Quantum State Projection with Various Measurement Strengths

Kosuke Kakuyanagi, Hayato Nakano, Kouichi Semba*, and Shiro Saito
Physical Science Laboratory, *NII

 A superconducting loop, which has Josephson junctions, exhibits discrete energy levels. In particular, in an external magnetic field of around Φ = 0.5Φ0, we can ignore the higher energy levels of this superconducting circuit, and so the circuit works as a two-level quantum system called a superconducting flux qubit. These quantum systems can represent both an excited state and a ground state, which correspond to "1" and "0", respectively, and the superposition of two states. When we measure a quantum superposition state, the quantum state is probabilistically projected to an excited state or a ground state. By using a superconducting qubit, we can generate a superposition state and measure a quantum state on the superconducting circuit.
 We measure a superconducting flux qubit state using the Josephson bifurcation readout method, which employs the bistable state of a non-linear resonator. With this readout method, we can detect convergent states of a nonlinear resonator that depend on the qubit state by achieving coupling between a superconducting qubit and a non-linear resonator. This readout method has advantages including a fast and low measurement back-action. To understand how the projection occurs, we performed an experiment in which we undertook a readout strength dependent measurement [1].
 First, we generate an arbitrary superposition state by operating a rotation gate. Next, we apply various amplitude readout pulses to the qubit. At that time, if state projection occurs, a mixed state consisting of an excited state and a ground state appears. On the other hand, if projection does not occur, the quantum state maintains a pure state. To distinguish between these two states, we measure the final state of the qubit after employing a rotation operation. The experiment was performed at a few 10 mK to avoid the effect of thermal excitation. Figure 1 shows the readout pulse amplitude dependence of the dephasing indicator α using the usual readout pulse amplitude as a standard. When the pulse amplitude reaches h = 0.9, the α value suddenly decreases. This result means the projection suddenly occurs when we increase the measurement strength. This experimental result supports a theoretical analysis of the Josephson bifurcation readout method [2].

K. Kakuyanagi, S. Kagei, R. Koibuchi, S. Saito, A Lupaşcu, K. Semba, and H. Nakano, New J. Phys. 15 (2013) 043028.
H. Nakano, S. Saito, K. Semba, and H. Takayanagi, Phys. Rev. Lett. 102 (2009) 257003.
Fig. 1.
 Measurement strength dependence of α.