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For questions about different types of noise a quantum computer (or qubits) may experience; how this affects the outcome of the computation; how to reduce a specific type of noise on a specific implementation of quantum computer; or how to simulate noise.

Noise is a general term for unwanted modifications that a signal may suffer during capture, storage, transmission, processing, or conversion. [1]

In the context of Quantum Computing, noise can be a number of different things, although generally either arises as a result of an interaction with an environment, also sometimes referred to as a bath, or as a result of the Heisenberg uncertainty principle.

Representing noise

  • Shot noise: Is Poissonian noise that arises from a process such as tunnelling electrons or fluctuations in the number of photons as a result of the uncertainty principle. Using e.g. squeezed light states can give sub-poissonian statistics (where the variance is less than that of Poissonian statistics with the same mean), often referred to as below the shot noise limit. Similarly, can also have super-Poissonian statistics.

  • Markovian noise: Where the environment is unable to 'remember' what has happened in the past. Often a good approximation. Leads to the Lindblad Master equation, also known as the Lindbladian. Can either be described in a 'coarse grained' manner (useful for simulations) or a more continuous manner.

  • Kraus operators: Described using a quantum channel where (usually) a single operation of the Kraus operators is performed.

  • Non-Markovian noise: A more realistic noise model than Markovian; the assumption that the environment forgets the past is forgotten. As a result, the environment can act not entirely dissimilarly to some form of memory. Can lead to phenomena such as entanglement revival and other effects where noise that arises from Markovian noise is reversed to a certain extent.

Common types of noise on qubits

  • Dephasing: Causes the system to decohere - this gets rid of/reduces the entanglement (i.e. coherence) of the system, necessarily making it more mixed, unless already maximally mixed.

  • Depolarising: Upon measuring, either a bit flip ($\sigma_x$), phase flip ($\sigma_z$), or both bit and phase flip ($\sigma_y$) will have occurred with some probability.

  • Amplitude Damping: Represents the system decaying from one state to a different state, such as when an atom emits a photon. Leads to a simple version of coherence times.

Measuring noise

  • Fidelity: Measures how much two quantum states overlap. Often used to characterise quantum processors by comparing the final output state with the ideal result. Is a number between $0$ and $1$.
  • Other distance measures: Other measures, such as the 1-norm/trace distance also exist, which measure the difference between two states.

One of the biggest challenges currently facing quantum computing is that of reducing (by a myriad of experimental techniques) and mitigating (by quantum error correction) the amount of noise on a system.

References and further reading:

[1] Wikipedia page on Noise (signal processing)

Nielsen, M.A. and Chuang, I.L., 2010. Quantum computation and quantum information. Cambridge university press.

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