Quantum states for error correction are described by their stabilizer, a commuting group of tensor products of Pauli matrices, enabling analysis of a rich class of quantum effects short of full quantum computation.
Fault-tolerant quantum computation
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abstract
Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties of realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer, thus making long computations impossible. A futher difficulty is that inaccuracies in quantum state transformations throughout the computation accumulate, rendering the output of long computations unreliable. It was previously known that a quantum circuit with t gates could tolerate O(1/t) amounts of inaccuracy and decoherence per gate. We show, for any quantum computation with t gates, how to build a polynomial size quantum circuit that can tolerate O(1/(log t)^c) amounts of inaccuracy and decoherence per gate, for some constant c. We do this by showing how to compute using quantum error correcting codes. These codes were previously known to provide resistance to errors while storing and transmitting quantum data.
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quant-ph 3representative citing papers
Empirically learned dynamical decoupling sequences reduce average error rates in dynamic quantum circuits by a factor of three and enable nontrivial process fidelity for quantum Fourier transforms on up to 20 qubits.
Compares resource costs of logical T-state preparation via distillation, cultivation, and code switching using native metrics from existing literature plus a Shor factoring case study.
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The Heisenberg Representation of Quantum Computers
Quantum states for error correction are described by their stabilizer, a commuting group of tensor products of Pauli matrices, enabling analysis of a rich class of quantum effects short of full quantum computation.