Higher-order exceptional surface in a pseudo-Hermitian superconducting circuit

  1. Guo-Qiang Zhang,
  2. Wei Feng,
  3. Yu Wang,
  4. and Chui-Ping Yang
In the last few years, much attention has been paid to exceptional surfaces (ESs) owing to various important physical phenomena and potential applications. However, high-order ESs in
pseudo-Hermitian systems have not been reported until now. Here, we study the high-order ES in a pseudo-Hermitian superconducting (SC) circuit system. In our proposal, the SC circuit system is composed of three circularly coupled SC cavities, where the gain and loss are balanced. According to the eigenvalue properties of the pseudo-Hermitian Hamiltonian, we derive the general pseudo-Hermitian conditions for the ternary SC system. In the special pseudo-Hermitian case with parity-time symmetry, all third-order exceptional points (EP3s) of the SC system form a third-order exceptional line in the parameter space. Under the general pseudo-Hermitian conditions, more EP3s are found, and all EP3s are located on a surface, i.e., a third-order exceptional surface is constructed. Moreover, we also investigate the eigenvalues of the pseudo-Hermitian SC circuit around EP3s. Our work opens up a door for exploring high-order ESs and related applications in pseudo-Hermitian systems.

Efficient scheme for realizing a multiplex-controlled phase gate with photonic qubits in circuit quantum electrodynamics

  1. Qi-Ping Su,
  2. Yu Zhang,
  3. Liang Bin,
  4. and Chui-Ping Yang
We propose an efficient scheme to implement a multiplex-controlled phase gate with multiple photonic qubits simultaneously controlling one target photonic qubit based on circuit quantum
electrodynamics (QED). For convenience, we denote this multiqubit gate as MCP gate. The gate is realized by using a two-level coupler to couple multiple cavities. The coupler here is a superconducting qubit. This scheme is simple because the gate implementation requires only \textit{one step} of operation. In addition, this scheme is quite general because the two logic states of each photonic qubit can be encoded with a vacuum state and an arbitrary non-vacuum state (e.g., a Fock state, a superposition of Fock states, a cat state, or a coherent state, etc.) which is orthogonal or quasi-orthogonal to the vacuum state. The scheme has some additional advantages: Because only two levels of the coupler are used, i.e., no auxiliary levels are utilized, decoherence from higher energy levels of the coupler is avoided; the gate operation time does not depend on the number of qubits; and the gate is implemented deterministically because no measurement is applied. As an example, we numerically analyze the circuit-QED based experimental feasibility of implementing a three-qubit MCP gate with photonic qubits each encoded via a vacuum state and a cat state. The scheme can be applied to accomplish the same task in a wide range of physical system, which consists of multiple microwave or optical cavities coupled to a two-level coupler such as a natural or artificial atom.

Entanglement-interference complementarity and experimental demonstration in a superconducting circuit

  1. Xin-Jie Huang,
  2. Pei-Rong Han,
  3. Wen Ning,
  4. Shou-Ban Yang,
  5. Xin Zhu,
  6. Jia-Hao Lü,
  7. Ri-Hua Zheng,
  8. Hekang Li,
  9. Zhen-Biao Yang,
  10. Qi-Cheng Wu,
  11. Kai Xu,
  12. Chui-Ping Yang,
  13. Dongning Zheng,
  14. Heng Fan,
  15. and Shi-Biao Zheng
Quantum entanglement between an interfering particle and a detector for acquiring the which-path information plays a central role for enforcing Bohr’s complementary principle,
but the quantitative relation between this entanglement and the fringe visibility remains untouched upon. Here we find an equality for quantifying this relation. Our equality characterizes how well the interference pattern can be preserved when an interfering particle, initially carrying a definite amount of coherence, is entangled with a which-path detector to a certain degree. This equality provides a connection between entanglement and interference in the unified framework of coherence, revealing the quantitative entanglement-interference complementarity for the first time. We experimentally demonstrate this relation with a superconducting circuit, where a resonator serves as a which-path detector for an interfering qubit. The results demonstrate quantum entanglement is the mechanism for prohibiting any detector from acquiring which-path information without deteriorating the interference pattern, which was not confirmed previously.

