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Threshold theorem in isolated quantum dynamics with stochastic control errors.

Manaka Okuyama1, Kentaro Ohki2, Masayuki Ohzeki1,3,4

  • 1Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 4, 2022
PubMed
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Stochastic control errors in quantum dynamics can be managed. A new theorem shows that below a noise threshold, achieving target quantum states requires few measurements, ensuring reliable quantum computation.

Keywords:
adiabatic quantum computationquantum annealingstochastic control errorstochastic differential equationthreshold theorem

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Area of Science:

  • Quantum Physics
  • Quantum Information Science
  • Computational Science

Background:

  • Isolated quantum dynamics are susceptible to control errors.
  • These errors manifest as time-dependent stochastic noise in the Schrödinger equation.
  • Understanding error thresholds is crucial for reliable quantum computation.

Purpose of the Study:

  • To investigate the impact of stochastic control errors on isolated quantum dynamics.
  • To establish a threshold theorem for achieving target quantum states amidst noise.
  • To analyze the relationship between measurement count and noise strength.

Main Methods:

  • Formulating control errors as time-dependent stochastic noise.
  • Developing a threshold theorem for a class of stochastic errors.
  • Analyzing the scaling of measurements with computational time and noise strength.

Main Results:

  • A threshold theorem is established, defining conditions for obtaining target states.
  • If noise strength is below a critical value (inverse of computational time), a constant number of measurements suffices.
  • Exceeding this threshold necessitates an exponential increase in measurements with computational time.

Conclusions:

  • The derived threshold theorem provides a sufficient condition for robust quantum state preparation.
  • The findings are applicable to various isolated quantum dynamics, including quantum annealing and adiabatic quantum computation.
  • This work offers insights into managing noise for scalable and reliable quantum computing.