Superconducting Bosonic Qubits

Encoding quantum information in non-classical states of harmonic oscillators (bosonic modes) was among the first conceptual schemes for the realization of quantum computers. In the past decade, quantum control and measurement of bosonic degrees of freedom have been reliably implemented in superconducting microwave circuits with Josephson junctions. Superconducting bosonic qubits are a leading platform for demonstrating error-correctable quantum logical memories in a hardware-efficient architecture, which opens a highly innovative subfield in superconducting quantum technology.

Compared to other architectures for fault-tolerant quantum processors - for instance, those based on the planar integration of two-level quantum systems (physical qubits) to achieve topological protection of quantum information (e.g., surface codes) - superconducting bosonic qubits show a list of main advantages:

• Bosonic modes provide more energy levels for the redundant encoding of quantum information, without introducing extra hardware elements or noise/decoherence channels
• Linear resonators typically have longer intrinsic physical lifetimes than nonlinear Josephson-junction elements
• The loss mechanism in bosonic quantum memories is dominated by photon dissipation, which can be detected and/or compensated through various quantum error correction protocols
• Superconducting bosonic qubits are compatible with autonomous (feedback-free) quantum-state stabilization through Hamiltonian engineering for driven-dissipative open quantum systems in addition to measurement-based quantum error correction schemes

Major challenges of superconducting bosonic qubits include designing and implementing more robust and efficient quantum error correction codes, improving single- and two-logical-qubit gate fidelities as well as the connectivity and scalability of logical quantum modules.

A superconducting bosonic qubit is typically based on a low-loss, linear microwave resonator as the bosonic quantum memory. This resonator is coupled to one or more nonlinear superconducting Josephson circuit elements to form ancillary modes that enable the control and measurement of the linear quantum memory.

Candidates of the bosonic quantum memory include superconducting microwave electromagnetic resonators, as well as micromechanical oscillators and collective spin excitation modes. The ancillary mode(s) can be provided by a superconducting qubit (e.g., transmon, fluxonium, etc.) or other quantum-limited Josephson parametric devices. The ancilla qubit has its separate control and measurement circuitry, including a microwave readout resonator.

The Zurich Instruments SHFQC Qubit Controller combines a qubit readout channel with up to 6 microwave control channels and thus offers a standalone solution for many bosonic qubit experiments  For experiments with additional need for high-frequency flux control, or with a need for more microwave channels, the SHFQC can be integrated in a Quantum Computing Control System (QCCS), providing automatic timing synchronization and system-level feedback. Setups of all sizes are controlled through the LabOne Q software, providing hardware abstraction, an experiment control framework, and an interface to higher software layers. Zurich Instruments' solutions provide key features that particularly benefit bosonic qubit experiments in the following experimental methods:

System characterization and calibration

• Fast and parallel spectroscopy and coherence time measurements of microwave resonators and ancilla qubits
• High-fidelity ancilla qubit readout with a dedicated signal processing chain on the SHFQC and the SHFPPC Parametric Pump Controller for operating quantum-limited parametric amplifiers
• Fast and accurate magnetic flux control of flux-tunable ancilla qubits or Josephson parametric devices using the HDAWG
• Efficient system calibration orchestrated and automated by the quantum control software framework LabOne Q
• High-purity control signal generation from DC to 8.5 GHz with a direct extension to higher frequencies using external microwave mixers 

Quantum memory state preparation, control, and tomography

• High-density arbitrary-wave signal synthesis at microwave frequencies for both the bosonic quantum memory and the ancilla qubit:
  • State-of-the-art spurious-free dynamic range (SFDR) achieved through the double-superheterodyne frequency conversion technique
  • Temperature-stable microwave analog front end free of IQ-mixer calibration
  • Memory-efficient waveform programming and upload
• Low-latency internal feedback within the SHFQC or global feedback via the QHub for measurement-based quantum state preparation and stabilization
• Stable initial phase difference between multiple output and input channels at arbitrary frequencies for phase coherent microwave drives and parametric measurement of nonlinear quantum devices

Measurement-based quantum error correction

• Projective error syndrome measurement of the bosonic quantum memory via mapping the error syndrome operator to the ancilla qubit state using microwave pulses, followed by the high-fidelity single-shot readout of the ancilla qubit
• Low-latency internal feedback within the SHFQC or global feedback via the PQSC or QHub for real-time adaptive microwave control pulse generation (see Quantum Feedback Measurements)

Remote quantum entanglement and communication

• Quantum state transfer between standing microwave photons in the bosonic memory and flying photons in the communication channel using microwave pulses generated by the SHFQC
• Control and measurement operations of multiple bosonic quantum modules synchronized by the QHub in a scalable architecture