Quantum Error Correction

Ryan-Anderson, Ciarán

doi:10.1142/9789812385253_0007

Cited by 32 publications

(38 citation statements)

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“…Error correction processes are generally assumed to be applied in parallel across the entire machine. Executing gates on the encoded qubits, in some cases, requires additional ancillae, so multiple concurrent logical gates will require growth in physical qubit storage space [20,21]. Thus, both physical and logical concurrency are important; in this paper we consider only logical concurrency.…”

Section: A Modular Exponentiation and Shor's Algorithmmentioning

confidence: 99%

Fast quantum modular exponentiation

2005

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We present a detailed analysis of the impact on quantum modular exponentiation of architectural features and possible concurrent gate execution. Various arithmetic algorithms are evaluated for execution time, potential concurrency, and space tradeoffs. We find that to exponentiate an n-bit number, for storage space 100n (twenty times the minimum 5n), we can execute modular exponentiation two hundred to seven hundred times faster than optimized versions of the basic algorithms, depending on architecture, for n = 128. Addition on a neighboronly architecture is limited to O(n) time while non-neighbor architectures can reach O(log n), demonstrating that physical characteristics of a computing device have an important impact on both real-world running time and asymptotic behavior. Our results will help guide experimental implementations of quantum algorithms and devices.

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Section: A Modular Exponentiation and Shor's Algorithmmentioning

confidence: 99%

Fast quantum modular exponentiation

2005

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“…In our approach to decrease errors we do not use error correcting codes for the following reasons: we want to remove as many errors as we can on the lowest possible level and second, the intrinsic and external errors are not easily handled by error correcting codes (see Ref. [10] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Stability of the Quantum Fourier Transformation on the Ising Quantum Computer

Celardo

Pineda

Žnidarič

2005

Int. J. Quantum Inform.

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We analyze the influence of errors on the implementation of the quantum Fourier transformation (QFT) on the Ising quantum computer (IQC). Two kinds of errors are studied: (i) due to spurious transitions caused by pulses and (ii) due to external perturbation. The scaling of errors with system parameters and number of qubits is explained. We use two different procedures to fight each of them. To suppress spurious transitions we use correcting pulses (generalized 2πk method) while to suppress errors due to external perturbation we use an improved QFT algorithm. As a result, the fidelity of quantum computation is increased by several orders of magnitude and is thus stable in a much wider range of physical parameters.

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“…The duration of such shuttling has to be much faster than the relevant decoherence times [4]. Furthermore, it is desirable to reduce the total time consumption of all relevant operations, where shuttling will contribute a considerable amount [5], and aim for the performance of the naturally fast solid state architectures [6]. So far, ion shuttling in a multiplexed trap has been demonstrated together with additional sympathetic cooling [7], and in the adiabatic regime, where the transient displacement of the ion is smaller than the size of the its wavepacket [8,9].…”

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Controlling Fast Transport of Cold Trapped Ions

et al. 2012

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We realize fast transport of ions in a segmented micro-structured Paul trap. The ion is shuttled over a distance of more than 10 4 times its groundstate wavefunction size during only 5 motional cycles of the trap (280 µm in 3.6 µs). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10±0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing. . Scalable information processing in a multiplexed ion trap can be accomplished by having fixed processing sites where logic operations are performed, and ion qubits will be moved in and out of these regions by shuttling operations. The duration of such shuttling has to be much faster than the relevant decoherence times [4]. Furthermore, it is desirable to reduce the total time consumption of all relevant operations, where shuttling will contribute a considerable amount [5], and aim for the performance of the naturally fast solid state architectures [6]. So far, ion shuttling in a multiplexed trap has been demonstrated together with additional sympathetic cooling [7], and in the adiabatic regime, where the transient displacement of the ion is smaller than the size of the its wavepacket [8,9]. Transport of neutral atoms have also been performed using magnetic [10] or optical [11] techniques.Because quantum gate operations require ions close to the motional ground state and fast transport inherently creates motional excitation, the challenge is to develop transport protocols that guarantee sufficiency small energy transfer. In this work we demonstrate shuttling operations that are highly non-adiabatic while the final state of the ion is close to the motional groundstate. We also show that quantum information stored in both the motional and the spin degree of freedom is preserved through the shuttling.During a shuttling operation, the ion motion in the harmonic trapping potential is excited when the acceleration is sufficiently strong. This motional excitation is a harmonic oscillation, characterized by a well defined phase, thus allowing it to be canceled out by proper management of the forces involved during or after the transport. We experimentally demonstrate two methods of canceling the acquired motional excitation. One method uses two shuttles, where the transport to the destination generates the same net momentum transfer as the transport back, but is applied 180 • out of phase with respect to the secular oscillation of the ion (Fig. 1b). We refer to this as the pairwise energy-neutral transport. For the second scheme, the self-neutral transport we apply a sharp counter-"kick" to the ion at the end of a single transport operation, stopping its motion (Fig. 1c). This case of single-sided transport allows even faster shuttling and can be sequentially repeated since it is ener...

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Quantum Error Correction

Cited by 32 publications

References 0 publications

Fast quantum modular exponentiation

Fast quantum modular exponentiation

Stability of the Quantum Fourier Transformation on the Ising Quantum Computer

Controlling Fast Transport of Cold Trapped Ions

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