arXiv:1802.00958 · Physical Review A

Arbitrarily accurate twin composite π -pulse sequences

Boyan T. Torosov, Nikolay V. Vitanov

Published Apr 9, 2018• 20 citations

Abstract

We present three classes of symmetric broadband composite pulse sequences. The composite phases are given by analytic formulas (rational fractions of $\ensuremath{\pi}$) valid for any number of constituent pulses. The transition probability is expressed by simple analytic formulas and the order of pulse area error compensation grows linearly with the number of pulses. Therefore, any desired compensation order can be produced by an appropriate composite sequence; in this sense, they are arbitrarily accurate. These composite pulses perform equally well as or better than previously published ones. Moreover, the current sequences are more flexible as they allow total pulse areas of arbitrary integer multiples of $\ensuremath{\pi}$.

DOI: 10.1103/physreva.97.043408

Related papers

Arbitrarily accurate narrowband composite pulse sequences

Nikolay V. Vitanov

Physical Review ADec 14, 201135 citations

Arbitrarily accurate variable rotations on the Bloch sphere by composite pulse sequences

Boyan T. Torosov, Nikolay V. Vitanov

arXiv:1810.03833Physical Review AJan 3, 201933 citations

Composite pulses with errant phases

Boyan T. Torosov, Nikolay V. Vitanov

arXiv:1904.13168Physical Review AAug 12, 201921 citations

Smooth composite pulses for high-fidelity quantum information processing

Boyan T. Torosov, Nikolay V. Vitanov

Physical Review AMay 23, 2011125 citations

Efficient composite pulse sequences for arbitrarily accurate z-axis rotation gates

Li Zhang, Shihao Zhang

arXiv:1910.00923Oct 2, 20190 citations

Arbitrarily accurate passband composite pulses for dynamical suppression of amplitude noise

Elica S. Kyoseva, Nikolay V. Vitanov

arXiv:1310.7145Physical Review ADec 20, 201330 citations

arXiv:1802.00958 · Physical Review A

Arbitrarily accurate twin composite π -pulse sequences

Boyan T. Torosov, Nikolay V. Vitanov

Published Apr 9, 2018• 20 citations

arXiv HTML PDF

Abstract

We present three classes of symmetric broadband composite pulse sequences. The composite phases are given by analytic formulas (rational fractions of

\ensuremath{\pi}

) valid for any number of constituent pulses. The transition probability is expressed by simple analytic formulas and the order of pulse area error compensation grows linearly with the number of pulses. Therefore, any desired compensation order can be produced by an appropriate composite sequence; in this sense, they are arbitrarily accurate. These composite pulses perform equally well as or better than previously published ones. Moreover, the current sequences are more flexible as they allow total pulse areas of arbitrary integer multiples of

\ensuremath{\pi}

DOI: 10.1103/physreva.97.043408

Related papers

Arbitrarily accurate narrowband composite pulse sequences

Nikolay V. Vitanov

Narrowband composite pulse sequences containing an arbitrary number $N$ of identical pulses are presented. The composite phases are given by a very simple analytic formula and the transition probability is merely ${\mathrm{sin}}^{2N}(A/2)$ , where $A$ is the pulse area. These narrowband sequences can be made accurate to any order with respect to variations in $A$ for sufficiently many constituent pulses, i.e., excitation can be suppressed below any desired value for any pulse area but $\ensuremath{\pi}$.Narrowband composite pulse sequences containing an arbitrary number $N$ of identical pulses are presented. The composite phases are given by a very simple analytic formula and the transition probability is merely ${\mathrm{sin}}^{2N}(A/2)$, where $A$ is the pulse area. These narrowband sequences can be made accurate to any order with respect to variations in $A$ for sufficiently many constituent pulses, i.e., excitation can be suppressed below any desired value for any pulse area but $\ensuremath{\pi}$.

