High-quality two-qubit gate (2QG) control policies for preparing Bell states are vital for uni-versal quantum computation, yet the successful implementations have been achieved only in few-qubit systems. State-of-the-art (SotA) two-qubit gates for trapped ions employ open-loop control that rely on simplified models to precompute control sequences. Such methods employ rigid simplifications, such as the presumption of unitary evolution to obtain a closed mathematical expression for trapped-particle dynamics and may employ greedy optimisa-tion to devise control policies. Nonetheless, quantum information processing based on cold trapped particles is susceptible to significant decoherence and fluctuation. Therefore, such control approaches do not scale properly for chains of more than two trapped ions or deliver feasible control sequences. In the present work, we aim to develop and implement novel techniques for open- and closed-loop quantum control for high-quality 2QG gates in realistic scenarios. Here, a comprehensive simulated ion trap environment is experimentally validated and used to develop and test two control protocols. First, a global optimisation algorithm finds robust solutions for a chain of seven ions with improved gate infidelity by at least one order of magnitude and a gate time of 35 μs, which is the shortest reported in the literature. Second, we demonstrate the feasibility of closed-loop control by introducing a spectator ion to the chain used for quantum logic processing for two-qubit gates to correct disturbances as they occur during gate implementations. This method improves the gate infidelity by one order of magnitude in the presence of motional heating and drift. The spectator ion’s posi-tion is continuously monitored by driving the dipole transitions and detecting the resultant fluorescence. In this work a global optimisation algorithm is able to navigate the non-convexity of the space solution to devise feasible control sequences. On the other side, we introduce the continuous monitoring of a spectator ion’s position to construct feasible control policies in realistic scenarios for implementing 2QG gates. We show that our methods for linear Paul trap implementations are expected to reduce the two-qubit gate Bell-state preparation infidelity with deleterious disturbances in realistic scenarios. The methods devised here are unique in the field of quantum control for 2QG and open up a new trend of techniques aiming to overcome the scalability challenges of quantum pro-cessor units. Our on-the-fly control method employs reinforcement learning with the reward function based on the actual geometric phase of the spectator ion. A key advantage of our approach is that we introduce a control method that involves ‘learning’ and correcting dis-turbances occurring in the trap on-the-fly, thus achieving high-fidelity gates. Our approach will lead to a significantly higher two-qubit gate fidelity with a reduced calibration overhead owing to the small parameter drift in the control system.
High-quality two-qubit gate (2QG) control policies for preparing Bell states are vital for uni-versal quantum computation, yet the successful implementations have been achieved only in few-qubit systems. State-of-the-art (SotA) two-qubit gates for trapped ions employ open-loop control that rely on simplified models to precompute control sequences. Such methods employ rigid simplifications, such as the presumption of unitary evolution to obtain a closed mathematical expression for trapped-particle dynamics and may employ greedy optimisa-tion to devise control policies. Nonetheless, quantum information processing based on cold trapped particles is susceptible to significant decoherence and fluctuation. Therefore, such control approaches do not scale properly for chains of more than two trapped ions or deliver feasible control sequences. In the present work, we aim to develop and implement novel techniques for open- and closed-loop quantum control for high-quality 2QG gates in realistic scenarios. Here, a comprehensive simulated ion trap environment is experimentally validated and used to develop and test two control protocols. First, a global optimisation algorithm finds robust solutions for a chain of seven ions with improved gate infidelity by at least one order of magnitude and a gate time of 35 μs, which is the shortest reported in the literature. Second, we demonstrate the feasibility of closed-loop control by introducing a spectator ion to the chain used for quantum logic processing for two-qubit gates to correct disturbances as they occur during gate implementations. This method improves the gate infidelity by one order of magnitude in the presence of motional heating and drift. The spectator ion’s posi-tion is continuously monitored by driving the dipole transitions and detecting the resultant fluorescence. In this work a global optimisation algorithm is able to navigate the non-convexity of the space solution to devise feasible control sequences. On the other side, we introduce the continuous monitoring of a spectator ion’s position to construct feasible control policies in realistic scenarios for implementing 2QG gates. We show that our methods for linear Paul trap implementations are expected to reduce the two-qubit gate Bell-state preparation infidelity with deleterious disturbances in realistic scenarios. The methods devised here are unique in the field of quantum control for 2QG and open up a new trend of techniques aiming to overcome the scalability challenges of quantum pro-cessor units. Our on-the-fly control method employs reinforcement learning with the reward function based on the actual geometric phase of the spectator ion. A key advantage of our approach is that we introduce a control method that involves ‘learning’ and correcting dis-turbances occurring in the trap on-the-fly, thus achieving high-fidelity gates. Our approach will lead to a significantly higher two-qubit gate fidelity with a reduced calibration overhead owing to the small parameter drift in the control system.
