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The error-correction demonstration was performed on Schrödinger-cat states encoded in a superconducting resonator, and employed a quantum controller capable of performing real-time feedback operations including read-out of the quantum information, its analysis, and the correction of its detected errors. The work demonstrated how the quantum ...
It is a CSS code (Calderbank-Shor-Steane), using the classical binary [7,4,3] Hamming code to correct for both qubit flip errors (X errors) and phase flip errors (Z errors). The Steane code encodes one logical qubit in 7 physical qubits and is able to correct arbitrary single qubit errors. Its check matrix in standard form is
Once the logical qubit is encoded, errors on the physical qubits can be detected via stabilizer measurements. A lookup table that maps the results of the stabilizer measurements to the types and locations of the errors gives the control system of the quantum computer enough information to correct errors. [4]
Quantum error-correcting codes restore a noisy, decohered quantum state to a pure quantum state. A stabilizer quantum error-correcting code appends ancilla qubits to qubits that we want to protect. A unitary encoding circuit rotates the global state into a subspace of a larger Hilbert space .
An important element of the KLM scheme is the conditional sign flip or nonlinear sign flip gate (NS-gate) as shown in the figure below on the right. It gives a nonlinear phase shift on one mode conditioned on two ancilla modes. Linear optics implementation of NS-gate.
Two types of parity measurement are indirect and direct. Indirect parity measurements coincide with the typical way we think of parity measurement as described above, by measuring an ancilla qubit to determine the parity of the input bits.
The errors, in this case, are therefore not corrected but consolidated. The topologically nontrivial loops of the torus. Moving anyons along these implement logical Pauli operators on the stored qubits. Consider the noise model for which bit and phase errors occur independently on each spin, both with probability p.
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