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Quantum Feedback Measurements


Application Description

In quantum feedback measurements, the results of single-shot qubit measurements are used as decision input for an immediate feedback action on the qubits. The lower the feedback latency, the smaller the error rate of the feedback operation and the higher the fidelity of the overall quantum information processing operation. To ensure repeatability, the entire feedback loop needs to be completed with deterministic timing even when passing through multiple instruments. Quantum feedback is used in applications such as rapid qubit initialization, quantum state stabilization, and quantum error correction. Use cases differ in the complexity of the required signal processing between measurement and feedback; the signal processing step ranges from a simple forwarding of digital bits of information to demanding error syndrome decoding.

Zurich Instruments' products cover the full range of configurations required in superconducting and spin qubit experiments to make sure that the best trade-off between feedback speed and complexity handling is achieved.

A Zurich Instruments Quantum Computing Control System (QCCS) of the first generation relies on qubit control and readout signals generated in the baseband; the QCCS of the second generation operates directly at microwave frequencies up to 8.5 GHz. Both generations of instruments support the same feedback methods, but with differences in the implementation. In the following, we describe the possibilities and implementations for both generations.

Measurement Strategies

Feedback configurations with a QCCS of the first generation

Figure 1: Connection diagrams for realizing event-based, point-to-point and PQSC-enabled feedback operations with a QCCS of the first generation.

Feedback configurations with a QCCS of the second generation

Figure 2: Connection diagrams for realizing event-based, point-to-point and PQSC-enabled feedback operations with a QCCS of the second generation.

Event-based: Down to 50 ns latency

In the fastest possible configuration shown in Figure 1a, a TTL rising edge is sent to one of the trigger inputs of the HDAWG Arbitrary Waveform Generator to generate an analog signal (first-sample-out) on one pair of outputs 50 ns later. This configuration is suitable when the readout signal of one qubit is deliberately fed back onto one specific qubit, as is the case in active qubit reset. The TTL signal can be supplied by third-party equipment for qubit readout. The SHFSG Signal Generator also supports this functionality as shown in Figure 2b, however with a higher latency of about 200 ns.

Point-to-point: Down to 300 ns latency

In this configuration, shown in Figures 1b and 2b, the readout result of one qubit is fed back to the control line of the same qubit through a fixed point-to-point connection. This matches well the use case of active reset. In a QCCS of the first generation, this can be realized by connecting a UHFQA Quantum Analyzer through a VHDCI cable (DIO link) to an HDAWG Arbitrary Waveform Generator. The DIO link transfers up to 10 qubit readout signals as digital bits; these 10 bits of information can be used to control 8 HDAWG output signals. The latency of 380 ns is measured from the time when the last sample of a readout pulse enters the Signal Input of the UHFQA to the time when the first sample of a control pulse is generated on the Wave Output of the HDAWG. In a QCCS of the second generation, a point-to-point feedback loop can be realized directly inside an instrument: the SHFQC Qubit Controller includes control and readout functionalities, and feedback latency is further reduced to 300 ns.

PQSC-enabled: Down to 550 ns latency

Adding the PQSC Programmable Quantum System Controller as a central hub enables feedback between any two qubits in a system. Multi-qubit data can be processed in real time and with low latency on the way. This method is more powerful than point-to-point feedback and is a prerequisite for scalable quantum computing and quantum error correction. In a QCCS of the first generation shown in Figure 1c, multiple HDAWGs are connected through ZSync cables to a PQSC and multiple UHFQAs are connected to the HDAWGs via VHDCI cables (DIO links). Each DIO link/ZSync connection transfers up to 10 qubit readout signals from a UHFQA to the PQSC. The ZSync connection also transfers bit words from the PQSC to the HDAWG, which may be used as decision input for waveform selection. On the fastest possible path, the latency between the last sample in on any UHFQA and the first sample out on any HDAWG is lower than 700 ns. In a QCCS of the second generation shown in Figure 2c, all components connect directly via ZSync to the PQSC and the latency is reduced below 550 ns.

Local and global feedback with the SHFQC

In a large system, it's valuable to combine point-to-point with PQSC-enabled feedback capabilities. This allows users to achieve the best latency for local feedback operations such as ancilla qubit reset as well as for global feedback operations such as error syndrome decoding and correction. Figure 3 shows how such a configuration can be realized in a QCCS of the second generation. Each SHFQC is used to control subgroups of ancilla qubits connected to one readout line. Additional SHFSGs provide further control lines for data qubits that don't require reset operations during the processing of a quantum circuit, and the HDAWGs provide flux pulses to tune qubit or coupler frequencies.

Local and global feedback with the QCCS

Figure 3: Connection diagram for realizing simultaneous local and global feedback operations with the QCCS.

The Benefits of Choosing Zurich Instruments

  • Low latency, scalability, powerful real-time data processing: all critical requirements for quantum feedback measurements are met at the same time.
  • Take advantage of the flexibility to choose the optimal configuration for your experiment among the scenarios discussed above.
  • You can use state-of-the-art experimental methods without the need for extensive knowledge of FPGA programming.

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Andersen, C.K. et al.

Entanglement stabilization using ancilla-based parity detection and real-time feedback in superconducting circuits

npj Quantum Inf. 5, 69 (2019)

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