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 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.
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 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.
Recently, remote-controlled quantum information processing has been proposed for its applications in secure quantum processing protocols and distributed quantum networks. For remote-controlled quantum gates, the experimental realization of controlled unitary (CU) gates between any quantum gates is an essential task. Here, we propose and experimentally demonstrate a scheme for implementing CU gates between arbitrary pairs of unitary gates using the polarization and time-bin degrees of freedom of single-photons. Then, we experimentally implement remote-controlled single-qubit unitary gates by controlling either the state preparation or measurement of the control qubit with high process fidelities. We believe that the proposed remote-controlled quantum gate model can pave the way for secure and efficient quantum information processing.
Processes with indefinite causal orders (ICOs), such as the quantum switch, are higher-order quantum processes that superpose the order in which quantum operations are performed. Such coherent control yields computational advantages but is not faithfully captured by existing quantum programming languages: either they are restricted to the unitary case, and thus cannot combine ICOs with measurement, or they treat coherent control nonlinearly. In both cases, they do not realize the full computational power of ICOs. We introduce a higher-order quantum functional language that supports general quantum computation, not merely the permutation of channels, and whose linear type system allows quantum control to be well-defined beyond the unitary case, on arbitrary quantum channels. We equip this language with a small-step operational semantics that synchronizes measurement outcomes across superposed branches, using device references and a memory function. We also give a denotational semantics by means of completely positive maps. With linearity as the only constraint, some well-typed terms would denote unphysical maps. We therefore impose a typing discipline that goes beyond linearity, and interpret programs in the causal category Caus[CPM], under which every well-typed program is physically meaningful, a property that can be checked statically and efficiently. We prove soundness, and study the language's expressive power: it can express every quantum channel at first order, and at second order a large subclass of the so-called quantum circuits with quantum control (QC-QCs), containing the quantum switch. Last but not least, we show that this language is well-designed enough to be extended to the nonlinear setting with recursion.
Quantum entanglement plays an irreplaceable role in various remote quantum information processing tasks. Here we present protocols for generating deterministic and heralded N-qubit entangled states across multiple network nodes. By utilizing a pre-shared maximally entangled state and single-qubit operations within an indefinite causal order framework, the multi-qubit entangled state between distant parties can be generated deterministically. The complex entangled state measurements and multiple pre-shared entangled states, are essential in conventional entanglement swapping technique, but are not required in our approach. This greatly reduces the complexity of the quantum circuit and makes it more experimentally feasible. Furthermore, we develop optical architectures to implement these protocols by encoding qubits in polarization degree of freedom. The results indicate that our protocols significantly improve the efficiency of long-distance entanglement generation and provide a practical framework for establishing large-scale quantum networks.