Realization of quantum gates with multiple control qubits or multiple target qubits in a cavity

Waseem, Muhammad; Irfan, Muhammad; Qamar, Shahid

doi:10.1007/s11128-015-0947-7

Cited by 10 publications

(6 citation statements)

References 36 publications

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“…We stress that this work is on the implementation of a MCP gate with multiple control qubits simultaneously controlling one target qubit (Fig. 1b), thus it is obviously different from the previous works (e.g., [20,[60][61][62][63][64][65][66][67][68]) on the realization of a multi-target-qubit gate with one control qubit simultaneously controlling multiple target qubits (Fig. 2).…”

Section: Introductionmentioning

confidence: 79%

“…1b), with multiple qubits simultaneously controlling one target qubit, is denoted as a MCP gate throughout this paper. Over the past years, a number of theoretical proposals have been put forward for directly realizing a Toffoli gate or a MCP gate using matter qubits, such as trapped ionic qubits [14][15][16], quantum-dot qubits [17], atomic qubits [18][19][20][21][22][23][24][25],…”

Section: Introductionmentioning

confidence: 99%

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

Su¹,

Liang²,

Yang³

2022

Preprint

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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.

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Section: Introductionmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

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

Su¹,

Liang²,

Yang³

2022

Preprint

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“…There has been plenty of investigations on multiple control Toffoli gates (multi-qubit controlled NOT gate). [77][78][79][80] Among them the Toffoli gates with relative phase are generally simpler [79] and, since our algorithm is unaffected by any relative phase transform on the ancillary qubit, the best choice for us may be the one proposed in ref. [79], which transforms the state |1⟩ ⊗n |0⟩ to e i𝜋∕2 |1⟩ ⊗n |1⟩ while keeping any other states invariant via 8n − 17 T gates, 6n − 12 CNOT gates, 4n − 10 Hadamard gates and, ⌈ n−3 2 ⌉ ancillary qubits initialized and returned to |0⟩.…”

Section: Appendix A: Multiple Control Toffoli Gatementioning

confidence: 99%

Quantum‐Accelerated Algorithms for Generating Random Primitive Polynomials Over Finite Fields

Huang,

Yin,

Chen

et al. 2023

Adv Quantum Tech

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Primitive polynomials over finite fields are crucial resources with broad applications across various domains in computer science, including classical pseudo‐random number generation, coding theory, and post‐quantum cryptography. Nevertheless, the pursuit of an efficient classical algorithm for generating random primitive polynomials over finite fields remains an ongoing challenge. In this work, it shows how this problem can be solved efficiently with the help of quantum computers. Moreover, the designs of specific quantum circuits to implement them are also presented. The research paves the way for the rapid and real‐time generation of random primitive polynomials in diverse quantum communication and computation applications.

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“…Therefore, it is worth finding effective ways to directly implement multi-target-qubit quantum gates. We should point out that over the past years, many efficient methods have been proposed to directly realize multi-target-qubit gates in various physical systems [54,[76][77][78][79][80]. However, it is noted that the previous works [54,[76][77][78][79][80] focus on the implementation of a non-hybrid multi-target-qubit gate.…”

Section: Introductionmentioning

confidence: 99%

“…We should point out that over the past years, many efficient methods have been proposed to directly realize multi-target-qubit gates in various physical systems [54,[76][77][78][79][80]. However, it is noted that the previous works [54,[76][77][78][79][80] focus on the implementation of a non-hybrid multi-target-qubit gate. They are different from the present work which aims at implementing a hybrid multi-target-qubit gate .…”

Section: Introductionmentioning

confidence: 99%

Single-step implementation of a hybrid controlled-not gate with one superconducting qubit simultaneously controlling multiple target cat-state qubits

Yang

2022

Phys. Rev. A

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Hybrid quantum gates have recently drawn considerable attention. They play significant roles in connecting quantum information processors with qubits of different encoding and have important applications in the transmission of quantum states between a quantum processor and a quantum memory. In this work, we propose a single-step implementation of a multi-target-qubit controlled-NOT gate with one superconducting (SC) qubit simultaneously controlling n target cat-state qubits. In this proposal, the gate is implemented with n microwave cavities coupled to a three-level SC qutrit. The two logic states of the control SC qubit are represented by the two lowest levels of the qutrit, while the two logic states of each target cat-state qubit are represented by two quasi-orthogonal cat states of a microwave cavity. This proposal operates essentially through the dispersive coupling of each cavity with the qutrit. The gate realization is quite simple because it requires only a single-step operation. There is no need of applying a classical pulse or performing a measurement. The gate operation time is independent of the number of target qubits, thus it does not increase as the number of target qubits increases. Moreover, because the third higher energy level of the qutrit is not occupied during the gate operation, decoherence from the qutrit is greatly suppressed. As an application of this hybrid multi-target-qubit gate, we further discuss the generation of a hybrid Greenberger-Horne-Zeilinger (GHZ) entangled state of SC qubits and cat-state qubits. As an example, we numerically analyze the experimental feasibility of generating a hybrid GHZ state of one SC qubit and three cat-state qubits within present circuit QED technology. This proposal is quite general and can be extended to implement a hybrid controlled-NOT gate with one matter qubit (of different type) simultaneously controlling multiple target cat-state qubits in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a three-level natural or artificial atom.

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Realization of quantum gates with multiple control qubits or multiple target qubits in a cavity

Cited by 10 publications

References 36 publications

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

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

Quantum‐Accelerated Algorithms for Generating Random Primitive Polynomials Over Finite Fields

Single-step implementation of a hybrid controlled-not gate with one superconducting qubit simultaneously controlling multiple target cat-state qubits

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