Abstract: Systems and methods are provided for quantum error correction. A quantum system includes an array of qubits configured to store an item of quantum information. The array of qubits includes a plurality of data qubits and a plurality of measurement qubits configured to extract a syndrome representing agreement among the plurality of data qubits. The quantum system further includes an integrated circuit comprising validation logic configured to determine if the syndrome is valid, decoding logic configured to determine evaluate the syndrome to determine location of errors within the plurality of data qubits, and an error register configured to store locations of the determined errors.

Abstract: Systems and methods are provided for quantum error correction. A quantum system includes an array of qubits configured to store an item of quantum information. The array of qubits includes a plurality of data qubits and a plurality of measurement qubits configured to extract a syndrome representing agreement among the plurality of data qubits. The quantum system further includes an integrated circuit comprising validation logic configured to determine if the syndrome is valid, decoding logic configured to determine evaluate the syndrome to determine location of errors within the plurality of data qubits, and an error register configured to store locations of the determined errors.

Abstract: Systems and methods are provided for generating at least one high fidelity resource state. A classical code and punctured to provide a first set of generators and a second set of generators. The first set of generators is mapped to a set of stabilizer generators, and the second set of generators is mapped to a set of logical operators. A set of resource states are prepared in physical qubits. A decoding process is performed on the resource states according to a quantum code represented by the set of stabilizer generators and the set of logical operators, and qubits corresponding to the stabilizers are measured.

Abstract: Systems and methods are provided for generating at least one high fidelity resource state. A classical code and punctured to provide a first set of generators and a second set of generators. The first set of generators is mapped to a set of stabilizer generators, and the second set of generators is mapped to a set of logical operators. A set of resource states are prepared in physical qubits. A decoding process is performed on the resource states according to a quantum code represented by the set of stabilizer generators and the set of logical operators, and qubits corresponding to the stabilizers are measured.

Abstract: Systems and methods are provided for generating at least one high fidelity resource state. A classical code and punctured to provide a first set of generators and a second set of generators. The first set of generators is mapped to a set of stabilizer generators, and the second set of generators is mapped to a set of logical operators. A set of resource states are prepared in physical qubits. A decoding process is performed on the resource states according to a quantum code represented by the set of stabilizer generators and the set of logical operators, and qubits corresponding to the stabilizers are measured.

Abstract: Systems and methods are provided for generating a high-fidelity Toffoli state from a plurality of low-fidelity single qubit magic states. First and second qubits are prepared in a high-fidelity initial state. N target qubits are prepared in the single qubit magic state. A series of gates are performed on the qubits, such that the system is in a state ½|0001 . . . 0N+½|0101 . . . 0N+½|1001 . . . 0N+½|1111 . . . 1N. A parity check is performed on the N target qubits. The parity check provides at least a first measurement value. The first qubit, the second qubit, and the first target qubit are accepted as the Toffoli state if the measurement values assume the desired values.

Abstract: Systems and methods are provided for generating a high-fidelity Toffoli state from a plurality of low-fidelity single qubit magic states. First and second qubits are prepared in a high-fidelity initial state. N target qubits are prepared in the single qubit magic state. A series of gates are performed on the qubits, such that the system is in a state ½|0001 . . . 0N+½|0101 . . . 0N+|½|1001 . . . 0N+½|1111 . . . 1N. A parity check is performed on the N target qubits. The parity check provides at least a first measurement value. The first qubit, the second qubit, and the first target qubit are accepted as the Toffoli state if the measurement values assume the desired values.

Abstract: Systems and methods are provided for generating at least one high fidelity resource state. A classical code and punctured to provide a first set of generators and a second set of generators. The first set of generators is mapped to a set of stabilizer generators, and the second set of generators is mapped to a set of logical operators. A set of resource states are prepared in physical qubits. A decoding process is performed on the resource states according to a quantum code represented by the set of stabilizer generators and the set of logical operators, and qubits corresponding to the stabilizers are measured.