QBithm: towards the coherent control of robust spin qubits in quantum algorithms

Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles, it is now timely to zoom out and take the whole picture: concerning applications that require user-driven evolutions, qubits should be assessed within the desired algorithm. This means to test qubits under external control while relaxation is active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit algorithms subject to relaxation. It is handled via a code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their ab initio computation. We calculate fidelities against relaxation and imperfections, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-qubit systems driven under relaxation and imperfections in quantum algorithms.Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles, it is now timely to zoom out and take the whole picture: concerning applications that require user-driven evolutions, qubits should be assessed within the desired algorithm. This means to test qubits under external control while relaxation is active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit algorithms subject to relaxation. It is handled via a code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their ab initio computation. We calculate fidelities against relaxation and imperfections, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-qubit systems driven under relaxation and imperfections in quantum algorithms.

Mar 13, 20230 citations

Towards the coherent control of robust spin qubits in quantum algorithms

Luis Escalera‐Moreno

Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles at a mature stage, it is now timely to widen the scope and take the whole picture: concerning applications that require user-driven coherent evolutions, qubits should be assessed operating within the desired algorithm. This means to test qubits under external control while relaxation and imperfections are active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit gate-based algorithms subject to relaxation. It is handled via a home-made code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their $\textit{ab initio}$ computation. We evaluate the impact of relaxation and potential experimental imperfections in the calculated fidelities, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-spin-qubit systems in quantum algorithms, and will serve as a help to design robust spin qubits against decoherence and to perform better-characterized experiments.Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles at a mature stage, it is now timely to widen the scope and take the whole picture: concerning applications that require user-driven coherent evolutions, qubits should be assessed operating within the desired algorithm. This means to test qubits under external control while relaxation and imperfections are active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit gate-based algorithms subject to relaxation. It is handled via a home-made code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their $\textit{ab initio}$ computation. We evaluate the impact of relaxation and potential experimental imperfections in the calculated fidelities, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-spin-qubit systems in quantum algorithms, and will serve as a help to design robust spin qubits against decoherence and to perform better-characterized experiments.

arXiv:2303.12655Mar 10, 20231 citation

Coherent control for quantum information processing

Gaurav Bhole

An exquisite control over the dynamics of a quantum system is essential for realizing any quantum technology. This thesis presents some practical and efficient strategies for coherent quantum control: a paradigm for controlling quantum dynamics using electromagnetic fields. Coherent control is a common framework for describing the physical implementation of quantum logic gates in several quantum information processing platforms including superconducting qubits and trapped ions. For the purpose of demonstration, however, liquid-state Nuclear Magnetic Resonance (NMR) is used in this thesis as it is an ideal test-bed for developing, testing and benchmarking coherent control tools and techniques. Coherent control was revitalised in 2005 by the development of Gradient Ascent Pulse Engineering (GRAPE), a powerful optimal control technique that is widely used for designing shaped pulses for a variety of tasks. GRAPE, like any other closed-loop optimal control algorithm, requires multiple evaluations of the computationally expensive matrix exponential and the full time-evolution propagator. To this end, I present strategies to sidestep the explicit evaluation of matrix exponentials, thereby offering substantial speed-ups over conventional implementations of the GRAPE algorithm. The results are demonstrated experimentally in NMR, but also in simulations of ultracold molecules and superconducting qubits. Beyond GRAPE, this thesis also considers methods for designing spin-echo sequences for implementing any arbitrary network of controlled-Z gates in a system of qubits with zz-couplings. First, a method based on linear-programming provides near time-optimal sequences in fully-coupled systems having up to a few hundred qubits. Further, an analytic method based on graph colouring finds near time-optimal spin echo sequences in engineered systems with any number of qubits having only nearest and next-nearest neighbour-couplings.An exquisite control over the dynamics of a quantum system is essential for realizing any quantum technology. This thesis presents some practical and efficient strategies for coherent quantum control: a paradigm for controlling quantum dynamics using electromagnetic fields. Coherent control is a common framework for describing the physical implementation of quantum logic gates in several quantum information processing platforms including superconducting qubits and trapped ions. For the purpose of demonstration, however, liquid-state Nuclear Magnetic Resonance (NMR) is used in this thesis as it is an ideal test-bed for developing, testing and benchmarking coherent control tools and techniques. Coherent control was revitalised in 2005 by the development of Gradient Ascent Pulse Engineering (GRAPE), a powerful optimal control technique that is widely used for designing shaped pulses for a variety of tasks. GRAPE, like any other closed-loop optimal control algorithm, requires multiple evaluations of the computationally expensive matrix exponential and the full time-evolution propagator. To this end, I present strategies to sidestep the explicit evaluation of matrix exponentials, thereby offering substantial speed-ups over conventional implementations of the GRAPE algorithm. The results are demonstrated experimentally in NMR, but also in simulations of ultracold molecules and superconducting qubits. Beyond GRAPE, this thesis also considers methods for designing spin-echo sequences for implementing any arbitrary network of controlled-Z gates in a system of qubits with zz-couplings. First, a method based on linear-programming provides near time-optimal sequences in fully-coupled systems having up to a few hundred qubits. Further, an analytic method based on graph colouring finds near time-optimal spin echo sequences in engineered systems with any number of qubits having only nearest and next-nearest neighbour-couplings.

