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Standard Randomised Benchmarking: Difference between revisions
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[https://arxiv.org/abs/1109.6887v2 Randomized benchmarking] is a | [https://arxiv.org/abs/1109.6887v2 Randomized benchmarking] is a protocol that yields estimates of the computationally relevant errors without relying on accurate quantum state preparation and measurement. This is used to determine the error probability per gate in computational context and also gives an overall [[average fidelity]] for the noise in the gates. | ||
'''Tags:''' [[:Category: Certification protocol|Certification Protocol | '''Tags:''' [[:Category: Certification protocol|Certification Protocol]], [[:Category: Average gate fidelity|Average gate fidelity]], [[Randomised Benchmarking]], Clifford group | ||
==Assumptions== | ==Assumptions== | ||
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* '''Figure of merit''': average error rate, average gate fidelity | * '''Figure of merit''': average error rate, average gate fidelity | ||
* The errors which are considered here are State preparation and measurement errors, error on the final gate, which are gate and time-independent errors. Gate and time-dependent errors can also be taken into consideration. This method is insensitive to SPAM error. | * The errors which are considered here are State preparation and measurement errors, error on the final gate, which are gate and time-independent errors. Gate and time-dependent errors can also be taken into consideration. This method is insensitive to SPAM error. | ||
* The random gates are picked from the Clifford group. | * The random gates are picked from the Clifford group. | ||
* For noise estimation, the uniform probability distribution over Clifford group comprises a [[unitary 2-design]]. | * For noise estimation, the uniform probability distribution over Clifford group comprises a [[unitary 2-design]]. | ||
* This protocol provides a scalable method for benchmarking the set of Clifford gates. | * This protocol provides a scalable method for benchmarking the set of Clifford gates. | ||
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* The case where Randomized benchmarking fails: Suppose the noise is time dependent and for each <math>i, \Lambda_i = C_i^{\dagger}</math>. Then <math>F_g(m, \psi) = 1</math> for every <math>m</math> even though there is a substantial error on each <math>C_i</math> and so benchmarking fails. | * The case where Randomized benchmarking fails: Suppose the noise is time dependent and for each <math>i, \Lambda_i = C_i^{\dagger}</math>. Then <math>F_g(m, \psi) = 1</math> for every <math>m</math> even though there is a substantial error on each <math>C_i</math> and so benchmarking fails. | ||
* [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.080505 Interleaved Randomized Benchmarking]: This protocol consists of interleaving random Clifford gates between the gate of interest and provides an estimate as well as theoretical bounds for the average error of the gate under test, so long as the average noise variation over all Clifford gates is small. Here the procedure followed is: | * [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.080505 Interleaved Randomized Benchmarking]: This protocol consists of interleaving random Clifford gates between the gate of interest and provides an estimate as well as theoretical bounds for the average error of the gate under test, so long as the average noise variation over all Clifford gates is small. Here the procedure followed is: | ||
** Choose <math>K</math> sequences of Clifford elements where the first Clifford <math>C_{i_1}</math> in each sequence is chosen uniformly at random from Clif | ** Choose <math>K</math> sequences of Clifford elements where the first Clifford <math>C_{i_1}</math> in each sequence is chosen uniformly at random from Clif<math>_n</math>, the second is always chosen to be <math>C</math>(gate of interest), and alternate between uniformly random Clifford elements and deterministic <math>C</math> up to the <math>m^{th}</math> random gate. | ||
** The <math>(m+1)^{th}</math> gate is chosen to be the inverse of the composition of the first <math>m</math> random gates and interlaced <math>C</math> gates. | ** The <math>(m+1)^{th}</math> gate is chosen to be the inverse of the composition of the first <math>m</math> random gates and interlaced <math>C</math> gates. | ||
** The rest of the steps remain the same and finally after plotting the new average sequence fidelity with the sequence length and fitting it into either the gate and time dependent or the gate and time independent model, we receive the new depolarizing parameter obtained is <math>p_c</math>, which replaces <math>p</math>. | ** The rest of the steps remain the same and finally after plotting the new average sequence fidelity with the sequence length and fitting it into either the gate and time dependent or the gate and time independent model, we receive the new depolarizing parameter obtained is <math>p_c</math>, which replaces <math>p</math>. | ||