Quantum Gate Teleportation

Updated 7 July 2026

Quantum gate teleportation is a protocol that implements remote quantum operations by consuming entangled resource states and performing local measurements with classical feedforward.
It leverages specialized measurement bases and correction rules to deterministically teleport both Clifford and non-Clifford gates based on the resource and operational framework.
Its practical applications span modular quantum computing, fault-tolerant logical operations, blind computation, and various experimental platforms ranging from photonic to superconducting systems.

Quantum gate teleportation is a measurement-driven method for implementing a quantum operation by consuming entanglement, performing local operations and measurements, and applying classical feedforward, so that the logical effect of a gate appears on distant or otherwise uncoupled data qubits without a direct two-qubit interaction at the moment of computation. Unlike ordinary state teleportation, the objective is not merely to transfer an unknown state, but to obtain the transformed state $U|\psi\rangle$ , typically up to known Pauli byproducts that are corrected physically or tracked in a Pauli frame. The paradigm appears in remote entangling-gate protocols, non-Clifford and logical-gate implementations, blind circuit execution, higher-dimensional Clifford-hierarchy constructions, and stored-program models based on Choi states (Mendes et al., 2013, Chou et al., 2018, Wang, 2019).

1. Core mechanism and circuit identity

At the operational level, gate teleportation combines the ingredients of ordinary teleportation with a gate-dependent resource or conjugation rule. In the two-qubit formulation studied in basis-dependent analyses, the central condition is

$U_T B_{jk} = V_{jk} U_T,$

where $U_T$ is the target gate, $B_{jk}$ is the basis operator associated with a measurement outcome, and $V_{jk}$ is the correction operator. Deterministic teleportation requires that the correction exist for every outcome and, if only local feedforward is allowed, that $V_{jk}$ factor into single-qubit gates (Mendes et al., 2013).

The resource-state viewpoint makes this mechanism concrete. In the Gottesman–Chuang style used in optical demonstrations, one prepares a special multi-qubit entangled state offline, performs Bell-state measurements between the input qubits and part of that resource, and then applies single-qubit corrections conditioned on the Bell outcomes. The remaining qubits become the output of the desired gate. The essential distinction from standard teleportation is that “the input states have undergone a CNOT gate after teleportation” (Gao et al., 2010).

When a gate is realized through repeated teleportation steps, byproduct operators accumulate. In the circuit-model blind-computation formulation, a teleported sequence $U_3U_2U_1|\psi\rangle$ yields

$P_3U_3P_2U_2P_1U_1|\psi\rangle,$

with $P_i$ determined by Bell-measurement outcomes. The protocol remains computationally useful because later gates or later correction stages are adapted to the running Pauli frame; for rotation-based decompositions this relies on explicit commutation identities such as $R_x(\beta)Z=ZR_x(-\beta)$ and $U_T B_{jk} = V_{jk} U_T,$ 0 (Zhang, 2018).

A common misconception is that nonlocal gate implementation must proceed by teleporting states to one location, applying the gate there, and teleporting them back. In the trapped-ion analysis, that state-teleportation approach requires at least two shared entangled pairs for a nonlocal two-qubit gate, whereas a teleported CNOT following the Eisert-style protocol uses only one shared entangled pair together with local operations and classical communication (Wan et al., 2019).

2. Teleportability, measurement basis, and gate classes

The measurement basis is not an incidental design choice. In a general analysis based on the KAK decomposition

$U_T B_{jk} = V_{jk} U_T,$ 1

deterministic teleportation occurs only when a basis-dependent separability condition holds for all measurement outcomes; if it holds only for some outcomes, teleportation is probabilistic, with success probability $U_T B_{jk} = V_{jk} U_T,$ 2 (Mendes et al., 2013).

This basis dependence produces a sharp classification. With the Bell basis, the correction operators are Pauli matrices and Clifford gates are teleported deterministically because Clifford conjugation preserves the Pauli group. The same gate can change class under a different measurement basis: in the examples reported, CNOT is deterministically teleported with the Bell basis, probabilistically teleported with the basis $U_T B_{jk} = V_{jk} U_T,$ 3, and not teleported with the basis $U_T B_{jk} = V_{jk} U_T,$ 4. The same work also gives explicit non-Clifford deterministic examples, including the diagonal family $U_T B_{jk} = V_{jk} U_T,$ 5; the gates

$U_T B_{jk} = V_{jk} U_T,$ 6

are deterministically teleported with $U_T B_{jk} = V_{jk} U_T,$ 7 but do not belong to the Clifford group (Mendes et al., 2013).

The same analysis also isolates structural limitations. A basis containing even one disentangled state has zero teleportation capability because the corresponding basis matrix is not unitary. Likewise, replacing two Bell pairs with the genuinely four-way entangled resource

$U_T B_{jk} = V_{jk} U_T,$ 8

does not straightforwardly improve gate teleportation. In that construction the output becomes a superposition of differently transformed states, and the authors conclude that successful deterministic teleportation of the two-qubit gate itself cannot be achieved with that resource (Mendes et al., 2013).