State-of-the-art two-qubit gates with trapped ions employ open-loop control that rely on simplified models to precompute control sequences. Our aim is to introduce closed-loop control for two-qubit gates to correct disturbances as they occur during the gate implementation. We introduce a spectator ion into the ion chain used for quantum logic processing, where it couples with the other ions through collective motional modes. The spectator ion's position is continuously monitored by driving dipole transitions and detecting the resultant fluorescence. We show that incorporating a spectator ion is feasible for linear Paul trap implementations and is expected to reduce the two-qubit gate Bell-state preparation infidelity by an order of magnitude with the deleterious effects of position monitoring being negligible compared to the thermal effects that exist in the system, even in the absence of the spectator ions. Mathematically, we describe driven ion-trap dynamics, including the spectator ion, by a stochastic quantum master equation involving the amplitude-modulation multimode-motional coupling gate, motional drift, thermal effects, recoil from photon scattering, spontaneous decay, and light shift. Our on-the-fly control method employs reinforcement learning with the reward function based on the actual geometric phase of the spectator ion. A key advantage of our approach is that we introduce a control method that involves `learning' and correcting disturbances happening in the trap on-the-fly, thus achieving high-fidelity gates. Our approach will lead to a significantly higher two-qubit gate fidelity at a reduced calibration overhead owing to the small parameter drift in the control system.
Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate duration and gate error rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-ion chain by a quantum master equation (QME). The QME incorporates the single-ion two-photon effective Rabi frequency, Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing beams, and an imperfect initial motional ground state, with no fitting parameters, whereas state-of-the-art methods are oblivious to these effects in the gate design procedure. We employ global optimization to design pulse sequences for achieving a robust rapid two-qubit gate for a simulated chain of seven trapped 171Yb+ ions by optimizing over numerically integrated QME solutions. Here, robust means resilient against slow drift of motional frequencies, and rapid means gate execution where the effective Rabi frequency is comparable to the detuning of the laser from the ion's bare electronic transition. Our robust quantum control delivers rapid high-quality two-qubit gates in long ion chains, enabling scalable quantum computing with trapped ions.
This thesis describes experimental work on implementing single and two qubit gates in ¹7¹Yb+ ions using methods suitable for a large scale quantum computer. By combining a magnetic field gradient with microwave and radiofrequency radiation, the spin and motional states of the ions are coupled which allows multi-qubit operations to be performed, as well as providing individual addressing of ions in frequency space. A dressed state qubit is used which exhibits an increase of over two orders of magnitude in the coherence time for a qubit that it is sensitive to the magnetic field gradient. Using this system, single qubit gates are characterised using the technique of randomised benchmarking, resulting in a measured average error per gate of 9(3)x10¯4. A new type of two qubit gate is experimentally demonstrated, which in comparison to a standard two qubit gate shows significantly increased resilience to two major sources of gate infidelity: heating of the motional mode of the ions during gate operations, and incorrectly set gate field frequencies. These types of errors are expected to become increasingly important with the move towards quantum processors with large numbers of qubits. Using this same technique, a two qubit gate is also demonstrated at a higher initial temperature with a significantly improved fidelity compared to standard methods. These gate techniques are used to demonstrate work towards implementing positiondependent quantum logic, a method which could remove the correlation between the number of ions and the number of gate fields required in a large scale quantum computing architecture. A method to move the dressed state qubit through a magnetic field gradient while preserving quantum information is demonstrated, as well as a method to optimise the phase of a two qubit gate of unknown phase in order to implement a CNOT logic gate. This provides a path forwards to demonstrating a CNOT gate using position-dependent quantum logic.