Jan 1, 20200 citations

High-fidelity single-qubit gates in multi-qubit environments using spin qubits in Silicon quantum dots

Vincent Bejach

Electron spins trapped in quantum dots have recently proven to be a promising technology for the implementation of qubits, already demonstrating high fidelity single- and two-qubits gates. The next step towards fault-tolerant quantum computing is to increase the number of so-called spin qubits on the processor. However, this poses several challenges, one of which being how to implement single-qubit gates in multi-qubit systems, with high fidelity. This work focused on two aspects. The first one was to identify the physical phenomena and limitations that hinder the realisation of high fidelity single-qubit gates in multi-qubit environments. The second objective was to investigate, implement and optimise methods in order to minimise the impact of these perturbing phenomena. The identified perturbing effects include unwanted driving between a pulse and the neighbouring qubits, as well as frequency shifts induced by drive-spin coupling and non-ideal pulse in experimental setups. Crosstalk was addressed using pulse shaping (i.e. amplitude or phase modulation of the driving pulse to tailor its spectral characteristics and reduce the energy transmitted at unwanted frequencies). The performance of shapes taken from both NMR and signal processing literature was investigated, for various pulse parameters, through an extensive grid search. In addition, a frequency correction algorithm was devised: off-resonant drive frequencies are selected so that the shifted qubits are resonantly driven. It currently accounts for two phenomena: the AC Stark and Bloch-Siegert shifts. The algorithm furthermore tracks the changes caused by the time-dependent characteristics of the shaped pulses. The proposed frequency correction algorithm was shown to almost entirely negate the effects of the considered shifts, leading to unitary fidelity improvements by up to 55%. In addition, pulse shaping was demonstrated to noticeably improve the fidelity of simultaneous single-qubit rotations compared to unshaped driving. Rotations with fidelities as high as 99.98% were obtained for pi/2 rotations on two-qubits systems. Moreover, shapes whose Fourier transform is narrow and sharp, associated with low Rabi frequencies, were demonstrated to generally provide the highest fidelities of the tested configurations. Lastly, the trends and guidelines highlighted by these results were shown to scale to systems with larger numbers of qubits. The correction techniques investigated in this work have proven promising for the implementation of high fidelity single-qubit gates in multi-qubit systems. In particular, the guidelines for selecting a well-performing pulse shape should also be useful for the design of optimised driving schemes, regardless of the number of qubits involved. Additionally, the proposed frequency shift correction algorithm is expected to be able to handle arbitrary shifts, and so to be easily adaptable to use in experiments.Electron spins trapped in quantum dots have recently proven to be a promising technology for the implementation of qubits, already demonstrating high fidelity single- and two-qubits gates. The next step towards fault-tolerant quantum computing is to increase the number of so-called spin qubits on the processor. However, this poses several challenges, one of which being how to implement single-qubit gates in multi-qubit systems, with high fidelity. This work focused on two aspects. The first one was to identify the physical phenomena and limitations that hinder the realisation of high fidelity single-qubit gates in multi-qubit environments. The second objective was to investigate, implement and optimise methods in order to minimise the impact of these perturbing phenomena. The identified perturbing effects include unwanted driving between a pulse and the neighbouring qubits, as well as frequency shifts induced by drive-spin coupling and non-ideal pulse in experimental setups. Crosstalk was addressed using pulse shaping (i.e. amplitude or phase modulation of the driving pulse to tailor its spectral characteristics and reduce the energy transmitted at unwanted frequencies). The performance of shapes taken from both NMR and signal processing literature was investigated, for various pulse parameters, through an extensive grid search. In addition, a frequency correction algorithm was devised: off-resonant drive frequencies are selected so that the shifted qubits are resonantly driven. It currently accounts for two phenomena: the AC Stark and Bloch-Siegert shifts. The algorithm furthermore tracks the changes caused by the time-dependent characteristics of the shaped pulses. The proposed frequency correction algorithm was shown to almost entirely negate the effects of the considered shifts, leading to unitary fidelity improvements by up to 55%. In addition, pulse shaping was demonstrated to noticeably improve the fidelity of simultaneous single-qubit rotations compared to unshaped driving. Rotations with fidelities as high as 99.98% were obtained for pi/2 rotations on two-qubits systems. Moreover, shapes whose Fourier transform is narrow and sharp, associated with low Rabi frequencies, were demonstrated to generally provide the highest fidelities of the tested configurations. Lastly, the trends and guidelines highlighted by these results were shown to scale to systems with larger numbers of qubits. The correction techniques investigated in this work have proven promising for the implementation of high fidelity single-qubit gates in multi-qubit systems. In particular, the guidelines for selecting a well-performing pulse shape should also be useful for the design of optimised driving schemes, regardless of the number of qubits involved. Additionally, the proposed frequency shift correction algorithm is expected to be able to handle arbitrary shifts, and so to be easily adaptable to use in experiments.