Physical Review ADec 14, 201135 citations

Arbitrarily accurate variable rotations on the Bloch sphere by composite pulse sequences

Boyan T. Torosov, Nikolay V. Vitanov

Composite pulse sequences, which produce arbitrary predefined rotations of a two-state system at an angle $\ensuremath{\theta}$ on the Bloch sphere, are presented. The composite sequences can contain arbitrarily many pulses and can compensate experimental errors in the pulse amplitude and duration to any desired order. A special attention is devoted to two classes of $\ensuremath{\pi}/2$ sequences---symmetric and asymmetric---the phases of which are given by simple formulas in terms of rational multiples of $\ensuremath{\pi}$ for any number of constituent pulses. This allows one to construct arbitrarily accurate $\ensuremath{\pi}/2$ composite rotations. These $\ensuremath{\pi}/2$ composite sequences are used to construct three classes of arbitrarily long composite $\ensuremath{\theta}$ sequences by pairing two $\ensuremath{\pi}/2$ composite sequences, one of which is shifted by a phase $\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta}$ with respect to the other one.Composite pulse sequences, which produce arbitrary predefined rotations of a two-state system at an angle $\ensuremath{\theta}$ on the Bloch sphere, are presented. The composite sequences can contain arbitrarily many pulses and can compensate experimental errors in the pulse amplitude and duration to any desired order. A special attention is devoted to two classes of $\ensuremath{\pi}/2$ sequences---symmetric and asymmetric---the phases of which are given by simple formulas in terms of rational multiples of $\ensuremath{\pi}$ for any number of constituent pulses. This allows one to construct arbitrarily accurate $\ensuremath{\pi}/2$ composite rotations. These $\ensuremath{\pi}/2$ composite sequences are used to construct three classes of arbitrarily long composite $\ensuremath{\theta}$ sequences by pairing two $\ensuremath{\pi}/2$ composite sequences, one of which is shifted by a phase $\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta}$ with respect to the other one.

arXiv:1810.03833Physical Review AJan 3, 201933 citations

Composite pulses with errant phases

Boyan T. Torosov, Nikolay V. Vitanov

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.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.

arXiv:1904.13168Physical Review AAug 12, 201921 citations

Smooth composite pulses for high-fidelity quantum information processing

Boyan T. Torosov, Nikolay V. Vitanov

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.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.

Physical Review AMay 23, 2011125 citations

Efficient composite pulse sequences for arbitrarily accurate z-axis rotation gates

Li Zhang, Shihao Zhang

We propose various composite $π$ -pulse sequences for implementing robust z-axis rotation gates widely used in quantum information processing (QIP) scenarios, and discuss their error tolerance of the pulse strength error (PSE) and off-resonance error (ORE), i.e., two typical systematic errors in NMR systems. Compared to existing composite gates, our designed composite pulses exhibit higher gate fidelity and shorter sequence time cost. Furthermore, such short pulse sequences are generalized by simple analytic formulas which can suppress these errors to any desired order simultaneously with linear length scaling, indicating an efficient construction of them with arbitrary accuracy.We propose various composite $π$-pulse sequences for implementing robust z-axis rotation gates widely used in quantum information processing (QIP) scenarios, and discuss their error tolerance of the pulse strength error (PSE) and off-resonance error (ORE), i.e., two typical systematic errors in NMR systems. Compared to existing composite gates, our designed composite pulses exhibit higher gate fidelity and shorter sequence time cost. Furthermore, such short pulse sequences are generalized by simple analytic formulas which can suppress these errors to any desired order simultaneously with linear length scaling, indicating an efficient construction of them with arbitrary accuracy.

arXiv:1910.00923Oct 2, 20190 citations

Arbitrarily accurate passband composite pulses for dynamical suppression of amplitude noise

