Parallel Teleportation via AME(5,2) States on IBM Quantum Hardware

AI summary

Overview

Research area: Quantum communication and quantum information processing — specifically multipartite entanglement (Absolutely Maximally Entangled states) as a networking resource, demonstrated on superconducting quantum hardware.

Technical level: Advanced. The paper assumes familiarity with Bell measurements, Clifford circuits, Pauli frames, entanglement fidelity and dynamical decoupling. The conceptual motivation is accessible, but the decoder construction and error-mitigation methodology are specialist material.

Scope: A hardware demonstration on the 156-qubit ibm_pittsburgh processor that a single shared AME(5,2) state can supply two teleportation channels in parallel and retain entanglement across both channels through three successive teleportation rounds.

What This Paper Is About

Normally, teleporting two qubits requires two separately distributed Bell pairs. An AME(5,2) state — a five-qubit state in which every pair of qubits is maximally mixed, so all its information lives in non-local correlations — could instead serve as one shared resource from which two Bell pairs are extracted by a joint three-qubit decoding operation, allowing two qubits to be teleported in parallel. The problem the authors address is that experimental implementations of this idea are scarce, and the one prior related demonstration on IBM hardware was limited to a single round of application and had rather low fidelity. The goal is therefore to build compact decoders for this resource and test, on real hardware over multiple rounds, whether the resulting channels actually keep their entanglement.

Key Contributions

1. Compact decoders for every role assignment. For each of the 60 inequivalent sender-receiver assignments of the five AME qubits, the authors enumerate 64 Clifford completions of the decoder's action, synthesise them via the Bravyi-Maslov Clifford decomposition, and verify the target identity numerically. Every assignment admits a decoder with three logical two-qubit gates plus single-qubit gates. Assignments are ranked lexicographically by logical two-qubit-gate count, single-qubit gate count and depth; the two extremes benchmarked on hardware are rank 1 (V_014) and rank 58 (V_234).

2. A cascaded, multi-round hardware experiment. Three successive rounds of parallel teleportation are run on ibm_pittsburgh, with a fresh five-qubit AME register per round and each round's logical output feeding the next round's input, while the same reference qubits are retained throughout. Checkpoints R0 (no teleportation) through R3 (three rounds) are compared.

3. Schedule-level optimisations quantified separately. Two strategies — parallelisation of independent operations and classical Pauli frame post-processing instead of physical mid-circuit feed-forward — are timed independently. Relative to sequential feed-forward, the combined schedule shortens from approximately 23.9 to 14.5 μs for rank 1 (39.4%, 9.42 μs) and from 25.3 to 16.2 μs for rank 58 (35.9%, 9.11 μs).

4. A controlled comparison of decoder depth and dynamical decoupling. Two decoder constructions (depth six vs depth ten) and three DD settings (none, XX, XY4) at Qiskit optimisation levels 2 and 3 are compared using baseline-adjusted, M3-mitigated entanglement fidelities with pointwise 99% confidence intervals.

Main Findings

• Entanglement survives three rounds on both channels. With rank 1, XY4 and optimisation level 2, the M3-mitigated final fidelities at R3 are 0.704 ± 0.028 and 0.680 ± 0.022, where uncertainties are pointwise 99% confidence-interval half-widths over eight trials. The corresponding lower interval bounds, 0.676 and 0.658, exceed the 1/2 separability threshold, as do the raw lower bounds.

• Fidelity declines monotonically across rounds. For rank 1 with XY4, the channel means fall from (0.983, 0.988) at R0 to (0.903, 0.904) at R1, (0.817, 0.800) at R2, and (0.704 ± 0.028, 0.680 ± 0.022) at R3. Rank 58 follows the same trend: (0.973, 0.981) at R0, (0.872, 0.873) at R1, (0.760, 0.770) at R2, and (0.655 ± 0.059, 0.663 ± 0.036) at R3.

• Readout mitigation is not doing the heavy lifting. Raw R3 fidelities are (0.703 ± 0.029, 0.678 ± 0.022) for rank 1 and (0.654 ± 0.059, 0.662 ± 0.036) for rank 58 — close to the M3-mitigated values, especially at the last round.

