arXiv:0805.0970

Coherent Quantum Control to Arbitrary Accuracy using the Uhrig Sequence of Ideal or Finite-Width $π$-Pulses

John Cardy, Deepak Dhar

Published May 7, 2008• 0 citations

arXiv HTML PDF

Abstract

This paper has been withdrawn by the authors owing to a mistake in the proof of the basic lemma.

DOI: 10.48550/arxiv.0805.0970

Related papers

Coherent control of infinite-dimensional quantum systems

Chitra Rangan

Bulletin of the American Physical SocietyJun 6, 20070 citations

Quadratic dynamical decoupling: Universality proof and error analysis

Wan-Jung Kuo, Daniel A. Lidar

arXiv:1106.2151Physical Review AOct 17, 201142 citations

Error Exponents in Quantum Hypothesis Testing

Masahito Hayashi

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

arXiv:quant-ph/0607009Jul 3, 20060 citations

Coherent Quantum H∞ Control via a Strict Bounded Real Quantum Controller*

Hendra G. Harrie, Ian R. Petersen

IFAC Proceedings VolumesJan 1, 20110 citations

Coherent control of N-level quantum systems with shaped electromagnetic pulses

Ryan Murray, Chitra Rangan

APSOct 1, 20040 citations

Gallager Bound of Classical-Quantum Channel Coding

Masahito Hayashi

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

arXiv:quant-ph/0607010Jul 3, 20060 citations

arXiv:0805.0970

Coherent Quantum Control to Arbitrary Accuracy using the Uhrig Sequence of Ideal or Finite-Width $π$ -PulsesCoherent Quantum Control to Arbitrary Accuracy using the Uhrig Sequence of Ideal or Finite-Width $π$-Pulses

John Cardy, Deepak Dhar

Published May 7, 2008• 0 citations

arXiv HTML PDF

Abstract

This paper has been withdrawn by the authors owing to a mistake in the proof of the basic lemma.

DOI: 10.48550/arxiv.0805.0970

Related papers

Coherent control of infinite-dimensional quantum systems

Chitra Rangan

Bulletin of the American Physical SocietyJun 6, 20070 citations

Quadratic dynamical decoupling: Universality proof and error analysis

Wan-Jung Kuo, Daniel A. Lidar

We prove the universality of the generalized QDD ${}_{{N}_{1}{N}_{2}}$ (quadratic dynamical decoupling) pulse sequence for near-optimal suppression of general single-qubit decoherence. Earlier work showed numerically that this dynamical decoupling sequence, which consists of an inner Uhrig DD (UDD) and outer UDD sequence using ${N}_{1}$ and ${N}_{2}$ pulses, respectively, can eliminate decoherence to $O({T}^{N})$ using $O({N}^{2})$ unequally spaced ``ideal'' (zero-width) pulses, where $T$ is the total evolution time and $N={N}_{1}={N}_{2}$ . A proof of the universality of QDD has been given for even ${N}_{1}$ . Here we give a general universality proof of QDD for arbitrary ${N}_{1}$ and ${N}_{2}$ . As in earlier proofs, our result holds for arbitrary bounded environments. Furthermore, we explore the single-axis (polarization) error suppression abilities of the inner and outer UDD sequences. We analyze both the single-axis QDD performance and how the overall performance of QDD depends on the single-axis errors. We identify various performance effects related to the parities and relative magnitudes of ${N}_{1}$ and ${N}_{2}$ . We prove that using QDD ${}_{{N}_{1}{N}_{2}}$ decoherence can always be eliminated to $O({T}^{\mathrm{min}{{N}_{1},{N}_{2}}})$ .We prove the universality of the generalized QDD${}_{{N}_{1}{N}_{2}}$ (quadratic dynamical decoupling) pulse sequence for near-optimal suppression of general single-qubit decoherence. Earlier work showed numerically that this dynamical decoupling sequence, which consists of an inner Uhrig DD (UDD) and outer UDD sequence using ${N}_{1}$ and ${N}_{2}$ pulses, respectively, can eliminate decoherence to $O({T}^{N})$ using $O({N}^{2})$ unequally spaced ``ideal'' (zero-width) pulses, where $T$ is the total evolution time and $N={N}_{1}={N}_{2}$. A proof of the universality of QDD has been given for even ${N}_{1}$. Here we give a general universality proof of QDD for arbitrary ${N}_{1}$ and ${N}_{2}$. As in earlier proofs, our result holds for arbitrary bounded environments. Furthermore, we explore the single-axis (polarization) error suppression abilities of the inner and outer UDD sequences. We analyze both the single-axis QDD performance and how the overall performance of QDD depends on the single-axis errors. We identify various performance effects related to the parities and relative magnitudes of ${N}_{1}$ and ${N}_{2}$. We prove that using QDD${}_{{N}_{1}{N}_{2}}$ decoherence can always be eliminated to $O({T}^{\mathrm{min}{{N}_{1},{N}_{2}}})$.

arXiv:1106.2151Physical Review AOct 17, 201142 citations

Error Exponents in Quantum Hypothesis Testing

Masahito Hayashi

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

arXiv:quant-ph/0607009Jul 3, 20060 citations

Coherent Quantum H∞ Control via a Strict Bounded Real Quantum Controller*

Hendra G. Harrie, Ian R. Petersen

IFAC Proceedings VolumesJan 1, 20110 citations

Coherent control of N-level quantum systems with shaped electromagnetic pulses

Ryan Murray, Chitra Rangan

APSOct 1, 20040 citations

Gallager Bound of Classical-Quantum Channel Coding

Masahito Hayashi

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

arXiv:quant-ph/0607010Jul 3, 20060 citations

Coherent Quantum Control to Arbitrary Accuracy using the Uhrig Sequence of Ideal or Finite-Width

π

-Pulses

We prove the universality of the generalized QDD

{}_{{N}_{1}{N}_{2}}

(quadratic dynamical decoupling) pulse sequence for near-optimal suppression of general single-qubit decoherence. Earlier work showed numerically that this dynamical decoupling sequence, which consists of an inner Uhrig DD (UDD) and outer UDD sequence using

{N}_{1}

and

{N}_{2}

pulses, respectively, can eliminate decoherence to

O({T}^{N})

using

O({N}^{2})

unequally spaced ``ideal'' (zero-width) pulses, where

T

is the total evolution time and

N={N}_{1}={N}_{2}

. A proof of the universality of QDD has been given for even

{N}_{1}

. Here we give a general universality proof of QDD for arbitrary

{N}_{1}

and

{N}_{2}

. As in earlier proofs, our result holds for arbitrary bounded environments. Furthermore, we explore the single-axis (polarization) error suppression abilities of the inner and outer UDD sequences. We analyze both the single-axis QDD performance and how the overall performance of QDD depends on the single-axis errors. We identify various performance effects related to the parities and relative magnitudes of

{N}_{1}

and

{N}_{2}

. We prove that using QDD

{}_{{N}_{1}{N}_{2}}

decoherence can always be eliminated to

O({T}^{\mathrm{min}{{N}_{1},{N}_{2}}})