Jan 1, 20200 citations

Quantum control theory for coherence and information dynamics

Lorenza Viola, David J. Tannor

Precisely characterizing and controlling the dynamics of realistic open quantum systems has emerged in recent years as a key challenge across contemporary quantum sciences and technologies, with implications ranging from physics, chemistry and applied mathematics to quantum information processing (QIP) and quantum engineering. Quantum control theory aims to provide both a general dynamical-system framework and a constructive toolbox to meet this challenge. The purpose of this special issue of Journal of Physics B: Atomic, Molecular and Optical Physics is to present a state-of-the-art account of recent advances and current trends in the field, as reflected in two international meetings that were held on the subject over the last summer and which motivated in part the compilation of this volume—the Topical Group: Frontiers in Open Quantum Systems and Quantum Control Theory , held at the Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP) in Cambridge, Massachusetts (USA), from 1–14 August 2010, and the Safed Workshop on Quantum Decoherence and Thermodynamics Control , held in Safed (Israel), from 22–27 August 2010. Initial developments in quantum control theory date back to (at least) the early 1980s, and have been largely inspired by the well-established mathematical framework for classical dynamical systems. As the above-mentioned meetings made clear, and as the burgeoning body of literature on the subject testifies, quantum control has grown since then well beyond its original boundaries, and has by now evolved into a highly cross-disciplinary field which, while still fast-moving, is also entering a new phase of maturity, sophistication, and integration. Two trends deserve special attention: on the one hand, a growing emphasis on control tasks and methodologies that are specifically motivated by QIP, in addition and in parallel to applications in more traditional areas where quantum coherence is nevertheless vital (such as, for instance, quantum control of chemical reactions or high-resolution magnetic resonance spectroscopy); on the other hand, an unprecedented demand for close coupling between theory and experiment , with theoretical developments becoming more and more attuned to and driven by experimental advances as different quantum technologies continue to evolve at an impressive pace in the laboratory. Altogether, these two trends account for several of the recurrent themes in this volume, as well as in the current quantum control literature as a whole: namely, the quest for control strategies that can attain the highest degree of precision and robustness possible, while striving for efficiency and, ultimately, optimality in achieving the intended control task under realistic operational constraints. From a theory standpoint, this makes it imperative to take into account increasingly more realistic control settings; to assess the quantitative impact of limited control resources and/or system knowledge; and to provide a rigorous and general foundation for existing experimental approaches in order to further enhance applicability and performance. From an experimental standpoint, renewed emphasis is in turn placed on validating theoretical predictions and benchmarking performance, so that the limiting constraints can be singled out for additional theoretical analysis and guidance. This ongoing cross-talk is clearly reflected in this collection, which brings together theoreticians and experimentalists, with a significant fraction of the papers reporting on combined quantum control theory–experiment efforts. While a precise categorization would neither be possible nor desirable, contributions to this volume have been loosely grouped into five broad sections. This grouping has been made in the hope that connections between different problems and/or technical approaches will become more transparent, facilitating the transfer of concepts and methods. The special issue opens with a section devoted to open-loop control methods, with special emphasis on dynamical decoupling (DD), which is becoming an increasingly important tool for decoherence control at the physical 'quantum firmware' level. In addition to including original research results, the first two articles, by Brion et al and Biercuk et al , also serve to pedagogically review some background in their respective subjects. In particular, Brion et al revisit one of the conceptually simplest approaches to open-loop manipulation of both closed and open quantum systems, nonholonomic control , motivated by its broad applicability to QIP settings. A special instance of open-loop control based on sequences of (nearly) instantaneous `bang-bang' pulses is addressed by Biercuk et al , who reformulate the simplest DD scenario, suppression of phase decoherence in a single qubit, as a filter-design problem. Peng et al report on the