Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Science

Unitary Control in Quantum Ensembles: Maximizing Signal Intensity in Coherent Spectroscopy

Steffen J. Glaser, Thomas Schulte‐Herbrüggen, Malte Sieveking, Oliver Schedletzky, Niels Chr. Nielsen, Ole W. Sørensen, Christian Griesinger

Published Apr 17, 1998• 207 citations
Publisher

Abstract

Experiments in coherent magnetic resonance, microwave, and optical spectroscopy control quantum-mechanical ensembles by guiding them from initial states toward target states by unitary transformation. Often, the coherences detected as signals are represented by a non-Hermitian operator. Hence, spectroscopic experiments, such as those used in nuclear magnetic resonance, correspond to unitary transformations between operators that in general are not Hermitian. A gradient-based systematic procedure for optimizing these transformations is described that finds the largest projection of a transformed initial operator onto the target operator and, thus, the maximum spectroscopic signal. This method can also be used in applied mathematics and control theory.

DOI
10.1126/science.280.5362.421

Related papers

Optimal control of coupled spins in presence of longitudinal and transverse relaxation

Dionisis Stefanatos, Navin Khaneja, Steffen J. Glaser

Experiments in coherent spectroscopy correspond to control of quantum mechanical ensemble guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transformations should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in nuclear magnetic resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of coherence or polarization transfer between two spins in the presence of relaxation. Furthermore what is the optimal pulse sequence which achieves this efficiency? This manuscript extends our previous work in the above problems. Here, we take into account both the longitudinal and the transverse relaxation mechanisms, thus generalizing our previous results, where the former had been neglected.

IEEE International Workshop on Workload Characterization (WWC)•Apr 23, 2004•6 citations

Spin Solitons and Quantum Control of Spin Chain Dynamics

Navin Khaneja, Steffen J. Glaser

Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we present a radically different and generally applicable approach to efficient control of dynamics in spin chains of arbitrary length. The approach relies on the creation of localized spin waves, ``spin solitons'', and efficient propagation of these soliton states through the spin chain. The methods presented are expected to find immediate applications in control of spin dynamics in coherent spectroscopy and quantum information processing.

arXiv:quant-ph/0202013•Feb 1, 2002•0 citations

Efficient transfer of coherence through Ising spin chains

Navin Khaneja, Steffen J. Glaser

Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we present a novel approach for efficient control of dynamics in spin chains of arbitrary length. The approach relies on creating certain three spin encoded states, which can be efficiently transferred through a spin chain. The methods presented are expected to find applications in control of spin dynamics in coherent spectroscopy and quantum information processing.

Physical Review A•Dec 12, 2002•56 citations

Time optimal control in spin systems

Navin Khaneja, Roger W. Brockett, Steffen J. Glaser

In this paper, we study the design of pulse sequences for nuclear magnetic resonance spectroscopy as a problem of time optimal control of the unitary propagator. Radio-frequency pulses are used in coherent spectroscopy to implement a unitary transfer between states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group. What is the minimum time required to steer the system from some initial point to a specified final point? In nuclear magnetic resonance (NMR) spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two-spin system.

arXiv:quant-ph/0006114•Physical Review A•Feb 14, 2001•741 citations

Quantum control of nuclear magnetic resonance spin systems

Jun Li, Jiangyu Cui, Xiaodong Yang +6 more

With the development of quantum information science, the active manipulation of quantum systems is becoming an important research frontier. To build realistic quantum information processors, one of the challenges is to implement arbitrary desired operations with high precision on quantum systems. A large number of quantum control methods and relevant numerical techniques have been put forward in recent years, such as quantum optimal control and quantum feedback control. Nuclear magnetic resonance (NMR) spin systems offer an excellent testbed to develop benchmark tools and techniques for controlling quantum systems. In this review paper, we briefly introduce some of the basic control ideas developed for NMR systems in recent years. We first explain, for the liquid spin systems, the physics of various couplings and the causes of relaxation effects. These mechanisms govern the system dynamics, and thus are crucial for constructing rigorous and efficient control models. We also identify three types of available control means: 1) raido-frequency fields as coherent controls; 2) phase cycling, gradient fields and relaxation effects as non-unitary controls; 3) radiation damping effect as feedback control mechanism. Then, we elucidate some important control tasks, which may arise from the conventional NMR spectroscopy (e.g., pulse design and polarization transfer) or from quantum information science (e.g., algorithmic cooling and pseudo-pure state preparation). In the last part, we review some of the most important control methods that are applicable to NMR control tasks. For systems with a relatively small number of spins, it is possible to use analytic optimal control theory to realize the target unitary operations. However, for larger systems, numerical methods are necessary. The gradient ascent pulse engineering algorithm and pulse compiler techniques are the most successful techniques for implementing complicated quantum networks currently. There are some interesting topics of utilizing radiation damping and relaxation effects to achieve more powerful controls. Finally, we give an outline of the possible future work.

