Haidong Yuan

Elliptic functions and efficient control of Ising spin chains with unequal couplings

In this article, we study optimal control of dynamics of a linear chain of three spin

Time-optimal synthesis of unitary transformations in a coupled fast and slow qubit system

1∕2

Optimal feedback scheme and universal time scaling for Hamiltonian parameter estimation.

, weakly coupled with unequal Ising couplings. We address the problem of time-optimal synthesis of multiple spin quantum coherences. We derive time-optimal pulse sequences for creating desired spin order by computing geodesics on a sphere under a special metric. The solution to the geodesic equation is related to the nonlinear oscillator equation and the minimum time to create multiple spin order can be expressed in terms of an elliptic integral. These techniques are used for efficient creation of multiple spin coherences in Ising spin chains with unequal couplings.

Geodesics for Efficient Creation and Propagation of Order along Ising Spin Chains

In this paper, we study time-optimal control problems related to a system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case where unitary transformations produced by evolutions of the coupling take a much longer time as compared to the time required to produce unitary transformations on the first qubit, but a much shorter time as compared to the time to produce unitary transformations on the second qubit. We present a canonical decomposition of SU4 in terms of the subgroup SU2 SU2 U1, which is natural in understanding the time-optimal control problem of such a coupled qubit system with significantly different time scales. A typical setting involves dynamics of a coupled electron-nuclear spin system in pulsed electron paramagnetic resonance experiments at high fields. Using the proposed canonical decomposition, we give time-optimal control algorithms to synthesize various unitary transformations of interest in coherent spectroscopy and quantum-information processing.

Time-optimal excitation of maximum quantum coherence: Physical limits and pulse sequences

Time is a valuable resource and it is expected that a longer time period should lead to better precision in Hamiltonian parameter estimation. However, recent studies in quantum metrology have shown that in certain cases more time may even lead to worse estimations, which puts this intuition into question. In this Letter we show that by including feedback controls this intuition can be restored. By deriving asymptotically optimal feedback controls we quantify the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit under the optimal feedback scheme. Our study reveals an intriguing connection between noncommutativity in the dynamics and the gain of feedback controls in Hamiltonian parameter estimation.

Multiple-spin coherence transfer in linear Ising spin chains and beyond: numerically-optimized pulses and experiments

Experiments in coherent nuclear and electron magnetic resonance, and optical 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 decoherence and to optimize the sensitivity of the experiments. Here we give efficient syntheses of various unitary transformations on Ising spin chains of arbitrary length. The efficient realization of the unitary transformations presented here is obtained by computing geodesics on a sphere under a special metric. We show that contrary to the conventional belief, it is possible to propagate a spin order along an Ising spin chain with coupling strength J (in units of Hz), significantly faster than (2J){sup -1} per step. The methods presented here are expected to be useful for immediate and future applications involving control of spin dynamics in coherent spectroscopy and quantum information processing.

Time-optimal generation of cluster states

Here we study the optimum efficiency of the excitation of maximum quantum (MaxQ) coherence using analytical and numerical methods based on optimal control theory. The theoretical limit of the achievable MaxQ amplitude and the minimum time to achieve this limit are explored for a set of model systems consisting of up to five coupled spins. In addition to arbitrary pulse shapes, two simple pulse sequence families of practical interest are considered in the optimizations. Compared to conventional approaches, substantial gains were found both in terms of the achieved MaxQ amplitude and in pulse sequence durations. For a model system, theoretically predicted gains of a factor of three compared to the conventional pulse sequence were experimentally demonstrated. Motivated by the numerical results, also two novel analytical transfer schemes were found: Compared to conventional approaches based on non-selective pulses and delays, double-quantum coherence in two-spin systems can be created twice as fast using isotropic mixing and hard spin-selective pulses. Also it is proved that in a chain of three weakly coupled spins with the same coupling constants, triple-quantum coherence can be created in a time-optimal fashion using so-called geodesic pulses.

Controllability of the coupled spin- 1 2 harmonic oscillator system

We study multiple-spin coherence transfers in linear Ising spin chains with nearest neighbor couplings. These constitute a model for efficient information transfers in future quantum computing devices and for many multi-dimensional experiments for the assignment of complex spectra in nuclear magnetic resonance spectroscopy. We complement prior analytic techniques for multiple-spin coherence transfers with a systematic numerical study where we obtain strong evidence that a certain analytically-motivated family of restricted controls is sufficient for time-optimality. In the case of a linear three-spin system, additional evidence suggests that prior analytic pulse sequences using this family of restricted controls are time-optimal even for arbitrary local controls. In addition, we compare the pulse sequences for linear Ising spin chains to pulse sequences for more realistic spin systems with additional long-range couplings between non-adjacent spins. We experimentally implement the derived pulse sequences in three and four spin systems and demonstrate that they are applicable in realistic settings under relaxation and experimental imperfections—in particular—by deriving broadband pulse sequences which are robust with respect to frequency offsets.

Sequential Feedback Scheme Outperforms the Parallel Scheme for Hamiltonian Parameter Estimation

The definition of a cluster state naturally suggests an implementation scheme: find a physical system with an Ising coupling topology identical to that of the target state, and evolve freely for a time of 1/2J. Using the tools of optimal control theory, we address the question of whether or not this implementation is time-optimal. We present some examples where it is not and provide an explanation in terms of geodesics on the Bloch-sphere.

Efficient synthesis of quantum gates on indirectly coupled spins

We present a control-theoretic analysis of a system consisting of a two-level atom coupled with a quantum harmonic oscillator. We show that, by applying external fields with just two resonant frequencies, any desired unitary operator can be generated.