Quantum Errors
#Quantum30 Cohort 04
Day 17
Date: 3rd April, 2024.
Let’s discuss the details of QEC, examining the common source of errors in quantum information processing and what they imply for computing.
We will focus on several important sources of errors and how they influence two trivial, single Qubit quantum algorithms.
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The first algorithm is a computation consisting of a
single qubit, initialized in the |0⟩ state undergoing N
identity operations. If this algorithm is performed perfectly the final state is,
Measurement of the
qubit in the |0⟩, |1⟩ basis will consequently yield the result
0 with a probability of unity.
The second illustration is an algorithm of three gates,
This algorithm will ideally yield a result |0⟩ with probability of 1 when measured in the |0⟩, |1⟩ basis. This
algorithm implements two H ≡ Hadamard operations
separated by a wait stage, represented by the Identity
gate.
We examine, independently, several common sources
of error from the effect they have on these two quantum algorithms.
While quantum errors are complicated physical effects, in QIP the relevant measure is the theoretical
success probability of a given quantum algorithm.
Errors that exist on any quantum system are highly
dependent on the specific physical mechanisms that govern the system. The situations that follow are only basic
illustrative examples which can often arise in discussions
related to errors and QEC. It is important to stress that
the types of errors and the way in which they are analyzed needs to be considered in the context of the physical
system under consideration.
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