Acta Physica Sinica•Jan 1, 2015•4 citations

Relaxation Optimized Polarization-Coherence Transfer in Ising Spin Chains

Dionisis Stefanatos, Navin Khaneja, Steffen J. Glaser

Experiments in coherent spectroscopy correspond to control of quantum-mechanical ensembles guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transfers should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in Nuclear Magnetic Resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of polarization or coherence transfer between coupled spins in the presence of relaxation. Furthermore, what is the optimal pulse sequence which achieves this efficiency? This letter is a continuation of our previous work on the above problems. Here, we attempt to answer these questions for an Ising spin chain, under the presence of transverse relaxation. The methods presented in this paper are expected to find applications not only in coherent spectroscopy but also in quantum information processing.

•May 15, 2005•0 citations
Experiments in coherent magnetic resonance, microwave, and optical spectroscopy control quantum-mechanical ensembles by guiding them from initial states toward target states by unitary transformation. Often, the coherences detected as signals are represented by a non-Hermitian operator. Hence, spectroscopic experiments, such as those used in nuclear magnetic resonance, correspond to unitary transformations between operators that in general are not Hermitian. A gradient-based systematic procedure for optimizing these transformations is described that finds the largest projection of a transformed initial operator onto the target operator and, thus, the maximum spectroscopic signal. This method can also be used in applied mathematics and control theory.
Experiments in coherent spectroscopy correspond to control of quantum mechanical ensemble guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transformations should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in nuclear magnetic resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of coherence or polarization transfer between two spins in the presence of relaxation. Furthermore what is the optimal pulse sequence which achieves this efficiency? This manuscript extends our previous work in the above problems. Here, we take into account both the longitudinal and the transverse relaxation mechanisms, thus generalizing our previous results, where the former had been neglected.
Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we present a radically different and generally applicable approach to efficient control of dynamics in spin chains of arbitrary length. The approach relies on the creation of localized spin waves, ``spin solitons'', and efficient propagation of these soliton states through the spin chain. The methods presented are expected to find immediate applications in control of spin dynamics in coherent spectroscopy and quantum information processing.
Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we present a novel approach for efficient control of dynamics in spin chains of arbitrary length. The approach relies on creating certain three spin encoded states, which can be efficiently transferred through a spin chain. The methods presented are expected to find applications in control of spin dynamics in coherent spectroscopy and quantum information processing.
In this paper, we study the design of pulse sequences for nuclear magnetic resonance spectroscopy as a problem of time optimal control of the unitary propagator. Radio-frequency pulses are used in coherent spectroscopy to implement a unitary transfer between states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group. What is the minimum time required to steer the system from some initial point to a specified final point? In nuclear magnetic resonance (NMR) spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two-spin system.
With the development of quantum information science, the active manipulation of quantum systems is becoming an important research frontier. To build realistic quantum information processors, one of the challenges is to implement arbitrary desired operations with high precision on quantum systems. A large number of quantum control methods and relevant numerical techniques have been put forward in recent years, such as quantum optimal control and quantum feedback control. Nuclear magnetic resonance (NMR) spin systems offer an excellent testbed to develop benchmark tools and techniques for controlling quantum systems. In this review paper, we briefly introduce some of the basic control ideas developed for NMR systems in recent years. We first explain, for the liquid spin systems, the physics of various couplings and the causes of relaxation effects. These mechanisms govern the system dynamics, and thus are crucial for constructing rigorous and efficient control models. We also identify three types of available control means: 1) raido-frequency fields as coherent controls; 2) phase cycling, gradient fields and relaxation effects as non-unitary controls; 3) radiation damping effect as feedback control mechanism. Then, we elucidate some important control tasks, which may arise from the conventional NMR spectroscopy (e.g., pulse design and polarization transfer) or from quantum information science (e.g., algorithmic cooling and pseudo-pure state preparation). In the last part, we review some of the most important control methods that are applicable to NMR control tasks. For systems with a relatively small number of spins, it is possible to use analytic optimal control theory to realize the target unitary operations. However, for larger systems, numerical methods are necessary. The gradient ascent pulse engineering algorithm and pulse compiler techniques are the most successful techniques for implementing complicated quantum networks currently. There are some interesting topics of utilizing radiation damping and relaxation effects to achieve more powerful controls. Finally, we give an outline of the possible future work.
Experiments in coherent spectroscopy correspond to control of quantum-mechanical ensembles guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transfers should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in Nuclear Magnetic Resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of polarization or coherence transfer between coupled spins in the presence of relaxation. Furthermore, what is the optimal pulse sequence which achieves this efficiency? This letter is a continuation of our previous work on the above problems. Here, we attempt to answer these questions for an Ising spin chain, under the presence of transverse relaxation. The methods presented in this paper are expected to find applications not only in coherent spectroscopy but also in quantum information processing.