Schr\{o}dinger cat states are crucial for exploration of fundamental issues
of quantum mechanics and have important applications in quantum information
processing. Here, we propose and experimentally demonstrate a method for
manipulating cat states in a cavity with the Aharonov-Anandan phase acquired by
a superconducting qubit, which is dispersively coupled to the cavity. Based on
this dispersive coupling, the qubit can be forced to trace out a circuit in the
projective Hilbert space conditional on one coherent state. By preparing the
cavity in a superposition of two coherent states, the geometric phase
associated with this transport is encoded to the relative probability amplitude
of these two coherent states. We demonstrate the photon-number parity of a cat
state in a cavity can be controlled by adjusting this geometric phase, which
offers the possibility for protecting its quantum coherence from single-photon
loss. Based on this geometric effect, we realize phase gates for one and two
photonic qubits whose logical basis states are encoded in two quasi-orthogonal
coherent states. We further demonstrate two-cavity gates with symmetric and
asymmetric Fock state encoding schemes. Our method can be directly extended to
implementation of controlled-phase gates between error-correctable logical
qubits.
Schr{o}dinger cat states are crucial for exploration of fundamental issues
of quantum mechanics and have important applications in quantum information
processing. Here, we propose and experimentally demonstrate a method for
manipulating cat states in a cavity with the Aharonov-Anandan phase acquired by
a superconducting qubit, which is dispersively coupled to the cavity. Based on
this dispersive coupling, the qubit can be forced to trace out a circuit in the
projective Hilbert space conditional on one coherent state. By preparing the
cavity in a superposition of two coherent states, the geometric phase
associated with this transport is encoded to the relative probability amplitude
of these two coherent states. We demonstrate the photon-number parity of a cat
state in a cavity can be controlled by adjusting this geometric phase, which
offers the possibility for protecting its quantum coherence from single-photon
loss. Based on this geometric effect, we realize phase gates for one and two
photonic qubits whose logical basis states are encoded in two quasi-orthogonal
coherent states. We further demonstrate two-cavity gates with symmetric and
asymmetric Fock state encoding schemes. Our method can be directly extended to
implementation of controlled-phase gates between error-correctable logical
qubits.
To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.
In recent years, quantum state engineering and quantum information processing using microwave fields and photons have received increasing attention. In addition, multiqubit gates play an important role in quantum information processing. In this work, we propose to encode a photonic qubit via two arbitrary orthogonal eigenstates (with eigenvalues $\ifmmode\pm\else\textpm\fi{}1$, respectively) of the photon-number parity operator. With such encoding, we then present a single-step method to realize a multi-target-qubit controlled-phase gate with one photonic qubit simultaneously controlling $n\ensuremath{-}1$ target photonic qubits, by employing n microwave cavities coupled to one superconducting flux qutrit. This proposal can be applied not only to implement nonhybrid multi-target-qubit controlled-phase gates using photonic qubits with various encodings, but also to realize hybrid multi-target-qubit controlled-phase gates using photonic qubits with different encodings. The gate realization requires only a single-step operation. The gate operation time does not increase with the number of target qubits. Because the qutrit remains in the ground state during the entire operation, decoherence from the qutrit is greatly suppressed. As an application, we show how to apply this gate to generate a multicavity Greenberger-Horne-Zeilinger (GHZ) entangled state with general expression. Depending on the specific encodings, we further discuss the preparation of several nonhybrid and hybrid GHZ entangled states of multiple cavities. We numerically investigate the circuit-QED experimental feasibility of creating a three-cavity spin-coherent hybrid GHZ state. This proposal can be extended to accomplish the same tasks in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a three-level natural or artificial atom.
We propose an efficient scheme for implementing the universal controlled-phase gate with logical qubits encoded in the superpositions of 2d circularly distributed coherent states (d is a positive integer), which have the advantage of protecting quantum information against the $(d\ensuremath{-}1)$-photon loss errors. We first demonstrate explicitly how to engineer dispersive interaction between the microwave cavity modes and multilevel transmon ancilla in circuit quantum electro-dynamical (QED) system. With the cat-state qubits, we realize the two-qubit controlled phase gate, and its operation time scales as 1/d. This means that it will be less susceptible to environmental disturbances if we employ larger d to encode information. Finally, we employ the experimentally reachable parameters in circuit QED system to numerically study the influence of the photon loss, the qubit relaxation, and the Kerr nonlinearity. The average fidelity for a controlled-phase gate has reached 0.9955 for d=8 when the system imperfections are considered. The results demonstrate the great potential of our scheme for quantum computation in circuit QED system.
The large available Hilbert space and high coherence of cavity resonators make these systems an interesting resource for storing encoded quantum bits. To perform a quantum gate on this encoded information, however, complex nonlinear operations must be applied to the many levels of the oscillator simultaneously. In this work, we introduce the selective number-dependent arbitrary phase (snap) gate, which imparts a different phase to each Fock-state component using an off-resonantly coupled qubit. We show that the snap gate allows control over the quantum phases by correcting the unwanted phase evolution due to the Kerr effect. Furthermore, by combining the snap gate with oscillator displacements, we create a one-photon Fock state with high fidelity. Using just these two controls, one can construct arbitrary unitary operations, offering a scalable route to performing logical manipulations on oscillator-encoded qubits.
Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a paradigm, where quantum logic operations are realized through geometric phase manipulation that has some intrinsic noise-resilient advantages and may enable simplified implementation of multi-qubit gates compared to the dynamical approach. Here we report observation of a continuous-variable geometric phase and demonstrate a quantum gate protocol based on this phase in a superconducting circuit, where five qubits are controllably coupled to a resonator. Our geometric approach allows for one-step implementation of n-qubit controlled-phase gates, which represents a remarkable advantage compared to gate decomposition methods, where the number of required steps dramatically increases with n. Following this approach, we realize these gates with n up to 4, verifying the high efficiency of this geometric manipulation for quantum computation.
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 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 ∣ φ 〉 (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.