Transferring quantum entangled states between multiple single-photon-state qubits and coherent-state qubits in circuit QED

  1. Qi-Ping Su,
  2. Hanyu Zhang,
  3. and Chui-Ping Yang
We present a way to transfer maximally- or partially-entangled states of n single-photon-state (SPS) qubits onto n coherent-state (CS) qubits, by employing 2n microwave cavities coupled
to a superconducting flux qutrit. The two logic states of a SPS qubit here are represented by the vacuum state and the single-photon state of a cavity, while the two logic states of a CS qubit are encoded with two coherent states of a cavity. Because of using only one superconducting qutrit as the coupler, the circuit architecture is significantly simplified. The operation time for the state transfer does not increase with the increasing of the number of qubits. When the dissipation of the system is negligible, the quantum state can be transferred in a deterministic way since no measurement is required. Furthermore, the higher-energy intermediate level of the coupler qutrit is not excited during the entire operation and thus decoherence from the qutrit is greatly suppressed. As a specific example, we numerically demonstrate that the high-fidelity transfer of a Bell state of two SPS qubits onto two CS qubits is achievable within the present-day circuit QED technology. Finally, it is worthy to note that when the dissipation is negligible, entangled states of n CS qubits can be transferred back onto n SPS qubits by performing reverse operations. This proposal is quite general and can be extended to accomplish the same task, by employing a natural or artificial atom to couple 2n microwave or optical cavities.

Transferring quantum entangled states between multiple single-photon-state qubits and coherent-state qubits in circuit QED

  1. Qi-Ping Su,
  2. Hanyu Zhang,
  3. and Chui-Ping Yang
We present a way to transfer maximally- or partially-entangled states of n single-photon-state (SPS) qubits onto n coherent-state (CS) qubits, by employing 2n microwave cavities coupled
to a superconducting flux qutrit. The two logic states of a SPS qubit here are represented by the vacuum state and the single-photon state of a cavity, while the two logic states of a CS qubit are encoded with two coherent states of a cavity. Because of using only one superconducting qutrit as the coupler, the circuit architecture is significantly simplified. The operation time for the state transfer does not increase with the increasing of the number of qubits. When the dissipation of the system is negligible, the quantum state can be transferred in a deterministic way since no measurement is required. Furthermore, the higher-energy intermediate level of the coupler qutrit is not excited during the entire operation and thus decoherence from the qutrit is greatly suppressed. As a specific example, we numerically demonstrate that the high-fidelity transfer of a Bell state of two SPS qubits onto two CS qubits is achievable within the present-day circuit QED technology. Finally, it is worthy to note that when the dissipation is negligible, entangled states of n CS qubits can be transferred back onto n SPS qubits by performing reverse operations. This proposal is quite general and can be extended to accomplish the same task, by employing a natural or artificial atom to couple 2n microwave or optical cavities.

Transferring entangled states of photonic cat-state qubits in circuit QED

  1. Tong Liu,
  2. Zhen-Fei Zheng,
  3. Yu Zhang,
  4. Yu-Liang Fang,
  5. and Chui-Ping Yang
We propose a method for transferring quantum entangled states of two photonic cat-state qubits (cqubits) from two microwave cavities to the other two microwave cavities. This proposal
is realized by using four microwave cavities coupled to a superconducting flux qutrit. Because of using four cavities with different frequencies, the inter-cavity crosstalk is significantly reduced. Since only one coupler qutrit is used, the circuit resources is minimized. The entanglement transfer is completed with a single-step operation only, thus this proposal is quite simple. The third energy level of the coupler qutrit is not populated during the state transfer, therefore decoherence from the higher energy level is greatly suppressed. Our numerical simulations show that high-fidelity transfer of two-cqubit entangled states from two transmission line resonators to the other two transmission line resonators is feasible with current circuit QED technology. This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems, such as four microwave or optical cavities, which are coupled to a natural or artificial three-level atom.

