Abstract: Techniques for quantum error correction of a multi-level system are provided and described. In some aspects, techniques for encoding a state of a multi-level quantum system include encoding a quantum information in a two-mode state of two quantum mechanical oscillators. Techniques for protecting the two-mode state against dephasing and energy loss are described.

Abstract: Techniques are described in which a qubit is far off-resonantly, or dispersively, coupled to a quantum mechanical oscillator. In particular, a dispersive coupling between a physical qubit and a quantum mechanical oscillator may be selected such that control of the combined qubit-oscillator system can be realized. The physical qubit may be driven with an electromagnetic pulse (e.g., a microwave pulse) and the quantum mechanical oscillator simultaneously driven with another electromagnetic pulse, the combination of which results in a change in state of the qubit-oscillator system.

Abstract: Some aspects are directed to a method of operating an apparatus, the apparatus comprising a first quantum system having a plurality of coherent quantum states, the first quantum system being coupled to a second quantum system, the method comprising providing an input energy signal to the second quantum system that stimulates energy transfer between the first quantum system and the second quantum system and that causes net dissipation of energy to be output from the second quantum system, wherein the input energy signal includes at least two components having different frequencies and each having an amplitude and a phase, and adiabatically varying the amplitude and the phase of the at least two components of the input energy signal to cause a change in one or more of the plurality of coherent quantum states of the first quantum system.

Abstract: Some aspects are directed to a method of operating a circuit quantum electrodynamics system that includes a physical qubit dispersively coupled to a quantum mechanical oscillator, the method comprising measuring a parity of a first state of the quantum mechanical oscillator, subsequent to measuring the parity of the first state, measuring a parity of a second state of the quantum mechanical oscillator, the second state being different from the first state, applying a first drive waveform to the quantum mechanical oscillator, and applying a second drive waveform to the physical qubit concurrent with the application of the first drive waveform, wherein the first drive waveform and the second drive waveform are selected based at least in part on a result of comparing the measured parity of the second state to the measured parity of the first state.

Abstract: Techniques for quantum error correction of a multi-level system are provided and described. In some aspects, techniques for encoding a state of a multi-level quantum system include encoding a quantum information in a two-mode state of two quantum mechanical oscillators. Techniques for protecting the two-mode state against dephasing and energy loss are described.

Abstract: According to some aspects, a quantum information system is provided that includes an ancilla qubit; a qudit coupled to the ancilla qubit, a detector configured to generate a detection result based on a quantum state of the ancilla qubit, and a driving source coupled to the qudit and the ancilla qubit and configured to apply at least one qudit driving signal to the qudit based on the detection result and at least one qubit driving signal to the qudit based on the detection result.

Abstract: Some aspects are directed to a method of operating a circuit quantum electrodynamics system that includes a physical qubit dispersively coupled to a quantum mechanical oscillator, the method comprising measuring a parity of a first state of the quantum mechanical oscillator, subsequent to measuring the parity of the first state, measuring a parity of a second state of the quantum mechanical oscillator, the second state being different from the first state, applying a first drive waveform to the quantum mechanical oscillator, and applying a second drive waveform to the physical qubit concurrent with the application of the first drive waveform, wherein the first drive waveform and the second drive waveform are selected based at least in part on a result of comparing the measured parity of the second state to the measured parity of the first state.

Abstract: According to some aspects, a method is provided of operating a circuit quantum electrodynamics system that includes a physical qubit dispersively coupled to a quantum mechanical oscillator, the method comprising applying a first electromagnetic pulse to the physical qubit based on a number state of the quantum mechanical oscillator, wherein the first electromagnetic pulse causes a change in state of the quantum mechanical oscillator, and applying, subsequent to application of the first electromagnetic pulse, a second electromagnetic pulse to the quantum mechanical oscillator that coherently adds or removes energy from the quantum mechanical oscillator.

Abstract: According to some aspects, a method is provided of operating a circuit quantum electrodynamics system that includes a physical qubit dispersively coupled to a quantum mechanical oscillator, the method comprising applying a first electromagnetic pulse to the physical qubit based on a number state of the quantum mechanical oscillator, wherein the first electromagnetic pulse causes a change in state of the quantum mechanical oscillator, and applying, subsequent to application of the first electromagnetic pulse, a second electromagnetic pulse to the quantum mechanical oscillator that coherently adds or removes energy from the quantum mechanical oscillator.

Abstract: According to some aspects, a quantum information system is provided that includes an ancilla qubit; a qudit coupled to the ancilla qubit, a detector configured to generate a detection result based on a quantum state of the ancilla qubit, and a driving source coupled to the qudit and the ancilla qubit and configured to apply at least one qudit driving signal to the qudit based on the detection result and at least one qubit driving signal to the qudit based on the detection result.

Abstract: Some aspects are directed to a method of operating a circuit quantum electrodynamics system that includes a physical qubit dispersively coupled to a quantum mechanical oscillator, the method comprising applying a first drive waveform to the quantum mechanical oscillator, and applying a second drive waveform to the physical qubit concurrent with the application of the first drive waveform, wherein the first and second drive waveforms are configured to produce a state transition of the circuit quantum electrodynamics system from an initial state to a final state.

Abstract: According to some aspects, a method is provided of operating a circuit quantum electrodynamics system that includes a physical qubit dispersively coupled to a quantum mechanical oscillator, the method comprising applying a first electromagnetic pulse to the physical qubit based on a number state of the quantum mechanical oscillator, wherein the first electromagnetic pulse causes a change in state of the quantum mechanical oscillator, and applying, subsequent to application of the first electromagnetic pulse, a second electromagnetic pulse to the quantum mechanical oscillator that coherently adds or removes energy from the quantum mechanical oscillator.

Abstract: Some aspects are directed to a method of operating an apparatus, the apparatus comprising a first quantum system having a plurality of coherent quantum states, the first quantum system being coupled to a second quantum system, the method comprising providing an input energy signal to the second quantum system that stimulates energy transfer between the first quantum system and the second quantum system and that causes net dissipation of energy to be output from the second quantum system, wherein the input energy signal includes at least two components having different frequencies and each having an amplitude and a phase, and adiabatically varying the amplitude and the phase of the at least two components of the input energy signal to cause a change in one or more of the plurality of coherent quantum states of the first quantum system.