implementation of 'concatenated' DD for arbitrary single-qubit decoherence in the context of nuclear magnetic resonance QIP. A dedicated analysis of the performance of different DD schemes in the presence of realistic pulse errors is given by Wang and Dobrovitski. DD is also one of the strategies used by Lucamarini et al to reduce polarization decoherence in a photon qubit. These authors additionally report on the use of active feedback to counter transmission noise, effectively setting the stage for the second section, which is centered on closed-loop control. Unlike in open-loop control, measurement is an essential ingredient in closed-loop schemes aimed at both reliably identifying features of the target quantum system and further modifying its dynamics. The importance of directly measuring the spectrum of the underlying system-environment coupling is stressed by Almog et al , who show how this knowledge is crucial, in particular, for predicting the performance of DD sequences in experiments and for optimizing performance. Riofrio et al address a weak-measurement protocol for implementing quantum state tomography , which is a necessary 'primitive' for inferring the target quantum state and thereby diagnosing the control performance. Next, the impact of realistic control and system imperfections in continuous-time Markovian feedback strategies for rapid state preparation is analyzed by Combes and Wiseman. A prominent role is played in the special issue by optimal control (OC) approaches, reflecting their central importance for quantum control and QIP. The OC contributions have been divided into two separate sections, depending on whether the target dynamics is modeled as Hamiltonian (section 3) or dissipative (section 4), respectively. The contribution by Beltrani et al deals with `control landscapes', which provide a foundation for analyzing the performance of numerical OC algorithms and their robustness against control errors. Specifically, this paper characterizes geometric properties of the control landscape, relevant to the optimal control of state-to-state transitions. Application of OC theory to the problem of population transfer and coherence enhancement in Λ-systems is studied by Kumar et al , whereas Goerz et al report on the OC-design of a high-fidelity controlled phase-gate in atomic qubits. The robustness of an OC solution is specifically addressed by Negretti et al , along with an approach for identifying easily implementable while still 'close-to-optimal' control pulses. Powerful relaxation-optimized OC schemes (based on so-called opengrape algorithms) for generating unitary target gates in the presence of known dissipation parameters are discussed by Schulte-Herbrüggen et al . Next, Lapert et al report on the problem of time-optimal control of spin-1/2 systems undergoing Bloch relaxation dynamics, highlighting the crucial role played by singular extremals in the control synthesis. Alternative approaches for optimized control of qubits exposed to various decoherence processes are developed by Esher et al and Xue et al , based on a perturbative 'bath-optimized' formalism and on numerical optimization via a genetic algorithm, respectively. Testifying to the richness of the field, the volume concludes with four contributions that address a diverse range of problems. The exploitation of properties of adiabatic quantum evolutions is common to the first two papers. In particular, Legthtas et al offer a rigorous explanation for the robustness of a control protocol, chirped pulsing , that is widely employed in 'adiabatic rapid passage' experiments, while Han et al present a theoretical framework for adiabatic Raman photo-association schemes relevant to ultracold atomic systems. In the context of cavity quantum electrodynamics, Montenegro and Orszag describe how to engineer a system of two atoms coupled to distant lossy cavities so that stable atomic entanglement is generated. Finally, still very little is known about the physical mechanisms that are responsible for and control the experimentally observed 'coherent' features of transport phenomena in biological systems. The last contribution by Alicki and Giraldi analyzes energy transport in dynamical systems that can be modeled as 'quantum networks', and points to this fascinating emerging frontier. It is our hope that the above papers may help readers to gain an overview of some of the main trends in current quantum control efforts, both theoretical and experimental. In closing, we take the opportunity to thank the organizations which sponsored the above-mentioned ITAMP Topical Group (the United States National Science Foundation and Harvard University) and the Safed Workshop (the Israeli Science Foundation, the Safed Scientific Workshop program, CECAM and ACAM). Last but not least our sincere gratitude goes to all of the contributors to the volume and the reviewers as well as the J. Phys. B staff, for their respective efforts in preparing the