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Physical Review A

Optimized control of multistate quantum systems by composite pulse sequences

Genko T. Genov, Boyan T. Torosov, Nikolay V. Vitanov

Published Dec 14, 2011• 45 citations
Publisher

Abstract

We introduce a technique for derivation of high-fidelity composite pulse sequences for two types of multistate quantum systems: systems with the SU(2) and Morris-Shore dynamic symmetries. For the former type, we use the Majorana decomposition to reduce the dynamics to an effective two-state system, which allows us to find the propagator analytically and use the pool of available composite pulses for two-state systems. For the latter type of multistate systems, we use the Morris-Shore decomposition, which reduces the multistate dynamics to a set of two-state systems. We present examples which demonstrate that the multistate composite sequences open a variety of possibilities for coherent control of quantum systems with multiple states.

DOI
10.1103/physreva.84.063413

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We introduce a technique for derivation of high-fidelity composite pulse sequences for two types of multistate quantum systems: systems with the SU(2) and Morris-Shore dynamic symmetries. For the former type, we use the Majorana decomposition to reduce the dynamics to an effective two-state system, which allows us to find the propagator analytically and use the pool of available composite pulses for two-state systems. For the latter type of multistate systems, we use the Morris-Shore decomposition, which reduces the multistate dynamics to a set of two-state systems. We present examples which demonstrate that the multistate composite sequences open a variety of possibilities for coherent control of quantum systems with multiple states.
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Coherent control of two-state systems is traditionally achieved by resonant pulses of specific Rabi frequency and duration, by adiabatic techniques using level crossings or delayed pulses, or by sequences of pulses with precise relative phases (composite pulses). Here we develop a method for high-fidelity coherent control which uses a sequence of detuning pulses. By using the detuning pulse areas as control parameters, and driving on an analogy with composite pulses, we report a great variety of detuning pulse sequences for broadband and narrow-band transition probability profiles.
We present a systematic SU(2) approach for construction of composite sequences of pulses with smooth temporal shapes that produce high-fidelity two-state excitation profiles. This makes possible the application of composite pulses to quantum control and quantum information processing with short and ultrashort laser pulses. We present an exact analytic formula for the composite phases for arbitrarily accurate broadband pulses and examples of narrowband, passband, and fractional-$\ensuremath{\pi}$ pulses as well as composite pulses with detuning compensation.
Composite pulses---sequences of pulses with well-defined relative phases---are an efficient, robust, and flexible technique for coherent control of quantum systems. Composite sequences can compensate for a variety of experimental errors in the driving field (e.g., in the pulse amplitude, duration, detuning, chirp, etc.) or in the quantum system and its environment (e.g., inhomogeneous broadening, stray electric or magnetic fields, unwanted couplings, etc.). The control parameters are the relative phases between the constituent pulses in the composite sequence, an accurate control over which is required in all composite sequences reported hitherto. In this paper, we introduce two types of composite pulse sequences which, in addition to error compensation in the basic experimental parameters, compensate for systematic errors in the composite phases. In the first type of such composite sequences, which compensate for pulse area errors, relative phase errors of over 10% can be tolerated with reasonably short sequences while maintaining the fidelity above the 99.99% quantum computing benchmark. In the second type of composite sequences, which compensate for simultaneous pulse area and detuning errors, relative phase errors of over 5% can be compensated.