## Doctoral Theses

#### High-fidelity, near-field microwave gates in a cryogenic surface trap

Marius Weber 2022

Implementation of Mølmer-Sørensen two-qubit gates on ^{43}Ca^{+} hyperfine clock qubits in a cryogenic (≈25K) surface trap, driven by near-field microwaves. We achieve gate durations of 154µs (with 1.0(2)% error) and 331µs (0.5(1)% error), which approaches the performance of typical laser-driven gates. In the 331µs gate, we demonstrate a new Walsh-modulated dynamical decoupling scheme which suppresses errors due to fluctuations in the qubit frequency as well as imperfections in the decoupling drive itself. Development of an ion transport toolbox, with demonstrations of splitting and merging operations in two different traps.

#### Device-independent key distribution between trapped-ion quantum network nodes

David Nadlinger, 2022

Implementation of a complete protocol for device-independent quantum key distribution over a quantum network link, resulting in the generation of a 95884-bit shared private key, after 8.5 hours of run time. This is enabled by the high-rate (100s^{-1}), high-fidelity [96.0(1)%] generation of Bell states between remote trapped-ion qubits, yielding a detection-loophole-free CHSH inequality violation of 2.677(6) and quantum bit error rate of 1.44(2)%, both of which are stable during the generation of millions of Bell pairs. We also introduce a versatile method for micromotion compensation using time-stamped photon detection; we achieve a sensitivity to stray electric fields of 0.1 Vm^{-1}/\(\sqrt{\rm Hz}\).

#### An elementary quantum network of entangled optical atomic clocks

Bethan Nichol, 2022

Demonstration of entanglement-enhanced frequency comparison of two optical atomic clocks based on the 674nm quadrupole transition of ^{88}Sr^{+} ions, which are linked by a quantum-optical fibre link (\(\approx 2\)m long). We show that the use of an entangled state reduces the measurement uncertainty by nearly \(\sqrt{2}\), the value expected for the Heisenberg Limit. Today's optical clocks are typically limited by dephasing of the probe laser; in this regime, we find that entanglement yields a factor 2 reduction in the measurement uncertainty compared to conventional correlation spectroscopy techniques. We demonstrate this enhancement for the measurement of a frequency shift applied to one of the clocks.

#### A cryogenic trap for microwave-driven quantum logic using ^{43}Ca^{+} ions

Clemens Löschnauer, 2021

Development of single and two-qubit operations for a new hyperfine atomic clock qubit, operating at 28.8mT in ^{43}Ca^{+}, in a cryogenic surface-electrode trap. A single ion is laser-cooled to 0.5mK, close to the Doppler limit, by exploiting two-photon dark resonances that form between fine-structure levels. Resolved-sideband cooling on a Raman transition is used to cool the two-ion radial motional mode to an average occupation number \(\bar{n}=0.08\). Spin-motion entanglement driven by near-field microwaves is used to diagnose the Mølmer–Sørensen interaction. Initial two-qubit gate attempts give a fidelity 0.77(2).

#### Benchmarking memory and logic gates for trapped-ion quantum computing

Amy Hughes, 2021

Characterisation of the memory performance of a ^{43}Ca^{+ }clock qubit: randomised benchmarking is used to directly measure errors as small as 1.2(7) × 10^{−6} after a storage time of 1 ms. The memory error remains < 10^{−4} for up to 50 ms with no additional dynamical decoupling, or < 10^{−3} for up to 2 seconds with a simple CPMG sequence. Comparison of different implementations of mixed-element two-qubit gates on a ^{43}Ca^{+} - ^{88}Sr^{+} crystal: a light-shift gate with a fidelity of 99.8(1)% or 99.7(1)%, measured using partial state tomography or interleaved randomised benchmarking respectively, and several varieties of Mølmer–Sørensen gates with measured fidelities of up to 99.6(2)%.