papers and ensuring the overall quality of this special issue.Precisely characterizing and controlling the dynamics of realistic open quantum systems has emerged in recent years as a key challenge across contemporary quantum sciences and technologies, with implications ranging from physics, chemistry and applied mathematics to quantum information processing (QIP) and quantum engineering. Quantum control theory aims to provide both a general dynamical-system framework and a constructive toolbox to meet this challenge. The purpose of this special issue of Journal of Physics B: Atomic, Molecular and Optical Physics is to present a state-of-the-art account of recent advances and current trends in the field, as reflected in two international meetings that were held on the subject over the last summer and which motivated in part the compilation of this volume—the Topical Group: Frontiers in Open Quantum Systems and Quantum Control Theory , held at the Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP) in Cambridge, Massachusetts (USA), from 1–14 August 2010, and the Safed Workshop on Quantum Decoherence and Thermodynamics Control , held in Safed (Israel), from 22–27 August 2010. Initial developments in quantum control theory date back to (at least) the early 1980s, and have been largely inspired by the well-established mathematical framework for classical dynamical systems. As the above-mentioned meetings made clear, and as the burgeoning body of literature on the subject testifies, quantum control has grown since then well beyond its original boundaries, and has by now evolved into a highly cross-disciplinary field which, while still fast-moving, is also entering a new phase of maturity, sophistication, and integration. Two trends deserve special attention: on the one hand, a growing emphasis on control tasks and methodologies that are specifically motivated by QIP, in addition and in parallel to applications in more traditional areas where quantum coherence is nevertheless vital (such as, for instance, quantum control of chemical reactions or high-resolution magnetic resonance spectroscopy); on the other hand, an unprecedented demand for close coupling between theory and experiment , with theoretical developments becoming more and more attuned to and driven by experimental advances as different quantum technologies continue to evolve at an impressive pace in the laboratory. Altogether, these two trends account for several of the recurrent themes in this volume, as well as in the current quantum control literature as a whole: namely, the quest for control strategies that can attain the highest degree of precision and robustness possible, while striving for efficiency and, ultimately, optimality in achieving the intended control task under realistic operational constraints. From a theory standpoint, this makes it imperative to take into account increasingly more realistic control settings; to assess the quantitative impact of limited control resources and/or system knowledge; and to provide a rigorous and general foundation for existing experimental approaches in order to further enhance applicability and performance. From an experimental standpoint, renewed emphasis is in turn placed on validating theoretical predictions and benchmarking performance, so that the limiting constraints can be singled out for additional theoretical analysis and guidance. This ongoing cross-talk is clearly reflected in this collection, which brings together theoreticians and experimentalists, with a significant fraction of the papers reporting on combined quantum control theory–experiment efforts. While a precise categorization would neither be possible nor desirable, contributions to this volume have been loosely grouped into five broad sections. This grouping has been made in the hope that connections between different problems and/or technical approaches will become more transparent, facilitating the transfer of concepts and methods. The special issue opens with a section devoted to open-loop control methods, with special emphasis on dynamical decoupling (DD), which is becoming an increasingly important tool for decoherence control at the physical 'quantum firmware' level. In addition to including original research results, the first two articles, by Brion et al and Biercuk et al , also serve to pedagogically review some background in their respective subjects. In particular, Brion et al revisit one of the conceptually simplest approaches to open-loop manipulation of both closed and open quantum systems, nonholonomic control , motivated by its broad applicability to QIP settings. A special instance of open-loop control based on sequences of (nearly) instantaneous `bang-bang' pulses is addressed by Biercuk et al , who reformulate the simplest DD scenario, suppression of phase decoherence in a single qubit, as a filter-design problem. Peng et al report on the implementation of 'concatenated' DD for arbitrary single-qubit