Closing the loop: standardization is the key

Steane, Edwin A.; Steane, Susan M.

doi:10.1046/j.1537-2995.1996.36396182134.x

Cited by 15 publications

(28 citation statements)

References 7 publications

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“…Note that I am not requiring that the basis for errors be the X, Y , Z basis I have used in the rest of the paper. 3 Suppose there are l different degeneracy conditions describing the code. Each one equates two one-qubit errors, so at most 2l qubits are affected by the degenerate errors.…”

Section: The Codesmentioning

confidence: 99%

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Class of quantum error-correcting codes saturating the quantum Hamming bound

1996

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Section: The Codesmentioning

confidence: 99%

“…Calderbank and Shor [2] and Steane [3] demonstrated a method of converting certain classical error-correcting codes into quantum ones, and Laflamme et al [4] and Bennett et al [5] produced codes to correct one error that encode 1 qubit in 5 qubits.…”

Section: Introductionmentioning

confidence: 99%

Class of quantum error-correcting codes saturating the quantum Hamming bound

1996

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“…The quantum error correction codes [2,3] which make this possible are analogous to classical codes for binary memoryless channels. Corresponding codes for classical linear codes and Reed-Muller codes have been found [4,5].…”

Section: Introductionmentioning

confidence: 99%

Bosonic quantum codes for amplitude damping

1997

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Traditional quantum error correction involves the redundant encoding of k quantum bits using n quantum bits to allow the detection and correction of any t bit error. The smallest general t = 1 code requires n = 5 for k = 1. However, the dominant error process in a physical system is often well known, thus inviting the question: given a specific error model, can more efficient codes be devised? We demonstrate new codes which correct just amplitude damping errors which allow, for example, a t = 1, k = 1 code using effectively n = 4.6. Our scheme is based on using bosonic states of photons in a finite number of optical modes. We present necessary and sufficient conditions for the codes, and describe construction algorithms, physical implementation, and performance bounds.

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“…(12,14) by integrating the Ermakov equation and the phase equation, and finally compute the transferred energy at different times using Eqs. (19,20).…”

Section: Green's Function and General Solutionmentioning

confidence: 99%

“…A detailed scheme of how a viable architechture of an ion trap processor could look has been recently studied by Steane [20], fully incorporating quantum error correcting codes. The physical gate rate of this proposed 300 qubit processor unit was found to be limited by…”

Section: Introductionmentioning

confidence: 99%

Transport Dynamics of Single Ions in Segmented Microstructured Paul Trap Arrays

Reichle

Leibfried

Blakestad

et al. 2007

Elements of Quantum Information

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It was recently proposed to use small groups of trapped ions as qubit carriers in miniaturized electrode arrays that comprise a large number of individual trapping zones, between which ions could be moved [1,2]. This approach might be scalable for quantum information processing with a large numbers of qubits. Processing of quantum information is achieved by transporting ions to and from separate memory and qubit manipulation zones in between quantum logic operations. The transport of ion groups in this scheme plays a major role and requires precise experimental control and fast transport. In this paper we introduce a theoretical framework to study ion transport in external potentials that might be created by typical miniaturized Paul trap electrode arrays. In particular we discuss the relationship between classical and quantum descriptions of the transport and study the energy transfer to the oscillatory motion during near-adiabatic transport. Based on our findings we suggest a numerical method to find electrode potentials as a function of time to optimize the local potential an ion experiences during transport. We demonstrate this method for one specific electrode geometry that should closely represent the situation encountered in realistic trap arrays.

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Closing the loop: standardization is the key

Cited by 15 publications

References 7 publications

Class of quantum error-correcting codes saturating the quantum Hamming bound

Class of quantum error-correcting codes saturating the quantum Hamming bound

Bosonic quantum codes for amplitude damping

Transport Dynamics of Single Ions in Segmented Microstructured Paul Trap Arrays

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