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arXiv:2607.04672

A Path-Superposition Framework for Quantum Gate Teleportation

Santiago Ávila, Marco Enríquez

quant-phSubmitted Jul 6, 2026• Announced Jul 7, 2026• 0 citations
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Abstract

Quantum gate teleportation enables distant parties to implement nonlocal quantum operations without physically transferring the participating qubits, making it a promising primitive for distributed quantum computing. We introduce a general framework for deterministic quantum gate teleportation based on path superposition, in which the target nonlocal operation is specified through the phase of a preshared maximally entangled resource and a suitable family of path-dependent local unitary operators. The framework establishes general design conditions that guarantee deterministic teleportation after measurement of the control qubits and the application of local correction operations. As representative realizations, we construct teleportation protocols for controlled-NOT (CNOT) and controlled-Z (CZ) gates, demonstrating that different nonlocal operations can be implemented within the same protocol architecture through appropriate choices of the design parameters. We further outline a proof-of-concept photonic realization based on spatial-path and polarization degrees of freedom. The proposed framework identifies path superposition as a versatile resource for quantum gate teleportation and distributed quantum information processing.

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Quantum gate teleportation enables distant parties to implement nonlocal quantum operations without physically transferring the participating qubits, making it a promising primitive for distributed quantum computing. We introduce a general framework for deterministic quantum gate teleportation based on path superposition, in which the target nonlocal operation is specified through the phase of a preshared maximally entangled resource and a suitable family of path-dependent local unitary operators. The framework establishes general design conditions that guarantee deterministic teleportation after measurement of the control qubits and the application of local correction operations. As representative realizations, we construct teleportation protocols for controlled-NOT (CNOT) and controlled-Z (CZ) gates, demonstrating that different nonlocal operations can be implemented within the same protocol architecture through appropriate choices of the design parameters. We further outline a proof-of-concept photonic realization based on spatial-path and polarization degrees of freedom. The proposed framework identifies path superposition as a versatile resource for quantum gate teleportation and distributed quantum information processing.
Abstract Quantum gate teleportation enables spatially separated parties to implement nonlocal quantum operations using preshared entanglement, local operations, measurement, and classical communication. Here, we present a two-branch entanglement-assisted coherent-control architecture for the deterministic remote implementation of nonlocal two-qubit gates. In this architecture, the two parties coherently select between two pairs of local unitary operations acting on their respective input qubits, a structure that can be naturally encoded through spatial-path superposition. The protocol is formulated at the operator level, allowing deterministic operation to be established independently of the input-state parametrization and making its scope explicit. For two-qubit unitary targets, we show that the deterministic branch conditions restrict the nonlocal domain of the balanced two-branch ansatz: apart from local product operations, any implementable nonlocal unitary must be locally unitarily equivalent to the CNOT/CZ class. We construct explicit CNOT and controlled- Z realizations as two representatives of this unique nonlocal equivalence class. We also introduce a photonic path-encoding and destructive branch-readout scheme in which spatial path encodes the coherent-control degree of freedom and polarization carries the computational qubits, illustrating how the proposed architecture can be physically encoded.
Quantum gate teleportation enables the implementation of nonlocal quantum operations without direct interactions between distant nodes. We propose an efficient protocol for implementing arbitrary controlled-unitary (CU) gates acting on two spatially separated parties via indefinite causal order (ICO). By establishing a maximally entanglement between two remote nodes and coherently superposing orders of single-qubit gates, our protocol circumvents the drawback of complex local two-qubit operations. This ICO-based approach enables full programmability of CU gates by adjusting the inherent single-qubit operations, offering advantages over conventional fixed causal-order methods in terms of reduced circuit complexity and improved experimental flexibility. Furthermore, we develop an optical construction to implement the polarization CU gate using a stable and reciprocal Sagnac interferometer. Our work establishes a practical framework for scalable distributed quantum computation with flexible operations.
Quantum gate teleportation provides an approach to introduce nonlinear interactions between long-distance qubits, facilitating distributed quantum computation. We present two alternative protocols for deterministically teleporting controlled-not (cnot) and controlled-phase-flip (cpf) gates, using minimal resources---one entangled qubit (ebit) and two classical bits (cbits). Our protocols eliminate the need for local cnot gates at each party, which are typically required in the standard quantum circuit model [Eisert et al. Phys. Rev. A 62, 052317 (2000)]. Instead, by using a superposition of single-qubit gate orders, our approach makes quantum gate teleportation more experimentally feasible and flexible. Remarkably, the teleportation of the cpf gate and other two-qubit controlled unitary gates can be achieved by adjusting inherent single-qubit operations, reducing the need for single-qubit gates in cnot-based constructions. Additionally, we develop two optical architectures for the teleportation of these gates. The polarization-based and transverse spatial-based setups show that this approach is more feasible and practical, and pave a way for a distributed quantum computing network.
Gate teleportation allows us to implement a nonlocal unitary using local operations, classical communication (LOCC), and a shared entangled state. Known deterministic teleportation protocols consume at least one full ebit and achieve optimal entanglement consumption only for Clifford gates. Here, we present a deterministic LOCC protocol for implementing the two-qubit controlled-phase gate Uφ=diag(1,1,1,eiφ)U_φ=\mathrm{diag}(1,1,1,e^{i φ})Uφ​=diag(1,1,1,eiφ) with φ∈[0,π]φ\in [0,π]φ∈[0,π] whose entanglement consumption is close to optimal for every φφφ. In particular, vanishing rotation angles require vanishing entanglement.
Large-scale quantum computers will require quantum gate operations between widely separated qubits. A method for implementing such operations, known as quantum gate teleportation (QGT), requires only local operations, classical communication, and shared entanglement. We demonstrate QGT in a scalable architecture by deterministically teleporting a controlled-NOT (CNOT) gate between two qubits in spatially separated locations in an ion trap. The entanglement fidelity of our teleported CNOT is in the interval (0.845, 0.872) at the 95% confidence level. The implementation combines ion shuttling with individually addressed single-qubit rotations and detections, same- and mixed-species two-qubit gates, and real-time conditional operations, thereby demonstrating essential tools for scaling trapped-ion quantum computers combined in a single device.
Quantum networks provide a novel framework for quantum information processing, significantly improving system capacity through the interconnection of modular quantum nodes. Beyond the capability to distribute quantum states, the ability to remotely control quantum gates is a pivotal step for quantum networks. Here, we implement high-fidelity quantum controlled-not (cnot) gate teleportation with high-dimensional path encoded silicon photonic integrated circuits. Based on on-chip generation of the path-entangled quantum state, cnot gate operation, and chip-to-chip quantum photonic interconnect, the cnot gate is teleported between two remote quantum nodes connected by the single-mode optical fiber. Equip with 5 m (1 km)-long interconnecting fiber, quantum gate teleportation is verified by entangling remote qubits with 95.69%±1.19% (94.07%±1.54%) average fidelity and gate tomography with 94.81%±0.81% (93.04%±1.09%) fidelity. These results advance the realization of large-scale and practical quantum networks with photonic integrated circuits.