decoherence in the context of nuclear magnetic resonance QIP. A dedicated analysis of the performance of different DD schemes in the presence of realistic pulse errors is given by Wang and Dobrovitski. DD is also one of the strategies used by Lucamarini et al to reduce polarization decoherence in a photon qubit. These authors additionally report on the use of active feedback to counter transmission noise, effectively setting the stage for the second section, which is centered on closed-loop control. Unlike in open-loop control, measurement is an essential ingredient in closed-loop schemes aimed at both reliably identifying features of the target quantum system and further modifying its dynamics. The importance of directly measuring the spectrum of the underlying system-environment coupling is stressed by Almog et al , who show how this knowledge is crucial, in particular, for predicting the performance of DD sequences in experiments and for optimizing performance. Riofrio et al address a weak-measurement protocol for implementing quantum state tomography , which is a necessary 'primitive' for inferring the target quantum state and thereby diagnosing the control performance. Next, the impact of realistic control and system imperfections in continuous-time Markovian feedback strategies for rapid state preparation is analyzed by Combes and Wiseman. A prominent role is played in the special issue by optimal control (OC) approaches, reflecting their central importance for quantum control and QIP. The OC contributions have been divided into two separate sections, depending on whether the target dynamics is modeled as Hamiltonian (section 3) or dissipative (section 4), respectively. The contribution by Beltrani et al deals with `control landscapes', which provide a foundation for analyzing the performance of numerical OC algorithms and their robustness against control errors. Specifically, this paper characterizes geometric properties of the control landscape, relevant to the optimal control of state-to-state transitions. Application of OC theory to the problem of population transfer and coherence enhancement in Λ-systems is studied by Kumar et al , whereas Goerz et al report on the OC-design of a high-fidelity controlled phase-gate in atomic qubits. The robustness of an OC solution is specifically addressed by Negretti et al , along with an approach for identifying easily implementable while still 'close-to-optimal' control pulses. Powerful relaxation-optimized OC schemes (based on so-called opengrape algorithms) for generating unitary target gates in the presence of known dissipation parameters are discussed by Schulte-Herbrüggen et al . Next, Lapert et al report on the problem of time-optimal control of spin-1/2 systems undergoing Bloch relaxation dynamics, highlighting the crucial role played by singular extremals in the control synthesis. Alternative approaches for optimized control of qubits exposed to various decoherence processes are developed by Esher et al and Xue et al , based on a perturbative 'bath-optimized' formalism and on numerical optimization via a genetic algorithm, respectively. Testifying to the richness of the field, the volume concludes with four contributions that address a diverse range of problems. The exploitation of properties of adiabatic quantum evolutions is common to the first two papers. In particular, Legthtas et al offer a rigorous explanation for the robustness of a control protocol, chirped pulsing , that is widely employed in 'adiabatic rapid passage' experiments, while Han et al present a theoretical framework for adiabatic Raman photo-association schemes relevant to ultracold atomic systems. In the context of cavity quantum electrodynamics, Montenegro and Orszag describe how to engineer a system of two atoms coupled to distant lossy cavities so that stable atomic entanglement is generated. Finally, still very little is known about the physical mechanisms that are responsible for and control the experimentally observed 'coherent' features of transport phenomena in biological systems. The last contribution by Alicki and Giraldi analyzes energy transport in dynamical systems that can be modeled as 'quantum networks', and points to this fascinating emerging frontier. It is our hope that the above papers may help readers to gain an overview of some of the main trends in current quantum control efforts, both theoretical and experimental. In closing, we take the opportunity to thank the organizations which sponsored the above-mentioned ITAMP Topical Group (the United States National Science Foundation and Harvard University) and the Safed Workshop (the Israeli Science Foundation, the Safed Scientific Workshop program, CECAM and ACAM). Last but not least our sincere gratitude goes to all of the contributors to the volume and the reviewers as well as the J. Phys. B staff, for their respective efforts in preparing the papers and ensuring the overall quality of this special issue.

