Quantum error correction using weak measurements

  • Parveen KumarEmail author
  • Apoorva Patel


The standard quantum error correction protocols use projective measurements to extract the error syndromes from the encoded states. We consider the more general scenario of weak measurements, where only partial information about the error syndrome can be extracted from the encoded state. We construct a feedback protocol that probabilistically corrects the error based on the extracted information. Using numerical simulations of one-qubit error correction codes, we show that our error correction succeeds for a range of the weak measurement strength, where (a) the error rate is below the threshold beyond which multiple errors dominate, and (b) the error rate is less than the rate at which weak measurement extracts information. We observe that error correction based on projective measurements is always superior to that based on weak measurements; so the latter is worthwhile only if the former is unavailable due to some reason, and error correction with too small a measurement strength should be avoided.


Projective measurement Weak measurement Quantum error correction Quantum trajectory 



PK is supported by a CSIR research fellowship from the Government of India. We are grateful to Rajamani Vijayaraghavan for useful discussions and helpful comments on the earlier draft of this work.


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Authors and Affiliations

  1. 1.Centre for High Energy PhysicsIndian Institute of ScienceBangaloreIndia

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