Quantum Shift Register Circuits
arXiv:0903.3894 · doi:10.1103/PhysRevA.79.062325
Abstract
A quantum shift register circuit acts on a set of input qubits and memory qubits, outputs a set of output qubits and updated memory qubits, and feeds the memory back into the device for the next cycle (similar to the operation of a classical shift register). Such a device finds application as an encoding and decoding circuit for a particular type of quantum error-correcting code, called a quantum convolutional code. Building on the Ollivier-Tillich and Grassl-Roetteler encoding algorithms for quantum convolutional codes, I present a method to determine a quantum shift register encoding circuit for a quantum convolutional code. I also determine a formula for the amount of memory that a CSS quantum convolutional code requires. I then detail primitive quantum shift register circuits that realize all of the finite- and infinite-depth transformations in the shift-invariant Clifford group (the class of transformations important for encoding and decoding quantum convolutional codes). The memory formula for a CSS quantum convolutional code then immediately leads to a formula for the memory required by a CSS entanglement-assisted quantum convolutional code.
17 pages, 18 figures
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- Quantum resource theory of coding for error correction
- Minimal memory requirements for pearl-necklace encoders of quantum convolutional codes
- Examples of minimal-memory, non-catastrophic quantum convolutional encoders
- A dataflow programming framework for linear optical distributed quantum computing