Abstract: A method of probabilistically canceling noise in a measurement-based quantum device includes obtaining a sequence of ideal measurements included within a quantum algorithm and selecting a sequence of noisy measurements for emulating the sequence of ideal measurements. Each of the noisy measurements in the selected sequence approximates a corresponding one of the ideal measurements and is adjusted by a quantum correction, where the noisy measurements are selected according to a carefully chosen distribution to cancel known features of noise in those same noisy measurements in the sequence.

Abstract: A method to forecast the result of a Clifford circuit acting on the qubits comprises: for a fault operator F acting on the qubits, precomputing a backward cumulant of the fault operator for each row u of binary matrices Ms and Ml, the backward cumulant reflecting an effect f=effm(F) on measurement outcomes of the qubits according to the Clifford circuit and fault operator; sampling the fault operator F for the qubits according to the predetermined noise distribution in the Clifford circuit; computing a syndrome s=Msf corresponding to the effect based on a commutator of the backward cumulant versus a row of the binary matrix Ms; computing a set of logical flips f=Mlf corresponding to the effect based on a commutator of the backward cumulant versus a row of the binary matrix Ml; and returning the result based on the syndrome and on the set of logical flips.

Abstract: A method to correct a fault in the application of a Clifford circuit to a qubit register of a quantum computer comprises: (a) receiving circuit data defining the Clifford circuit; (b) receiving additional data identifying one or more measurements belonging to each of a plurality of faces of a lattice; (c) emitting an outcome code based on the circuit data, the outcome code including a series of outcome checks each corresponding to an anticipated error syndrome for the application of the Clifford circuit to the qubit register; and (d) emitting a topological outcome code based on the circuit data, the additional data, and the outcome code, the topological outcome code including a series of check operators that support quantum-error correction via a topological decoder, thereby enabling fault correction in the application of the Clifford circuit to the qubit register.

Abstract: A computing system including a processor configured to receive a stabilizer circuit specification of a stabilizer circuit that includes one or more elementary operations. The elementary operations are each selected from the group consisting of an allocation of one or more qubits in a stabilizer state, an allocation of one or more random classical bits, a Clifford unitary, a Pauli unitary conditional on respective parities of measurement outcomes and/or respective parities of the random classical bits, a joint multi-qubit Pauli measurement, and a destructive one-qubit Pauli measurement. The processor is further configured to compute a standardized stabilizer instrument specification of a stabilizer instrument based at least in part on the stabilizer circuit specification. The standardized stabilizer instrument specification includes an input Clifford unitary, an output Clifford unitary, and a plurality of bit matrices.

Abstract: A method to correct a fault in application of a Clifford circuit to a qubit register of a quantum computer comprises: (A) receiving circuit data defining the Clifford circuit; (B) emitting outcome code based on the circuit data, the outcome code including a series of outcome checks each corresponding to an anticipated error syndrome of the application of the Clifford circuit to the qubit register; and (C) emitting space-time quantum code corresponding to the Clifford circuit based on the circuit data and on the outcome code, the space-time quantum code including a series of check operators that support quantum-error correction, thereby enabling fault correction in the application of the Clifford circuit to the qubit register.

Abstract: A method to build a lookup decoder for mapping error syndromes based on quantum-stabilizer code to corresponding error corrections comprises (A) enumerating a subset of error syndromes up to a maximum error weight based on the quantum-stabilizer code; (B) iterating through the subset of error syndromes to compute an error state of highest probability for each error syndrome of the subset, where the error state defines error in a qubit register of a quantum computer; and (C) for each error syndrome of the subset of error syndromes, storing in classical computer memory an error correction based on the error state of highest probability and mapped to that error syndrome.

Abstract: A computing system including a processor configured to receive a first stabilizer instrument specification of a first stabilizer instrument. The first stabilizer instrument specification includes a first input Clifford unitary, a first output Clifford unitary, and first stabilizer instrument bit matrices. The processor is further configured to receive a second stabilizer instrument specification of a second stabilizer instrument. The second stabilizer instrument specification includes a second input Clifford unitary, a second output Clifford unitary, and second stabilizer instrument bit matrices. Based at least in part on the first stabilizer instrument specification and the second stabilizer instrument specification, the processor is further configured to determine whether the first stabilizer instrument is equal to the second stabilizer instrument up to measurement outcome relabeling.

Abstract: A computing system is provided, including a processor configured to receive a standardized stabilizer instrument specification including an input Clifford unitary, an output Clifford unitary, and a plurality of stabilizer instrument bit matrices. The processor is further configured to receive a logical instrument input error correction code and a logical instrument output error correction code. The processor is further configured to compute a logical instrument specification based at least in part on the standardized stabilizer instrument specification, the logical instrument input error correction code, and the logical instrument output error correction code. The logical instrument specification includes a logical input Clifford unitary, a logical output Clifford unitary, a plurality of logical instrument bit matrices, and a logical instrument relabeling matrix. The processor is further configured to store the logical instrument specification in memory.

Abstract: A computing system including a processor configured to receive a stabilizer circuit specification of a stabilizer circuit that includes one or more elementary operations. The elementary operations are each selected from the group consisting of an allocation of one or more qubits in a stabilizer state, an allocation of one or more random classical bits, a Clifford unitary, a Pauli unitary conditional on respective parities of measurement outcomes and/or respective parities of the random classical bits, a joint multi-qubit Pauli measurement, and a destructive one-qubit Pauli measurement. The processor is further configured to compute a standardized stabilizer instrument specification of a stabilizer instrument based at least in part on the stabilizer circuit specification. The standardized stabilizer instrument specification includes an input Clifford unitary, an output Clifford unitary, and a plurality of bit matrices.

Abstract: A method to correct a fault in application of a Clifford circuit to a qubit register of a quantum computer comprises: (A) receiving circuit data defining the Clifford circuit; (B) emitting outcome code based on the circuit data, the outcome code including a series of outcome checks each corresponding to an anticipated error syndrome of the application of the Clifford circuit to the qubit register; and (C) emitting space-time quantum code corresponding to the Clifford circuit based on the circuit data and on the outcome code, the space-time quantum code including a series of check operators that support quantum-error correction, thereby enabling fault correction in the application of the Clifford circuit to the qubit register.

Abstract: A method to build a lookup decoder for mapping error syndromes based on quantum-stabilizer code to corresponding error corrections comprises (A) enumerating a subset of error syndromes up to a maximum error weight based on the quantum-stabilizer code; (B) iterating through the subset of error syndromes to compute an error state of highest probability for each error syndrome of the subset, where the error state defines error in a qubit register of a quantum computer; and (C) for each error syndrome of the subset of error syndromes, storing in classical computer memory an error correction based on the error state of highest probability and mapped to that error syndrome.

Abstract: A method of probabilistically canceling noise in a measurement-based quantum device includes obtaining a sequence of ideal measurements included within a quantum algorithm and selecting a sequence of noisy measurements for emulating the sequence of ideal measurements. Each of the noisy measurements in the selected sequence approximates a corresponding one of the ideal measurements and is adjusted by a quantum correction, where the noisy measurements are selected according to a carefully chosen distribution to cancel known features of noise in those same noisy measurements in the sequence.