This suggests that “more entanglement” is not, by itself, the right criterion. What matters is compatibility among the target gate, the entangled resource, and the measurement basis.

Gate teleportation can be used to hide a circuit, not only to implement it remotely. In the GTUBQC protocol for universal blind quantum computation, a trusted center prepares arbitrary two-qubit computational states and Bell pairs, Alice has only $U_T B_{jk} = V_{jk} U_T,$ 9 and $U_T$ 0 capability and no quantum memory, and two servers perform rotation operations, controlled rotations, and Bell measurements. The computation is expressed in terms of single-qubit rotations, with

$U_T$ 1

and blindness is achieved by encrypting the rotation angles, splitting tasks between two servers, and tracking teleportation byproducts in a Pauli frame. The protocol proves blindness of inputs, algorithms, and outputs, includes a test process based on entanglement swapping, and is applied to a blind quantum Fourier transform (Zhang, 2018).

In higher-dimensional systems, efficient gate teleportation is organized by the Clifford hierarchy. For prime-dimensional qudits, semi-Clifford gates are those of the form

$U_T$ 2

with $U_T$ 3 Clifford and $U_T$ 4 diagonal. The qudit generalization of one-bit teleportation implements such gates efficiently from the magic state $U_T$ 5. Two structural results are especially strong: every third-level gate of one qudit, in any prime dimension, is semi-Clifford, and every third-level gate of two qutrits is semi-Clifford. In these cases efficient gate teleportation follows directly (Silva, 2020).

Logical teleportation circuits supply the same skeleton used by fault-tolerant gate teleportation. On the planar topological $U_T$ 6 color code, or Steane code, trapped-ion experiments implemented logical teleportation with both transversal gates and lattice surgery, using real-time syndrome decoding and Pauli-frame updates. The reported logical process fidelities are $U_T$ 7 for the transversal teleportation circuit and $U_T$ 8 for the lattice-surgery teleportation circuit; the simpler $U_T$ 9 lattice-surgery version is explicitly described as usable for gate teleportation and code-switching (Ryan-Anderson et al., 2024). A plausible implication is that fault-tolerant gate teleportation inherits not only the Bell-pair-and-joint-measurement structure, but also the real-time decoding and correction burden of logical state teleportation.

4. Experimental realizations across platforms

Experimental work spans photonic, trapped-ion, superconducting, and solid-state network platforms. The implementations differ in whether the protocol is post-selected or unconditional, whether the data qubits are physical or logical, and whether feedforward is applied in real time or absorbed into offline branch selection.

Platform and teleported gate	Representative reported performance	Remarks
Six-photon optical CNOT / four-photon hyper-entangled CPHASE (Gao et al., 2010)	CNOT truth-table fidelity $B_{jk}$ 0; CPHASE $B_{jk}$ 1	Smallest nontrivial Gottesman–Chuang module in linear optics
Trapped-ion processor, teleported CNOT between separated qubits (Wan et al., 2019)	Entanglement fidelity in $B_{jk}$ 2 at 95% confidence level	Deterministic remote gate with shuttling, mixed-species gates, and feedforward
Superconducting cavities, deterministic teleported logical CNOT (Chou et al., 2018)	Raw process fidelity $B_{jk}$ 3; inferred gate fidelity $B_{jk}$ 4	Gate enacted between logical qubits encoded in bosonic cavities
Chip-to-chip silicon photonic CNOT (Feng et al., 2024)	5 m: state fidelity $B_{jk}$ 5, process fidelity $B_{jk}$ 6; 1 km: $B_{jk}$ 7, $B_{jk}$ 8	Remote gate between two photonic chips linked by fiber
Remote NV-diamond CNOT between nuclear-spin registers (Iuliano et al., 8 Jan 2026)	Bell-state fidelity $B_{jk}$ 9; GHZ fidelity $V_{jk}$ 0	Unconditional, with single-shot readout and real-time feedforward
Silicon nanophotonic on-chip CNOT teleported to a non-local CNOT (Chang et al., 22 Jul 2025)	Truth-table fidelity $V_{jk}$ 1; process fidelity $V_{jk}$ 2; average non-local CNOT fidelity $V_{jk}$ 3	Post-selected photonic implementation of a teleported chip-scale CNOT

The superconducting-cavity experiment is notable because the gate acts between logical qubits with negligible direct coupling between the data cavities, using communication transmons, Bell-pair generation, $V_{jk}$ 4- and $V_{jk}$ 5-basis measurements, and real-time adaptive control within about $V_{jk}$ 6 (Chou et al., 2018). The diamond-NV work is notable for the opposite architectural emphasis: the communication qubits are NV electron spins, the data qubits are long-lived $V_{jk}$ 7C nuclear spins, and the gate is unconditional in the sense that all intermediate measurement outcomes are accepted and corrected without post-selection (Iuliano et al., 8 Jan 2026).

A related but distinct experimental milestone is deterministic teleportation of propagating microwave coherent states over $V_{jk}$ 8 cm, with fidelity $V_{jk}$ 9 exceeding the no-cloning threshold $V_{jk}$ 0 for $V_{jk}$ 1. That experiment is explicitly not a gate-teleportation demonstration, but it realizes the entanglement distribution, Bell-type measurement, and analog feedforward infrastructure that the authors identify as a key ingredient for teleportation-based quantum gates in modular superconducting computing (Fedorov et al., 2021).

