# SQUBIT-2 Résumé de rapport

Project ID:
IST-2001-39083

Financé au titre de:
FP5-IST

Pays:
Netherlands

## Non-destructive readout for a super-conducting flux qubit

Flux qubit quantum state readout is based on measuring the value of the magnetic moment resulting from the clockwise or anti-clockwise circulating current in the SQUID loop containing the three Josephson junctions. Equivalently one may readout the phase set up by the circulating current over a certain part of the loop. In both cases a DC-SQUID detector is employed, comprising two Josephson junctions in a loop. Commonly a "click"-type detection scheme is employed, where the SQUID is either not switched (OFF) or switched into the phase-evolving running state (ON). This discrimination yields a YES/NO output of the system, depending on its state.

This scheme is attractive because of its simplicity and potential large effective gain. It however suffers from a few serious drawbacks. Most pronounced, the vigorous perturbation resulting from the SQUID once it is in the ON state. The perturbation onto the qubit being measured is uncontrolled in strength and frequency spectrum, and leads to a back action onto the quantum state of that qubit way beyond anything close to the minimum quantum limit enforced by the fundamental quantum uncertainty. However, more serious, it also may affect nearby other qubits, the quantum evolution of which should not be influenced at all. As a (serious) side effect the switching of the SQUID leads to the generation of heat and of quasi particles. These two should be allowed to decay away, and bringing the system into the ground state again, before being able to redo a quantum operation. This limits the throughput rate.

The inductive dispersive readout allows a fully controlled approach, where the degree of system-detector interaction can be chosen at will, even in-situ during the experiment. The SQUID is assumed to be coupled to the qubit to be readout. Effectively the harmonic oscillator, formed by the SQUID (acting as a flux-dependent inductor) and the capacitor, transforms the qubit state dependent magnetic moment into a shift of the resonator frequency, and so in an amplitude and/or phase shift available in the ac voltage or the seusceptibility. The ac current driving strength of the harmonic oscillator is the knob allowing control on the detection strength of the SQUID, and so also on the degree of back action from detector to measured object (=qubit).

The system can also be operated in the non-linear driving mode. Following the developments at Yale (Devoret), this allows a strong enhancement of the sensitivity, augmented by an intrinsic latching capability due to a bifurcation phenomenon. We have used this second approach to reach our most optimal fidelity readout results. To check the fidelity of the readout a DC flux signal of the value generated by the qubit is applied, and the shift in switching is measured to be 98% at its optimum. If now operating the qubit, an optimal difference of 87% is found, implying a loss of only 11%. This is one of the best values reached so far in the community.

A careful analyses of the various contributions resulting from the different steps in the actual state measurement process yields the following numbers: 2% during (but not due to) the relaxation time T1; 7% from the adiabatic shift to bring the qubit from its optimal point to the readout point; and 3% from the dynamical readout itself. Within the errors this sums correctly. These results demonstrate the great capabilities of this readout system. Based we will introduce a similar detection system in our second measurement setup as well. The major change will be to enhance the frequency of the resonator. Based on the work of Patrice Bertet in our group and this current work it is a strong advantage to implement the next system at ~ 2GHz, in this way reducing de-phasing effects resulting from the thermal occupation variations of the harmonic oscillator.

This scheme is attractive because of its simplicity and potential large effective gain. It however suffers from a few serious drawbacks. Most pronounced, the vigorous perturbation resulting from the SQUID once it is in the ON state. The perturbation onto the qubit being measured is uncontrolled in strength and frequency spectrum, and leads to a back action onto the quantum state of that qubit way beyond anything close to the minimum quantum limit enforced by the fundamental quantum uncertainty. However, more serious, it also may affect nearby other qubits, the quantum evolution of which should not be influenced at all. As a (serious) side effect the switching of the SQUID leads to the generation of heat and of quasi particles. These two should be allowed to decay away, and bringing the system into the ground state again, before being able to redo a quantum operation. This limits the throughput rate.

The inductive dispersive readout allows a fully controlled approach, where the degree of system-detector interaction can be chosen at will, even in-situ during the experiment. The SQUID is assumed to be coupled to the qubit to be readout. Effectively the harmonic oscillator, formed by the SQUID (acting as a flux-dependent inductor) and the capacitor, transforms the qubit state dependent magnetic moment into a shift of the resonator frequency, and so in an amplitude and/or phase shift available in the ac voltage or the seusceptibility. The ac current driving strength of the harmonic oscillator is the knob allowing control on the detection strength of the SQUID, and so also on the degree of back action from detector to measured object (=qubit).

The system can also be operated in the non-linear driving mode. Following the developments at Yale (Devoret), this allows a strong enhancement of the sensitivity, augmented by an intrinsic latching capability due to a bifurcation phenomenon. We have used this second approach to reach our most optimal fidelity readout results. To check the fidelity of the readout a DC flux signal of the value generated by the qubit is applied, and the shift in switching is measured to be 98% at its optimum. If now operating the qubit, an optimal difference of 87% is found, implying a loss of only 11%. This is one of the best values reached so far in the community.

A careful analyses of the various contributions resulting from the different steps in the actual state measurement process yields the following numbers: 2% during (but not due to) the relaxation time T1; 7% from the adiabatic shift to bring the qubit from its optimal point to the readout point; and 3% from the dynamical readout itself. Within the errors this sums correctly. These results demonstrate the great capabilities of this readout system. Based we will introduce a similar detection system in our second measurement setup as well. The major change will be to enhance the frequency of the resonator. Based on the work of Patrice Bertet in our group and this current work it is a strong advantage to implement the next system at ~ 2GHz, in this way reducing de-phasing effects resulting from the thermal occupation variations of the harmonic oscillator.