Fault-tolerant quantum computation for local non-Markovian noise

By Barbara M. Terhal, G. Burkard. 2004

156 citations recorded by the source corpus.

We derive a threshold result for fault-tolerant quantum computation for local non-Markovian noise models. The role of error amplitude in our analysis is played by the product of the elementary gate time t{sub 0} and the spectral width of the interaction Hamiltonian between system and bath. We discuss extensions of our model and the applicability of our analysis.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/6e240352674099c59a62f21ddc9faab810a7b686

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Daniel Gottesman
2. John Preskill
3. Benjamin J. Brown
4. Chris N. Self
5. Daniel Loss
6. Daniel Alonso
7. Panos Aliferis
8. Jiannis K. Pachos

In Atomic and Molecular Physics, and Optics

1. Daniel Gottesman
2. John Preskill
3. Benjamin J. Brown
4. Daniel Alonso
5. I. D. Vega
6. Daniel Loss
7. Chris N. Self
8. Jiannis K. Pachos

Citations in the corpus

• Quantum computing and the entanglement frontier (2012, background): “44,48,49 If the noise Hamiltonian includes terms that act on k >> 1 qubits in the quantum computer (and in some complicated way on the environment), the proof of scalability works if these terms decay exponentially with k , and also decay rapidly enough as the qubits separate in space.”
• Quantum error correction below the surface code threshold (2024, unknown): “This is an important contributor to the overall reaction time, T react , which is the time it takes the quantum computer’s control system to react to a logical measurement by executing a dependent logical operation [22].”
• An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation (2009, background): “A similar theorem can be proven using more general noise produced by a weak interaction between the computer and a non-Markovian environment [ 3, 52 ].”
• Fault-tolerant quantum computation with constant overhead (2013, background): “The assumption of stochastic noise can largely be relaxed, and a threshold exists for noise caused by fairly general interactions with a non-Markovian environment [3, 35].”
• Quantum accuracy threshold for concatenated distance-3 codes (2005, methodology): “We will also present a proof of the quantum threshold theorem that applies to a local non-Markovian noise model, and which goes beyond the result found in [7] in two useful ways.”
• Quantum memories at finite temperature (2014, background): “In fact it is unknown if the model describing the full thermal evolution is analytically solvable (Terhal and Burkard, 2005).”
• Dynamics of non-Markovian open quantum systems (2015, methodology): “Nevertheless, a threshold analysis for some nonMarkovian error models was performed by Terhal and Burkard (2005).”