Efficient quantum error correction in neutral atoms by conversion to erasure errors

A method for quantum error correction, comprising:

• trapping and/or manipulating an array of qubits, wherein the array of qubits includes encoded neutral atoms or ions and forms a computational space;
• encoding the array of qubits to a state characterized in that an error during at least one operation including idling, a gate, or other operation results in a respective qubit transition to a disjointed state where that error can be detected without disturbing the qubits remaining in the computational space, wherein the array of qubits form a quantum error correcting code and the detected error comprises an erasure error;
• performing a syndrome measurement of a quantum error correcting code;
• identifying the presence and location of an error by detecting the corresponding neutral atom or ion has left the computational space after performing the at least one operation;
• identifying a logical error in the quantum error correcting code associated with a loss of qubit information based on the identified error location and results of the syndrome measurement;
• and
• adjusting subsequent computational steps based on the identified logical error.

A quantum system for quantum error correction, comprising:

• an optical system configured to trap, manipulate, and/or detect an array of qubits using light;
• a processor;
• and
• a memory, including instruction stored thereon, which when executed by the processor, cause the quantum system to:
• trap and/or manipulate the array of qubits, wherein the array of qubits includes encoded neutral atoms or ions and forms a computational space;
• encode the array of qubits to a state characterized in that an error during at least one of an idling, gate, or other operation results in a respective qubit transition to a disjointed state where that error can be detected without disturbing the qubits remaining in the computational space;
• for each gate operation detect an erasure error and replace or reinitialize an atom or an ion of a qubit associated with the detected erasure error;
• identify an error location within the quantum error correcting code based on the detected error;
• identify a logical error in the quantum error correcting code associated with a loss of qubit information based on the identified error location;
• and
• adjust the subsequent computational steps to correct the error.