An introduction to quantum error-correction Nanjing University Zhaohui Wei(Tsinghua University) July 2021
An introduction to quantum error-correction Nanjing University Zhaohui Wei (Tsinghua University) July 2021
Outline Background and motivation Some relevant properties of quantum information The Shor code-the first real quantum error-correcting code Quantum error-correction conditions Stabilizer codes Fault-tolerant quantum computation
Background and motivation Some relevant properties of quantum information The Shor code – the first real quantum error-correcting code Quantum error-correction conditions Stabilizer codes Fault-tolerant quantum computation
Remarkable progresses on quantum computation (QC) It is widely believed that quantum supremacy has been achieved The power of a baby quantum computer can surpass that of the most powerful supercomputer on a specific task ÷Google(0ct2019) The task:sample the output of a random circuit(53 qubits) Quantum 3 min vs.Supercomputer 10000 years ÷"九章”quantum computer(Dec2020) The task:Boson sampling(76 photos) Quantum 3 min vs.Supercomputer 600 million years The rise of quantum engineering and quantum industry Quantum computation in chemistry,drug research,machine learning... 。Quantum software
It is widely believed that quantum supremacy has been achieved ◦ The power of a baby quantum computer can surpass that of the most powerful supercomputer on a specific task Google (Oct 2019) ◦ The task: sample the output of a random circuit (53 qubits) ◦ Quantum 3 min vs. Supercomputer 10000 years “九章”quantum computer (Dec 2020) ◦ The task: Boson sampling (76 photos) ◦ Quantum 3 min vs. Supercomputer 600 million years The rise of quantum engineering and quantum industry ◦ Quantum computation in chemistry, drug research, machine learning… ◦ Quantum software
A fundamental difficulty in QC The sizes of quantum computers and other quantum schemes are still relatively small Main reason:Quantum information is extremely fragile The No.1 mission of the quantum computing:Implementing reliable quantum schemes (including quantum computers)with unreliable devices As a result,high precision of quantum controls is needed,and quantum error corrections (QEC)have to be performed
The sizes of quantum computers and other quantum schemes are still relatively small ◦ Main reason: Quantum information is extremely fragile The No. 1 mission of the quantum computing: Implementing reliable quantum schemes (including quantum computers) with unreliable devices As a result, high precision of quantum controls is needed, and quantum error corrections (QEC) have to be performed
Classical error correction The key idea:redundancy (cloning unknown information) 0→000 1→111 Suppose the noise flips the bit with probability p>0 1-p 0 0 1 1-p Decode the information by majority voting,then The probability that two or more of the bits are flipped:3p2-2p This is smaller than the original,whenever p<1/2
The key idea: redundancy (cloning unknown information) Suppose the noise flips the bit with probability Decode the information by majority voting, then ◦ The probability that two or more of the bits are flipped: ◦ This is smaller than the original, whenever