Elica S. Kyoseva, Nikolay V. Vitanov

We introduce high-fidelity passband (PB) composite pulse sequences constructed by concatenation of recently derived arbitrarily large and arbitrarily accurate broadband $\mathcal{B}$ and narrowband $\mathcal{N}$ composite sequences. Our PB sequences allow us to produce flexible and tunable nearly rectangular two-state inversion profiles as a function of the individual pulse area because the width and the rectangularity of these profiles can be adjusted at will. Moreover, these PB sequences suppress excitation around pulse area 0 and $2\ensuremath{\pi}$, and suppress deviations from complete population inversion around pulse area $\ensuremath{\pi}$ to arbitrarily high orders. These features make them a valuable tool for high-fidelity qubit operations in the presence of relatively strong amplitude noise. We construct two types of PB pulses: $\mathcal{N}(\mathcal{B})$ , in which a broadband pulse is nested into a narrowband pulse, and $\mathcal{B}(\mathcal{N})$ , in which a narrowband pulse is nested into a broadband pulse; the latter sequences deliver narrower profiles. We derive exact analytic formulas for the composite phases of the PB pulses and exact analytic formulas for the inversion profiles. These formulas allow an easy estimation of the experimental resources needed for any desired qubit inversion profile.We introduce high-fidelity passband (PB) composite pulse sequences constructed by concatenation of recently derived arbitrarily large and arbitrarily accurate broadband $\mathcal{B}$ and narrowband $\mathcal{N}$ composite sequences. Our PB sequences allow us to produce flexible and tunable nearly rectangular two-state inversion profiles as a function of the individual pulse area because the width and the rectangularity of these profiles can be adjusted at will. Moreover, these PB sequences suppress excitation around pulse area 0 and $2\ensuremath{\pi}$, and suppress deviations from complete population inversion around pulse area $\ensuremath{\pi}$ to arbitrarily high orders. These features make them a valuable tool for high-fidelity qubit operations in the presence of relatively strong amplitude noise. We construct two types of PB pulses: $\mathcal{N}(\mathcal{B})$, in which a broadband pulse is nested into a narrowband pulse, and $\mathcal{B}(\mathcal{N})$, in which a narrowband pulse is nested into a broadband pulse; the latter sequences deliver narrower profiles. We derive exact analytic formulas for the composite phases of the PB pulses and exact analytic formulas for the inversion profiles. These formulas allow an easy estimation of the experimental resources needed for any desired qubit inversion profile.

arXiv:1310.7145Physical Review ADec 20, 201330 citations

We present three classes of symmetric broadband composite pulse sequences. The composite phases are given by analytic formulas (rational fractions of

\ensuremath{\pi}

\ensuremath{\pi}

Narrowband composite pulse sequences containing an arbitrary number

N

of identical pulses are presented. The composite phases are given by a very simple analytic formula and the transition probability is merely

{\mathrm{sin}}^{2N}(A/2)

, where

A

is the pulse area. These narrowband sequences can be made accurate to any order with respect to variations in

A

for sufficiently many constituent pulses, i.e., excitation can be suppressed below any desired value for any pulse area but $\ensuremath{\pi}$.

We propose various composite

π

-pulse sequences for implementing robust z-axis rotation gates widely used in quantum information processing (QIP) scenarios, and discuss their error tolerance of the pulse strength error (PSE) and off-resonance error (ORE), i.e., two typical systematic errors in NMR systems. Compared to existing composite gates, our designed composite pulses exhibit higher gate fidelity and shorter sequence time cost. Furthermore, such short pulse sequences are generalized by simple analytic formulas which can suppress these errors to any desired order simultaneously with linear length scaling, indicating an efficient construction of them with arbitrary accuracy.

We introduce high-fidelity passband (PB) composite pulse sequences constructed by concatenation of recently derived arbitrarily large and arbitrarily accurate broadband

\mathcal{B}

and narrowband

\mathcal{N}

composite sequences. Our PB sequences allow us to produce flexible and tunable nearly rectangular two-state inversion profiles as a function of the individual pulse area because the width and the rectangularity of these profiles can be adjusted at will. Moreover, these PB sequences suppress excitation around pulse area 0 and $2\ensuremath{\pi}$, and suppress deviations from complete population inversion around pulse area $\ensuremath{\pi}$ to arbitrarily high orders. These features make them a valuable tool for high-fidelity qubit operations in the presence of relatively strong amplitude noise. We construct two types of PB pulses:

\mathcal{N}(\mathcal{B})

, in which a broadband pulse is nested into a narrowband pulse, and

\mathcal{B}(\mathcal{N})

, in which a narrowband pulse is nested into a broadband pulse; the latter sequences deliver narrower profiles. We derive exact analytic formulas for the composite phases of the PB pulses and exact analytic formulas for the inversion profiles. These formulas allow an easy estimation of the experimental resources needed for any desired qubit inversion profile.