#### High-fidelity mixed species entanglement of trapped ions

Keshav Thirumalai, 2019

High-fidelity mixed-species quantum logic gates between ^{43}Ca^{+} and ^{88}Sr^{+} ground-level qubits. Demonstration of a Ca-Sr logic gate, using a single 402nm laser system tuned midway between S-P dipole transitions of these two species, and characterization of the gate by several methods (Bell state tomography, process tomography and randomized benchmarking). An entangled state fidelity of up to 99.8% is achieved, comparable to that of the best same-species gates. A same-species Sr-Sr gate is also demonstrated, using the 674nm S-D quadrupole transition, with fidelity 96%.

#### Cryogenic, near-field quantum logic chips with passive field nulling on ^{43}Ca^{+}

Jochen Wolf, 2019

Design and characterization of our first cryogenic ion trap apparatus. Design of UHV system for both room temperature and cryogenic (LHe) operation using a flow cryostat. Description of new chip trap design for microwave-driven high-fidelity entangling gates, using a novel electrode layout for passive field nulling. Development of a wafer-scale chip fabrication process and eutectic chip bonding technique. Preliminary study of ion loading rates. Initial characterization of microwave field distribution above the chip using a single calcium-43 ion.

#### Entanglement between nodes of a quantum network

Laurent Stephenson, 2019

Construction of our first quantum networking experiment. Demonstration of high-rate, high-fidelity remote entanglement of two ^{88}Sr^{+} ions, trapped in two separate vacuum systems "Alice" and "Bob", connected by a 4m-long quantum-optical fibre link (qubit separation ~2m as the crow flies). Achievement of heralded entanglement with fidelity 94% at an average rate of 182 Bell pairs per second (success probability 0.022%). Generation of single-ion/single-photon entanglement with fidelity 97.9% at a rate of 5700 events per second.

#### Fast gates and mixed-species entanglement with trapped ions

Vera Schäfer, 2018

Fast entangling gates using amplitude-shaped pulses on ^{43}Ca^{+}, reaching a fidelity of 99.8% in 1.6µs and 60% in 480ns. Bell test experiment on ^{43}Ca^{+}-^{40}Ca^{+} mixed-species crystal and demonstration of mixed species entangling gate on ^{88}Sr^{+}-^{43}Ca^{+}.

#### Probing qubit memory errors at the 10^{−5} level

James Tarlton, 2018

Direct measurement of qubit memory errors in a calcium-43 "atomic clock" qubit. Randomized memory benchmarking is used to measure the memory error of a single qubit down to the few 10^{-6} level. The error is found to remain below the 10^{-3} level for up to 400ms. Surface trap designs for near-field microwave-driven two-qubit gates are explored.

#### A high-fidelity microwave driven two-qubit quantum logic gate in ^{43}Ca^{+}

Martin Sepiol, 2016

Experimental implementation of a microwave-driven two-qubit quantum logic gate in a room-temperature microfabricated surface ion trap. The gate scheme involves dynamical decoupling methods, which stabilise the qubits against fluctuations of the motional mode frequency and fluctuating energy shifts, and avoid the need to null the microwave field. The gate is applied directly to hyperfine "atomic clock" qubits in ^{43}Ca^{+} using the near-field microwave magnetic field gradient produced by an integrated trap electrode. The achieved gate fidelity is 99.7(1)%, after accounting for state preparation and measurement errors.

#### Near-field microwave addressing of trapped-ion qubits for scalable quantum computation

Diana Prado Lopes Aude Craik, 2016

Demonstration of high-fidelity spatial and polarization addressing of trapped-ion "atomic clock" memory qubits using near-field microwaves. Addressing is performed by interfering fields from integrated microwave electrodes to address a chosen trap zone whilst nulling crosstalk fields in the neighbour zone. Design of a next-generation ion trap which can perform near-field microwave addressing in a quantum CCD architecture without the need for nulling fields. Demonstration of a prototype micro-fabricated loop antenna for microwave characterization of chip ion traps.

