Propagation of generalized Pauli errors in qudit Clifford circuits

Miller, Daniel; Holz, Timo; Kampermann, Hermann; Bruß, Dagmar

doi:10.1103/physreva.98.052316

Cited by 21 publications

(29 citation statements)

References 44 publications

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“…Finally, the simulator applies an idle error to every qudit. This noise simulation methodology is consistent with previous simulation techniques which have accounted for either gate errors [42] or idle errors [43]. To simulate with noise, we first apply the ideal gates, followed by a gate error noise channel on each affected qudit.…”

Section: Noise Simulationmentioning

confidence: 82%

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Asymptotic improvements to quantum circuits via qutrits

Gokhale

Baker

Duckering

et al. 2019

Proceedings of the 46th International Symposium on Computer Architecture

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Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qutrits. Past work with qutrits has demonstrated only constant factor improvements, owing to the log 2 (3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic depth (runtime) decomposition of the Generalized Toffoli gate using no ancilla-a significant improvement over linear depth for the best qubit-only equivalent. Our circuit construction also features a 70x improvement in two-qudit gate count over the qubit-only equivalent decomposition. This results in circuit cost reductions for important algorithms like quantum neurons and Grover search. We develop an open-source circuit simulator for qutrits, along with realistic near-term noise models which account for the cost of operating qutrits. Simulation results for these noise models indicate over 90% mean reliability (fidelity) for our circuit construction, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path towards scaling quantum computation. CCS CONCEPTS• Computer systems organization → Quantum computing. KEYWORDS quantum computing, quantum information, qutrits ACM Reference Format:

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Section: Noise Simulationmentioning

confidence: 82%

“…We now use the generalized Pauli matrices: The Cartesian product of {I, X +1 , X 2 +1 } and {I, Z 3 , Z 2 3 } constitutes a basis for all 3x3 matrices. Hence, this Cartesian product also constitutes the Kraus operators for the single-qutrit gate error [42,65,66]:…”

Section: A1 Generic Noise Modelmentioning

confidence: 99%

Asymptotic improvements to quantum circuits via qutrits

Gokhale

Baker

Duckering

et al. 2019

Proceedings of the 46th International Symposium on Computer Architecture

View full text Add to dashboard Cite

show abstract

“…is an example of a generalized Pauli-error channel where the trivial error X 0 Z 0 = 1 occurs with probability p 0,0 = 1−f +f /D 2 and any other error occurs with probability f /D 2 [33].…”

Section: Abstract Description Of Quditsmentioning

confidence: 99%

“…The controlled-Z gate, Fock [33,[37][38][39]. Alice produces the two-qudit state |Φ = cz |+ ⊗2 , stores one qudit into a quantum memory (QM), and sends the other qudit to the first intermediate repeater station.…”

Section: Abstract Description Of Quditsmentioning

confidence: 99%

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Parameter regimes for surpassing the PLOB bound with error-corrected qudit repeaters

Miller

Holz

Kampermann

et al. 2019

Quantum

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A potential quantum internet would open up the possibility of realizing numerous new applications, including provably secure communication. Since losses of photons limit long-distance, direct quantum communication and widespread quantum networks, quantum repeaters are needed. The so-called PLOBrepeaterless bound [Pirandola et al., Nat. Commun. 8, 15043 (2017)] is a fundamental limit on the quantum capacity of direct quantum communication.Here, we analytically derive the quantum-repeater gain for error-corrected, one-way quantum repeaters based on higher-dimensional qudits for two different physical encodings: Fock and multimode qudits. We identify parameter regimes in which such quantum repeaters can surpass the PLOB-repeaterless bound and systematically analyze how typical parameters manifest themselves in the quantum-repeater gain. This benchmarking provides a guideline for the implementation of error-corrected qudit repeaters.Daniel Miller: daniel.miller@hhu.de arXiv:1906.05172v1 [quant-ph]

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High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges

et al. 2019

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In recent years, there has been a rising interest in high‐dimensional quantum states and their impact on quantum communication. Indeed, the availability of an enlarged Hilbert space offers multiple advantages, from larger information capacity and increased noise resilience, to novel fundamental research possibilities in quantum physics. Multiple photonic degrees of freedom have been explored to generate high‐dimensional quantum states, both with bulk optics and integrated photonics. Furthermore, these quantum states have been propagated through various channels, for example, free‐space links, single‐mode, multicore, and multimode fibers, and also aquatic channels, experimentally demonstrating the theoretical advantages over 2D systems. Here, the state‐of‐the‐art on the generation, propagation, and detection of high‐dimensional quantum states is reviewed. Quantum communication with states living in d‐dimensional Hilbert spaces, qudits, yields great benefits. However, qudits generation, transmission, and detection is not a simple task to accomplish. This review presents the state‐of‐the‐art on the generation, propagation, and measurement of high‐dimensional quantum states, highlighting their advantages, issues, and future perspectives.

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Propagation of generalized Pauli errors in qudit Clifford circuits

Cited by 21 publications

References 44 publications

Asymptotic improvements to quantum circuits via qutrits

Asymptotic improvements to quantum circuits via qutrits

Parameter regimes for surpassing the PLOB bound with error-corrected qudit repeaters

High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges

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