Efficient nonclassical state preparation via generalized parity measurement

Abstract

Nonclassical states of bosonic modes, especially the large number states, are valuable resources for quantum information processing and quantum metrology. It is however intricate to generate a desired Fock state of bosonic systems by unitary protocols due to their uniform energy spectrum. We here propose a nonunitary protocol that is based on the resonant Jaynes-Cummings interaction of the bosonic mode with an ancillary two-level atom and sequential projective measurements on the atom. Using the generalized parity-measurement operator constructed by several rounds of free evolution with stepwise halved intervals and measurement, we can efficiently filter out the unwanted population and push the target resonator conditionally toward the desired Fock state. In the ideal situation, a Fock state $|n_t\approx2000\rangle$ can be prepared with a fidelity over $98\%$ using only eight rounds of measurements. Under qubit dissipation and dephasing and cavity decay in the current circuit-QED platforms, a Fock state $|n_t\approx100\rangle$ can be prepared with a fidelity of about $80\%$ by six measurements. It is found that the number of measurement rounds for preparing a large Fock state $|n_t\rangle$ scales roughly as $\log_2\sqrt{n_t}$, which is similar to the number of ancillary qubits required in the state preparation via the quantum phase estimation algorithm and yet costs much less in gate operations. Our protocol can also be used to prepare a large Dicke state $|J\simeq1000,0\rangle$ of a spin ensemble with a sufficiently high fidelity by less than six measurements. It is qualified by the quantum Fisher information approaching the Heisenberg scaling in sensing the rotation phase along the $x$ axis.

Figures (8)

• Figure 1: (a) Circuit diagram for realizing GPM NP2024Deng through free joint evolution of the dispersively coupled resonator and the ancillary TLS, the Hadamard gates on the TLS, and the projective measurements on the ground state $|g\rangle$ of TLS. (b) Circuit diagram of our protocol for constructing approximated GPM on the target resonator by repeatedly measuring the excited state $|e\rangle$ of the ancillary TLS, which is coupled to the resonator through exchange interaction.
• Figure 2: Norm squared coefficient $\prod_{i=1}^{N}|\beta_n(l_it_{100})|^2$ as a function of the Fock index $n$ for (a) $N=1$ round and (b) $N=2$ rounds of evolution and measurement with various detunings $\Delta$. The target state is the Fock state $|n_t=100\rangle$.
• Figure 3: (a) Fidelity and (b) success probability as functions of the number $N$ of rounds of free evolution and measurement for various target Fock states $|n_t\rangle$.
• Figure 4: Number of evolution-measurement rounds for generating a Fock state $|n_t\rangle$ with a fidelity exceeding $98\%$ as a function of the target excitation number $n_t$. The red dashed line is the fitting curve $N_{\rm Fock}(n_t)\approx\log_2(\sqrt{n_t})+3.5$.
• Figure 5: Comparison of the resonant exchange coupling protocol [Fig. \ref{['Circuit']}(b)] and the dispersive-coupling protocol [Fig. \ref{['Circuit']}(a)] for GPM in generating Fock state $|n_t=100\rangle$ (a) under various cavity decay rates with $\gamma=\gamma_{\phi}=100$ kHz and (b) under various qubit decoherence rates ($\gamma=\gamma_\phi$) with $\kappa=5$ kHz. Here $g=100$ MHz and $\chi=2$ MHz.