) that can be operated as either single or

double quantum dots, where dots D1 and D2 are confined

underneath gates G1 and G2 respectively.2 While detuning

noise is largely eliminated, greater fidelity of qubits are

needed for noisier multi-qubit systems.

By pulsing an ac magnetic field Bac that is formed by passing

ac current Iac through the ESR line, qubits operations can be

achieved. Hence, to correct for the low frequency noise

prevalent is such devices, the GRAPE algorithm is

implemented to pulse shape microwaves from the ESR line

to optimise and improve upon the fidelity of the system.

The research performed involving pulse shaping via GRAPE

has been simulated using MATLAB under parameters set to

experimental specifications. In future, this process will be

tested experimentally.

Graph 1: Results of Simulation, all results from optimised pulses

calculated from point of optimal steady-state noise response

(a) Optimised XYXY Sequence with Shaping

Momentum and Error Rate

Figure 3: XYXY Dynamical Decoupling Sequence Optimisation at Various Initial Pulse Conditions

Legend as with Figure 2, Orange – Pulse Shaping Momentum (CH1)

(b) Double Optimised XYXY Sequence with Shaping

Momentum and Error Rate

Improvements in Dynamical Decoupling

• Directly applying GRAPE to the initial dynamical decoupling sequence yields an error rate reduction of 1 order of

magnitude

• The deviation of noise error is greatly reduce by 2 orders

• However, first optimising πx and πy rotations and sequencing in XYXY is a much better initial pulse

• Double optimising XYXY yields similar average error, but greatly reduces deviation

1 N. Khaneja et. al. Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. 2004

2 M. Veldhorst et. al. A two-qubit logic gate in Silicon. 2015

Future Work • Generalise GRAPE to two qubit systems

• Study the effects of noise coupling across tunnel-coupled two qubit systems

• Investigate how single gate optimisation affects two qubit pulse sequencing for noise error and

fidelity

1

10

100

1000

10000

πx Single Square Pulse (Unoptimised)

πx Single Square Pulse (Optimised)

XYXYSequence

(Unoptimised)

XYXYSequence

(Optimised)

XYXYSequence

(SingleOptimised

Stack)

XYXYSequence(Double

Optimised)

Mea

n E

rro

r (A

.U. x

10

-6)

Mean Error Rate of Pulse Operations

Mean

Gaussian Weighted Mean

(c) Optimised H-Rotation Pulse and Error

Rate