#### Optical Bloch equations for simulating trapped-ion qubits

Hugo Janacek, 2015

Modelling temperature and fluorescence of a trapped ion using the optical Bloch equations. Development of efficient simulations that solve the time-dependent and time-independent problems for systems with large numbers of states. Introduction of a routine designed to model the approach to the steady state. Analysis of Doppler cooling incorporating motion of a trapped ion and the effects of repumping from a D state. Development of cooling schemes for ^{43}Ca^{+} at 146G and comparison with experiment. Demonstration of Doppler cooling below the Doppler limit for this isotope. Analysis of resonant effects in systems with more than three levels and comparison with experiment.

#### Linear Paul trap design for high-fidelity, scalable quantum information processing

Sarah Woodrow (M.Sc. Thesis), 2015

Design of a new linear 'blade' trap, with improved optical access. Review of linear Paul trap theory. Discussion of axial micromotion and its use for ion addressing. Numerical simulations of trap fields. Technical drawings of trap components.

#### High-fidelity quantum logic in Ca^{+}

Christopher Ballance, 2014

High-fidelity single- and two-qubit laser-driven logic gates in ^{43}Ca^{+} hyperfine qubits. Theoretical and experimental study of speed/fidelity trade-off for two-qubit gates. Achievement of single-qubit gate fidelities above 99.99%, and two-qubit gate fidelities ranging between 97.1(2)% (for a gate time of 3.8µs) and 99.9(1)% (at 100µs), after accounting for single-qubit operation and readout errors (each at the 0.1% level). Demonstration of a mixed-species (^{43}Ca^{+} and ^{40}Ca^{+}) entangling gate with a fidelity of 99.8(5)%.

#### High-fidelity microwave-driven quantum logic in intermediate-field ^{43}Ca^{+}

Thomas Harty, 2013

Development of an intermediate magnetic field "atomic clock" qubit in ^{43}Ca^{+} at 146G and high-fidelity techniques to manipulate this qubit using microwaves and lasers in a microfabricated surface-electrode ion trap. Randomized benchmarking of a single qubit. Work towards microwave-driven two-qubit gates including a theoretical analysis of likely sources of experimental error.

#### Background-free detection and mixed-species crystals in micro- and macroscopic ion-traps for scalable QIP

Norbert Linke, 2012

Assembly and testing of a microstructured 3D ion trap. Background-free detection and read-out of trapped ions. Raman laser system consisting of two injection-locked frequency-doubled lasers. Ground-state cooling and coherent manipulation of a mixed-species crystal in a macroscopic ion trap.

#### Surface-electrode ion traps for scalable quantum computing

David Allcock, 2011

Design, fabrication and testing of microfabricated surface-electrode ion traps. Pulsed laser cleaning of ion traps to reduce anomalous heating. An intermediate-field hyperfine "atomic clock" qubit in ^{43}Ca^{+}. Design, construction and testing of an ion trap incorporating microwave resonators for microwave-driven quantum logic gates.

#### High fidelity readout of trapped ion qubits

Alice Burrell, 2010

High-fidelity readout of trapped ion qubits. Demonstration of time-arrival resolved discrimination of ion states (TARDIS) with a photomultiplier detector to perform single-shot readout of a single ^{40}Ca^{+} optical qubit with 99.991(1)% fidelity. Replacing the photomultipler by an electron-multiplying CCD camera, the TARDIS method allows discrimination in both spatial and temporal dimensions, enabling achievement of the same 99.99% readout fidelity for a 4-ion "qunybble", despite 4% optical cross-talk between neighbouring ions.

#### Measurement-selected ensembles in trapped-ion qubits

Michael Curtis, 2010

Segmented ion trap modelling; measurement-selected ensembles (weak measurement); operation of planar and 7-electrode traps; implementation of a qubit in D5/2 state of 40Ca; partial collapse and `uncollapse' experiments.

