- Clifford group quantum error correction how to#
- Clifford group quantum error correction full#
- Clifford group quantum error correction simulator#
Initialize a Clifford element from a QuantumCircuit/Gate/Instruction/Pauli.
Clifford group quantum error correction simulator#
Qiskit has 2 classes that enable you to implement Clifford Circuits in your experiments: the Clifford class (for preparing Clifford elements and circuits) and the StabilizerState class (a python simulator for Cliffords). Implementing Clifford Circuits Using Qiskit This provides us with an efficient mechanism for measuring the entanglement performance of real devices, which relies on the fact that Cliffords can be easily simulated classically. If we prepare large entangled states comprised only of Clifford elements we can efficiently simulate the outcomes and compare with outcomes from real hardware. You can learn more about Randomized Benchmarking in the Qiskit Textbook or in this blog post. By running numerous sequences, you can start to build up a picture of how likely it is for the initial state to be returned, and hence what the error rate is. It works by running sequences of random Clifford gates followed by their inverse in order to return the initial state. Randomized Benchmarking (RB) is a very useful algorithm for estimating the average error rate for a given set of gate operations on a given device.
Clifford group quantum error correction full#
It is far more convenient to work with calculations using a stabilizer format than writing out the full set of superpositions over every bit string! Randomized Benchmarking By using Clifford circuits exclusively you can still access any of the desired error correcting properties, but it becomes much easier to do the calculations. So, if they’re not universal and we can simulate them classically anyway then why on earth am I going to so much trouble to tell you about them?īecause of three reasons: Quantum Error Correctionįor research into error correction it is incredibly common to use stabilizer codes, these are error correcting codes that can be created entirely from stabilizer circuits (i.e. it’s not possible to produce any arbitrary unitary just using a combination of Clifford operators, as they only jump between 6 possible states in single qubit cases). Why are Clifford Circuits Useful in Quantum Computing?Ī Quantum Circuit that only contains Clifford gates can be efficiently simulated on a classical computer, and because the Clifford Group doesn’t include the T gate or Toffoli (CCX) they cannot by themselves achieve universality (i.e. At a high level this just helps make it more efficient to run measurement calculations on Cliffords. We won’t go into too much detail here on destabilizer groups, just know that a destabilizer generating set is a list of Pauli operators that, when combined with the stabilizer generators, produce the full Pauli group for a given number of qubits. So: the first n rows of the matrix represent the generators for the state’s destabilizer group, and the second n rows are generators of the stabilizer group.
Clifford group quantum error correction how to#
Producing Clifford tableaus is a complex process that is beyond the scope of this blog, but check out for more details! For now we’ll just be focusing on understanding how to interpret tableau representations and later on how to use Qiskit to produce them. Just as the stabilizer format makes it easier for humans to work with increasingly large Cliffords, this tableau format makes it more efficient for computers to run calculations on increasingly large Cliffords, so they are an incredibly useful computational tool.Īlso, be careful not to confuse Clifford tableaus with regular gate matrices. We can represent any n-qubit Clifford element by a 2nx2n binary matrix and a 2n binary (phase) vector called a Clifford tableau - and Qiskit can, too. Representing Cliffords with Matrices and Stabilizers
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