Deterministic generation of Greenberger-Horne-Zeilinger entangled states of cat-state qubits in circuit QED

  1. Chui-Ping Yang,
  2. and Zhen-Fei Zheng
We present an efficient method to generate a Greenberger-Horne-Zeilinger (GHZ) entangled state of three cat-state qubits (cqubits) via circuit QED. The GHZ state is prepared with three
microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the operation, decoherence caused by the energy relaxation and dephasing of the qutrit is greatly suppressed. The GHZ state is created deterministically because no measurement is involved. Numerical simulations show that high-fidelity generation of a three-cqubit GHZ state is feasible with present circuit QED technology. This proposal can be easily extended to create a N-cqubit GHZ state (N≥3), with N microwave or optical cavities coupled to a natural or artificial three-level atom.

Universal quantum gate with hybrid qubits in circuit quantum electrodynamics

  1. Chui-Ping Yang,
  2. Zhen-Fei Zheng,
  3. and Yu Zhang
Hybrid qubits have recently drawn intensive attention in quantum computing. We here propose a method to implement a universal controlled-phase gate of two hybrid qubits via two three-dimensional
(3D) microwave cavities coupled to a superconducting flux qutrit. For the gate considered here, the control qubit is a microwave photonic qubit (particle-like qubit), whose two logic states are encoded by the vacuum state and the single-photon state of a cavity, while the target qubit is a cat-state qubit (wave-like qubit), whose two logic states are encoded by the two orthogonal cat states of the other cavity. During the gate operation, the qutrit remains in the ground state; therefore decoherence from the qutrit is greatly suppressed. The gate realization is quite simple, because only a single basic operation is employed and neither classical pulse nor measurement is used. Our numerical simulations demonstrate that with current circuit QED technology, this gate can be realized with a high fidelity. The generality of this proposal allows to implement the proposed gate in a wide range of physical systems, such as two 1D or 3D microwave or optical cavities coupled to a natural or artificial three-level atom. Finally, this proposal can be applied to create a novel entangled state between a particle-like photonic qubit and a wave-like cat-state qubit.

One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED

  1. You-Ji Fan,
  2. Zhen-Fei Zheng,
  3. Yu Zhang,
  4. Dao-Ming Lu,
  5. and Chui-Ping Yang
We propose a single-step implementation of a muti-target-qubit controlled phase gate with one cat-state qubit ( extit{cqubit}) simultaneously controlling n−1 target extit{cqubits}.
The two logic states of a \textit{cqubit} are represented by two orthogonal cat states of a single cavity mode. In this proposal, the gate is implemented with n microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the gate operation, decoherence caused due to the qutrit’s energy relaxation and dephasing is greatly suppressed. The gate implementation is quite simple because only a single-step operation is needed and neither classical pulse nor measurement is required. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one cqubit simultaneously controlling two target cqubits is feasible with present circuit QED technology. This proposal can be extended to a wide range of physical systems to realize the proposed gate, such as multiple microwave or optical cavities coupled to a natural or artificial three-level atom.

Circuit QED: single-step realization of a multiqubit controlled phase gate with one microwave photonic qubit simultaneously controlling n−1 microwave photonic qubits

  1. Biaoliang Ye,
  2. Zhen-Fei Zheng,
  3. Yu Zhang,
  4. and Chui-Ping Yang
We present a novel method to realize a multi-target-qubit controlled phase gate with one microwave photonic qubit simultaneously controlling n−1 target microwave photonic qubits.
This gate is implemented with n microwave cavities coupled to a superconducting flux qutrit. Each cavity hosts a microwave photonic qubit, whose two logic states are represented by the vacuum state and the single photon state of a single cavity mode, respectively. During the gate operation, the qutrit remains in the ground state and thus decoherence from the qutrit is greatly suppressed. This proposal requires only a single-step operation and thus the gate implementation is quite simple. The gate operation time is independent of the number of the qubits. In addition, this proposal does not need applying classical pulse or any measurement. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one microwave photonic qubit simultaneously controlling two target microwave photonic qubits is feasible with current circuit QED technology. The proposal is quite general and can be applied to implement the proposed gate in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a natural or artificial Λ-type three-level atom.