5. Modular architectures, network execution, and compilation

In modular architectures, gate teleportation separates each node into long-lived data qubits and short-lived communication qubits. The teleported logical CNOT between bosonic cavities embodies this model directly: data cavities act as memories, communication transmons distribute entanglement and mediate the gate, and real-time adaptive control turns branch-dependent outcomes into a deterministic logical operation (Chou et al., 2018). The same three-part decomposition—remote entanglement, local quantum logic, and classical feedforward—also structures the solid-state NV realization of an unconditional remote CNOT (Iuliano et al., 8 Jan 2026).

Network-level studies treat gate teleportation as an execution primitive rather than only a physical demonstration. In multi-node simulations with SquidASM, arbitrary two-qubit Clifford gates and the Toffoli gate are teleported across noisy networks. For two-qubit Clifford gates, correction operations are constructed automatically by conjugating the Pauli basis under the target gate; for Toffoli, the correction becomes more complex because the gate is non-Clifford and belongs to the third level of the Clifford hierarchy. The same work uses gate teleportation for gate cutting and states that it enables precise gate cutting without additional classical overhead. Across the simulated regimes, device noise affects output fidelity more strongly than quantum-link noise (Uotila, 2024).

Compilation work extends the same logic to routing. One line uses ordinary state teleportation as a routing primitive in A $V_{jk}$ 2-based mapping on IBM Q Tokyo, treating Bell-pair channels as virtual long-range edges and reporting about $V_{jk}$ 3, and in some cases almost $V_{jk}$ 4, overhead reduction relative to SWAP-only mapping (Hillmich et al., 2020). A more direct gate-teleportation routing framework, RTG, uses auxiliary qubits to create virtual edges for teleported CNOT or controlled- $V_{jk}$ 5 interactions on heavy-hexagon topologies. Its optimization criterion combines temporal depth,

$V_{jk}$ 6

with a heuristic two-qubit error cost, and the reported benchmark improvements are roughly $V_{jk}$ 7 depth reduction in selected algorithms, with implemented QAOA reductions up to around $V_{jk}$ 8 in the best case (Babu et al., 6 Feb 2025).

These compiler results do not erase the distinction between state teleportation and gate teleportation. Rather, they show that both can be recast as connectivity resources: one moves quantum states across the coupling graph, the other synthesizes a remote interaction across that graph.

6. Stored programs, complexity, and conceptual extensions

A more abstract formulation identifies a gate or channel with its Choi state. If

$V_{jk}$ 9

then $U_3U_2U_1|\psi\rangle$ 0 is the stored quantum program for the channel $U_3U_2U_1|\psi\rangle$ 1. In the symmetry-based stored-program model, teleportation is interpreted as a symmetry phenomenon of the underlying tensor network, and deterministic execution is recovered for symmetric unitaries or, more generally, by factoring an arbitrary unitary into two symmetric unitaries. This yields a stored-program architecture in which Choi states are executed, composed, and teleported as quantum software (Wang, 2019).

Gate teleportation also has a complexity-theoretic role. For the single-qubit Clifford gate-teleportation family $U_3U_2U_1|\psi\rangle$ 2, the output is an $U_3U_2U_1|\psi\rangle$ 3-tuple of Pauli labels determined by Bell measurements on a cyclic arrangement of Bell pairs and Clifford gates. Even under the very weak notion of possibilistic simulation—outputting any string of nonzero probability—the problem cannot be solved by constant-depth bounded-fan-in classical circuits. The lower bound is unconditional and is obtained by reduction to parity (Caha et al., 2022). This places gate-teleportation circuits among the simplest quantum circuit families with a provable separation from $U_3U_2U_1|\psi\rangle$ 4-style classical computation.

Specialized extensions widen the conceptual boundary of the subject. One proposal uses a chained quantum Zeno effect to realize a universal exchange-free controlled-phase gate and then builds deterministic teleportation, complete Bell detection, and telecloning without particle exchange between control and target systems (Salih et al., 2020). Another related but distinct line inserts a cubic phase gate into a continuous-variable teleportation resource to reduce added noise; in the vacuum-state example, the reported fidelity exceeds $U_3U_2U_1|\psi\rangle$ 5 for $U_3U_2U_1|\psi\rangle$ 6 (Zinatullin et al., 2021). These cases are not equivalent to the standard remote-gate paradigm, but they show that teleportation can serve simultaneously as a communication primitive, a computational primitive, and a framework for modifying or encoding quantum dynamics.

Quantum gate teleportation is therefore best understood not as a single protocol, but as a unifying mechanism. In one regime it provides remote entangling gates for modular hardware; in another it implements non-Clifford or logical operations through resource states and feedforward; in another it supports blind computation, gate cutting, or stored-program execution. Across these regimes, the recurring technical themes are the same: entanglement as an offline resource, local measurements as the interface between quantum and classical control, and correction rules whose tractability depends sharply on the algebraic class of the teleported gate.