Journal of Physics B Atomic Molecular and Optical PhysicsJul 25, 20116 citations

High fidelity readout and protection of a 43Ca+ trapped ion qubit

D. J. Szwer

This thesis describes theoretical and experimental work whose main aim is the development of techniques for using trapped 43Ca⁺ ions for quantum information processing. I present a rate equations model of 43Ca⁺, and compare it with experimental data. The model is then used to investigate and optimise an electron-shelving readout method from a ground-level hyperfine qubit. The process is robust against common experimental imperfections. A shelving fidelity of up to 99.97% is theoretically possible, taking 100 μs. The laser pulse sequence can be greatly simplified for only a small reduction in the fidelity. The simplified method is tested experimentally with fidelities up to 99.8%. The shelving procedure could be applied to other commonly-used species of ion qubit. An entangling two-qubit quantum controlled-phase gate was attempted between a 40Ca⁺ and a 43Ca⁺ ion. The experiment did not succeed due to frequent decrystallisation of the ion pair, and strong motional decoherence. The source of the problems was never identified despite significant experimental effort, and the decision was made to suspend the experiments and continue them in an improved ion trap which is under construction. A sequence of pi-pulses, inspired by the Hahn spin-echo, was derived that is capable of greatly reducing dephasing of any qubit. If the qubit precession frequency varies with time as an nth-order polynomial, an (n+1) pulse sequence is theoretically capable of perfectly cancelling the resulting phase error. The sequence is used on a 43Ca+ magnetic-field-sensitive hyperfine qubit, with 20 pulses increasing the coherence time by a factor of 75 compared to an experiment without any spin-echo. In our ambient noise environment the well-known Carr-Purcell-Meiboom-Gill dynamic-decoupling method was found to be comparably effective.This thesis describes theoretical and experimental work whose main aim is the development of techniques for using trapped 43Ca⁺ ions for quantum information processing. I present a rate equations model of 43Ca⁺, and compare it with experimental data. The model is then used to investigate and optimise an electron-shelving readout method from a ground-level hyperfine qubit. The process is robust against common experimental imperfections. A shelving fidelity of up to 99.97% is theoretically possible, taking 100 μs. The laser pulse sequence can be greatly simplified for only a small reduction in the fidelity. The simplified method is tested experimentally with fidelities up to 99.8%. The shelving procedure could be applied to other commonly-used species of ion qubit. An entangling two-qubit quantum controlled-phase gate was attempted between a 40Ca⁺ and a 43Ca⁺ ion. The experiment did not succeed due to frequent decrystallisation of the ion pair, and strong motional decoherence. The source of the problems was never identified despite significant experimental effort, and the decision was made to suspend the experiments and continue them in an improved ion trap which is under construction. A sequence of pi-pulses, inspired by the Hahn spin-echo, was derived that is capable of greatly reducing dephasing of any qubit. If the qubit precession frequency varies with time as an nth-order polynomial, an (n+1) pulse sequence is theoretically capable of perfectly cancelling the resulting phase error. The sequence is used on a 43Ca+ magnetic-field-sensitive hyperfine qubit, with 20 pulses increasing the coherence time by a factor of 75 compared to an experiment without any spin-echo. In our ambient noise environment the well-known Carr-Purcell-Meiboom-Gill dynamic-decoupling method was found to be comparably effective.

Jan 1, 20098 citations

\textit{ab initio}

computation. We evaluate the impact of relaxation and potential experimental imperfections in the calculated fidelities, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-spin-qubit systems in quantum algorithms, and will serve as a help to design robust spin qubits against decoherence and to perform better-characterized experiments.