Quantum Error Corrections
The year 1994 saw a remarkable achievement in Quantum mechanics. The Quantum computing found it’s real exiting application that year. Peter Shor wrote a quantum algorithm to factorize integer numbers. He showed that factorization of a large integer number into its prime factors took Polynomial time.
Though it caused a stir, there was a stumbling block to realize it because of the quantum decoherence an effect that would disturb or deteriorate the quantum systems Shor himself came up with a simple yet an innovative solution by using 9 qubits to encode 1 logical qubit. This means in order to encode an information 9 physical qubits were used. This could correct an arbitrary error in any single qubit. However, it consumes space for encoding (bulk) information.
Continuous efforts were made to minimize the requirements of more qubits. In an improved & clever strategy, the information was encoded into 3 physical qubits. 2 ancilla qubits were used to compare the states & reveal the error ones. Note that the physical qubits were NOT measured in any of these approaches.
Then came the “stabilizer code” which, with the help of ancilla qubits, protects the logical qubits. One of the stabilizer codes is 5 qubit stabilizer where 5 physical qubits were used to encode 1 logical qubit.
Another interesting approach is Topological Error Correction — which has the highest known tolerable error rate for a local architecture. Unless the topological properties are disturbed, the systems do not undergo the decoherence.
A (torus shaped) donut is torus until the central hole gets destroyed. Any number of bites along the edges do not change its torus shape. The similar concept is incorporated in Topological Error Correction. Here the topological properties are
used to encode the logical qubit & until its topological property is disturbed, the qubit stays coherent. Another approach came from an unexpected quarter which connects the Quantum error correction with the spacetime structure. The anti deSitter/conformal field Theory correspondence conjectures the existence of a relationship between the quantum gravity in an AdS space & a CFT in a space one dimension less.
Almheiri team used quantum error correction approach on CFT side to get more insight on AdS/CFT duality. Thus was born the Holographic rror Correction. It provides a simple model for understanding many aspects of the duality & the emergence of spacetime. Thus, there is hope of new quantum error-correcting codes. Hence understanding the quantum gravity is essential.
Read: Why do we need Quantum Gravity? https://alam-hilaal.medium.com/why-do-we-need-quantum-gravity-7ab3b9206147