Non-adiabatic two-qubit gate proposals for trapped-ion systems offer superior performance and flexibility over adiabatic schemes at the cost of increased laser control requirements. Existing fast gate schemes are limited by single-qubit transition errors, which constrain the total number of pulses in high-fidelity solutions. We introduce an improved gate search scheme that enables both local and non-local two-qubit gates in chains containing tens of ions. These protocols use a multi-objective machine design approach that incorporates dominant sources of error in the design to ensure the solutions are compatible with existing fast laser controls. We also generalize previous schemes by allowing for unpaired pulses during the gate evolution. By imposing symmetries on the pulse sequences, we eliminate susceptibility to laser phase noise and further simplify the multi-mode control over the state-dependent motion of the ion crystal. We perform a comprehensive analysis of expected gate performance in the presence of random and systematic experimental errors to demonstrate the feasibility of performing microsecond two-qubit gates between arbitrary ion pairs in current linear ion-trap processors of up to 50 ions with fidelities approaching 99.9%.
Achieving precise control over quantum systems has groundbreaking ap-plications, such as simulating complex quantum systems, or implementing quantum algorithms with an improved efficiency over classical algorithms. Quantum computing has been under development for the last decades, re-sulting in the so-called Noisy Intermediate-Scale Quantum (NISQ) devices with about 50 qubits. While these devices are built with the purpose of achieving practical advantages over classical processors, they are vulnerable to noise sources. In order to account for error sources, one needs to im-plement Quantum Error Correction (QEC) techniques. These techniques protect quantum information by encoding a logical qubit into several phys-ical ones. For the implementation of NISQ devices and QEC techniques, it is vital to keep improving the quantum operations and states involved. Here we develop calibration protocols based on the application of Bayesian inference. We show their advantages compared to the more traditional frequentist approaches, such as their ability to maximise the information gained with each measurement, or their straightforward automation. In our first line of research, we develop a Bayesian protocol for the correction of unwanted phases appearing in the experimental preparation of Steane code states. This protocol requires 13 times less measurements than the frequentist approach. In our second line of research, we develop a proto-col for locking a laser to the qubit transition frequency in a trapped-ion architecture. This calibration is vital, since the correct implementation of single-qubit gates depends on it. In our final line of research, we study the Mølmer-Sørensen entangling gate, used in trapped-ion systems. First we introduce the calibration parameters, and derive a semianalytical model of the effects of one of them, for which there was no previous analytical understanding. Finally, we develop a Bayesian protocol for the calibration of these parameters, which was successfully implemented and tested in an experimental trapped-ion quantum processor.
This thesis describes the development of technology and experimental techniques for scalable trapped-ion quantum computing. An architecture for scalable quantum computing is presented in which 171Yb+ ions are trapped in linear R.F. Paul traps and their hyper-fine states are used to form qubits. Quantum logical operations can be carried out by applying R.F. and microwave fields. This thesis presents significant improvements in the experimental setup used for quantum computing, as well as new theoretical developments and experimental demonstrations of new high- fidelity quantum control methods. A new procedure for carrying out high- delity two qubit gates using static magnetic eld gradients and resonant microwave elds is presented. It is shown that this has the potential to enable signi cantly improved delities compared to current methods. Improved methods for measurement and statistical analysis in trapped-ion experiments are also shown. These should enable more accurate measurement of two-qubit gate delities, which becomes increasingly important as delities increase. A new system for generating arbitrary R.F. and microwave waveforms is presented, including a bespoke software control system allowing the user to de ne custom pulse sequences, which represents a signi cant improvement in the scalability of the quantum control system. Experimental developments towards a system for carrying out on-chip trapped-ion quantum logic in a static magnetic eld gradient are also presented. A new technique for generating multi-level control methods is introduced, based on reducing a multi-level system to an e ective two-level system. High- delity quantum control methods generated using this technique, which form a will form a key part of the scalable quantum computing architecture, are implemented experimentally.