#### High fidelity readout and protection of a ^{43}Ca^{+} trapped ion qubit

David Szwer, 2009

Rate equations programs for simulation of ^{43}Ca^{+}; comparison with experiment and Bloch equations. Simulation and optimisation of a robust, high-fidelity readout method from 43Ca+; experimental implementation. Attempted two-qubit gate with ^{40}Ca^{+} and ^{43}Ca^{+} mixed crystal; problems with crystallisation; electrode noise; measurement of heating rate, motional decoherence and "Schrodinger Cat" states. Derivation of Uhrig Dynamical Decoupling (UDD); review of the literature; experimental implementation of UDD and CPMG on ^{43}Ca^{+} hyperfine ground-state qubits.

#### Implementing segmented ion trap designs for quantum computing

Gergely Imreh, 2008

Numerical modelling of multiple-electrode traps. Ion shuttling and loading theory. Set-up of apparatus (including vacuum system, lasers and optics and control electronics) for trapping and experimenting with microfabricated "Sandia trap". Detailed evaluation of "Sandia trap": loading and micro-motion compensation; measurement of ion lifetime, motional frequency and heating rate; demonstration of ion shuttling.

#### A quantum memory qubit in calcium-43

Benjamin Keitch, 2007

Design and construction of various experimental apparatus: Laser Control Unit for precise pulse timing; master-slave 398nm laser system for Raman transitions in the hyperfine ground states of ^{43}Ca^{+}; KILL-110 system for PDH locking of lasers to optical cavities. Investigation of magnetic field fluctuations, using microwaves and ^{43}Ca^{+} hyperfine states; Spicer SC20 field cancelling system tested. Demonstration of long T2 coherence time of ^{43}Ca^{+} hyperfine clock state qubit.

#### Entanglement of two trapped-ion spin qubits

Jonathan Home, 2006

Careful study of sideband cooling and temperature diagnostics for one and two ions. Motional coherence measurements. Coherent manipulation of two ions. Spin state tomography for two ions. Quantum logic gate by oscillating force; deterministic entanglement. For electrode configurations for trap arrays, see Home and Steane paper, 2006.

#### Raman sideband cooling and coherent manipulation of trapped ions

Simon Webster, 2005

Photoionisation, Rabi/Ramsay experiments on single spin qubits by magnetic resonance and stimulated Raman transitions, continuous Raman sideband cooling using bright/dark resonance, pulsed Raman sideband cooling to the motional ground state, temperature diagnostics for 1 and 2 ions, rate equations for Ca-43.

#### Two-photon readout methods for an ion trap quantum information processor

Matthew McDonnell, 2003

MOPA 397 laser system, servo theory, Pound-Drever-Hall (and other) locking, optical Bloch equations, dark resonance fits, dark resonance cooling/heating, spin state readout: various methods, EIT method proposed and implemented.

#### Stabilization and control in a linear ion trap

John-Patrick Stacey, 2003

Reference cavities, improved photon counting, photon arrival time correlation method for micromotion compensation, new 850 laser, AOM optics, r.f. study towards helical resonator, magnetic field coils, dark resonances, isotope-selective photoionisation in detail.

#### Marek Šašura, 2002

Survey of ion/laser coupling theory, theoretical study of "pushing" gate method.

#### Development of an ion trap quantum information processor

Charles Donald, 2000

Some space charge ideas, general apparatus development, imaging, spectroscopy of blue laser diodes, field compensation drift, precise D_{5/2} lifetime measurement, upper bound on 2- and 3-ion quantum jump correlations and statistical analysis.

#### The quantum manipulation of ions

David Stevens, 1999

Construction from scratch of our first ion trap, some Mathieu equation and Doppler cooling theory, optogalvanic spectroscopy, frequency doubling, observations of crystals and quantum jumps, first look at D_{5/2} lifetime measurement.