#Quantum error correcting codes code
These underlying codes can be nested with quantum operations into codes of various complexity of particular importance among these are the duplication 8-tuple quantum code and the triple commutator code.ĭ. The fundamental block codes we are concerned with are the vector code over GF(3) with 9 codewords (2-tuples), the Boolean code over GF(2) with 16 codewords ( 4-tuples), a matrix code over GF(3) with 81 codewords ( 4-tuples), and the mod2 code over GF(2) with 16 codewords ( 9-tuples). To define a matrix code rigorously we consider the space of all n-tuples of 0's, 1's and -1's over the Galois field GF(k), the finite field with k elements. Because these optimal coding operations, as we will shortly find out, are quantum-mechanical in nature, we define our codes as matrix quantum codes where redundancy is of no fundamental significance. While in standard coding theory one deals with codewords represented by suitable operands, we seek suitable operations, which in themselves and by themselves can intelligently provide an effective defence against errors. Because we intend to construct codes which correct errors intrinsically, there is another feature which distinguishes our approach from conventional coding schemes. Introducing self-correcting codes, we depart from the principles of classical coding theory and provide codes with intrinsic built-in control over their own operations. Encoding and decoding in the brain rely on the built-in rules and not on the addition of an ancilla of redundant bits. There is no external supervisor which tells the brain when and where the error occurs and what has to be done to correct it. Clearly we are seeking a self-correcting intelligent code, able to take care of itself, very much as the human brain does. Instead of protecting a code through redundancy, what we want is to delegate the job of error correction to the code itself. However, a different strategy for performing error correction can be considered. In ideal circumstances there are syndromes for a code which enables one to determine the nature and location of errors. An example of a quantum error-correcting code is the Shor 9-qubit code.AUGUST STERN, in Quantum Theoretic Machines, 2000 SELF-CORRECTING CODESĪs we discussed earlier, in the existing classical and quantum codes one protects data through redundancy, and then checks for errors and revises them. Since we cannot clone quantum information, quantum error correction cannot be done by simply storing the same state multiple times. Now let’s see some quantum error correction schemes in a bit more detail. But as we saw earlier, we cannot clone quantum information, and so quantum error correction has to work differently from its classical counterparts. We can detect and correct these errors using quantum error correction. When these errors become too large, our computer might not be calculating the thing we wanted, but something completely different! However, these quantum computers are subject to errors due to the nature of qubits. We can already make basic quantum computers.
#Quantum error correcting codes drivers
01 /Quantum Computers 02 /How to build a qubit 03 /Spin qubits (beginner level) 04 /Operations on spin qubits (beginner level) 05 /Electron spin qubits 06 /Capturing a single electron 07 /Quantum dot qubits 08 /Quantum control and readout 09 /Qubit errors 10 /NV center qubits 11 /Operations on NV center qubits 12 /The Transmon Qubit - A basis for the Quantum Computer 13 /Operations on the Transmon Qubit - Circuit QED 14 /Single-qubit operations on the Transmon qubit 15 /Measurements on the Transmon Qubit 16 /Two-qubit operations on the Transmon qubit 17 /Topological qubits: Anyons 18 /Operations on anyons: Braiding 19 /Operations on anyons: Real-life experiments 20 /Topological quantum computing: Majorana fermions and where to find them 21 /Majorana bound states in superconductors 22 /How do you measure Majorana bound states? 23 /A framework for the future Quantum Computer 24 /The Building Blocks of a Quantum Computer 25 /How to build a Quantum Algorithm - Quantum Circuits 26 /How do you program a quantum algorithm? 27 /The compiler of a quantum computer 28 /Micro-architectures 29 /How do we connect our quantum system to a classical interface? 30 /Assembling a Quantum Processor 31 /Microwave drivers for qubits 32 /Implementation of microwave drivers 33 /Quantum error correction 34 /Surface codes 35 /Fault-tolerant Quantum Error Correction with surface codes
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