Abstract: A quantum computing method comprising constructing a dressing transformation V between a physical Hamiltonian H and an ideal Hamiltonian HID. The physical Hamiltonian H describes a physical quantum computer that comprises a plurality of qubits, including interactions between the plurality of qubits and a continuum. The ideal Hamiltonian HID describes the universal quantum computer that corresponds to the physical quantum computer. Each qubit in the plurality of qubits is initialized and quantum calculations are performed using the plurality of qubits. Measurement of the plurality of qubits is performed in the dressed state.

Abstract: The present invention involves a quantum computing structure, comprising: one or more logical qubits, which is encoded into a plurality of superconducting qubits; and each of the logical qubits comprises at least one operating qubit and at least one ancilla qubit. Also provided is a method of quantum computing, comprising: performing encoded quantum computing operations with logical qubits that are encoded into superconducting operating qubits and superconducting ancilla qubits. The present invention further involves a method of error correction for a quantum computing structure comprising: presenting a plurality of logical qubits, each of which comprises an operating physical qubit and an ancilla physical qubit, wherein the logical states of the plurality of logical qubits are formed from a tensor product of the states of the operating and ancilla qubits; and wherein the states of the ancilla physical qubits are suppressed; and applying strong pulses to the grouping of logical qubits.

Abstract: A method for performing a single-qubit gate on an arbitrary quantum state. An ancillary qubit is set to an initial state |I>. The data qubit is coupled to an ancillary qubit. The state of the ancillary qubit is measured, and the data qubit and the ancillary qubit are coupled for a first period of time. A method for applying a single-qubit gate to an arbitrary quantum state. A state of a first and second ancillary qubit are set to an entangled initial state |I>. A state of a data qubit and the first ancillary qubit are measured thereby potentially performing a single qubit operation on the arbitrary quantum state. A first result is determined. The first result indicates whether the single qubit operation applied the single qubit gate to the arbitrary quantum state.

Abstract: A quantum computing method comprising constructing a dressing transformation V between a physical Hamiltonian H and an ideal Hamiltonian HID. The physical Hamiltonian H describes a physical quantum computer that comprises a plurality of qubits, including interactions between the plurality of qubits and a continuum. The ideal Hamiltonian HID describes the universal quantum computer that corresponds to the physical quantum computer. Each qubit in the plurality of qubits is initialized and quantum calculations are performed using the plurality of qubits. Measurement of the plurality of qubits is performed in the dressed state.

Abstract: A method for performing a single-qubit gate on an arbitrary quantum state. An ancillary qubit is set to an initial state |I>. The data qubit is coupled to an ancillary qubit. The state of the ancillary qubit is measured, and the data qubit and the ancillary qubit are coupled for a first period of time. A method for applying a single-qubit gate to an arbitrary quantum state. A state of a first and second ancillary qubit are set to an entangled initial state |I>. A state of a data qubit and the first ancillary qubit are measured thereby potentially performing a single qubit operation on the arbitrary quantum state. A first result is determined. The first result indicates whether the single qubit operation applied the single qubit gate to the arbitrary quantum state.

Abstract: The present invention involves a quantum computing structure, comprising: one or more logical qubits, which is encoded into a plurality of superconducting qubits; and each of the logical qubits comprises at least one operating qubit and at least one ancilla qubit. Also provided is a method of quantum computing, comprising: performing encoded quantum computing operations with logical qubits that are encoded into superconducting operating qubits and superconducting ancilla qubits. The present invention further involves a method of error correction for a quantum computing structure comprising: presenting a plurality of logical qubits, each of which comprises an operating physical qubit and an ancilla physical qubit, wherein the logical states of the plurality of logical qubits are formed from a tensor product of the states of the operating and ancilla qubits; and wherein the states of the ancilla physical qubits are suppressed; and applying strong pulses to the grouping of logical qubits.