• The shallower decoder generally retains more fidelity. Rank 1 uses five single-qubit gates and depth six versus thirteen single-qubit gates and depth ten for rank 58, both with three CNOTs. At level 2, the baseline-adjusted rank 1 advantage is 2.12, 4.78 and 3.88 percentage points on channel A and 2.39, 2.31 and 0.96 percentage points on channel B at R1, R2 and R3. The R3 intervals for these between-rank differences include zero, so the ordering is not resolved at every round.

• XY4 generally beats XX and no DD. For rank 1 at level 2, M3-mitigated R3 means rise from (0.639, 0.643) without DD to (0.695, 0.668) with XX and (0.704, 0.680) with XY4. XY4 has better mean retention in eleven of twelve rank-channel comparisons at R1–R3; the exception is rank 58 channel A at R3, where XX gives 0.658 and XY4 gives 0.655. The XY4-over-no-DD advantage at R3 is 6.51 ± 6.39 percentage points on A and 3.73 ± 6.08 on B, the latter interval including zero.

• Higher optimisation level is not uniformly better. For XY4, level-3 M3 endpoints are (0.693, 0.676) for rank 1 and (0.643, 0.668) for rank 58, so level 2 is slightly better in most comparisons and is the focus of the analysis.

• The two channels are not perfectly balanced. For rank 1, both DD sequences show greater baseline-relative loss on B than on A, with the XY4 difference reaching −2.83 ± 2.65 percentage points at R3; for rank 58 the corresponding 0.09 ± 2.20 is consistent with comparable losses.

• Feed-forward waits were measured directly. Hardware compiler traces give scheduled feedback waits of (0.956, 0.956, 0.944) μs for rank 1 and (1.01, 0.948, 0.964) μs for rank 58 at R1–R3, measured from the end of the last Bell-readout capture to the start of the first conditional X correction.

Methodology in Plain English

The authors start from a five-qubit entangled resource with a special property: look at any one or two of its qubits and they look completely random on their own, so all the usable information sits in how the qubits are correlated with each other. Two of the five qubits are designated as "senders" and bypass the decoder; the remaining three are jointly processed by a small fixed circuit that converts the shared correlations into two ordinary Bell pairs, which then support two ordinary teleportation channels. Crucially, which qubit plays which role can be chosen after the resource is built — that is the flexibility the protocol offers.

To find good decoder circuits, the authors search over all the ways of completing the decoder's required action, keep the cheapest ones, and pick two to run: the shallowest (rank 1) and a deliberately more expensive one (rank 58) as a comparison point.

The experiment prepares two Bell pairs between reference qubits and input qubits, then repeatedly teleports the input halves through fresh AME registers. After each round, the output becomes the next round's input, while the reference qubits stay put — so if entanglement with the references survives, the teleportation genuinely transferred the state rather than copying or destroying it. Fidelity is computed from measured XX, YY and ZZ correlations using the standard formula (1 + ⟨XX⟩ − ⟨YY⟩ + ⟨ZZ⟩)/4, and a value above 1/2 certifies entanglement.

Two engineering tricks keep the circuits short. First, operations that do not depend on each other are allowed to overlap across rounds instead of being forced into a fixed sequence. Second, instead of physically applying the Pauli corrections that depend on Bell-measurement outcomes — which would mean waiting for mid-circuit readout — the authors track those corrections classically and apply sign changes only when computing the final correlations. Because all operations are Clifford, the Pauli byproducts stay Pauli operators as they propagate, so this bookkeeping is exact. They also compare no dynamical decoupling, XX and XY4 pulse sequences inserted into idle intervals, use Mapomatic to choose a qubit layout with matched readout error across the two channels, and apply matrix-free measurement error mitigation to the results. Each tomography setting and readout calibration uses 5000 shots, and results are means over eight selected trials.

Why This Matters

Impact on research. The work moves AME-assisted parallel teleportation from a protocol proposal to a measured, multi-round hardware result, and shows that the resource's flexibility — choosing who sends and who receives after the state is prepared — costs something quantifiable in fidelity but still leaves entanglement above the separability threshold. It also supplies a reusable library of verified compact decoders for all 60 role assignments, plus a concrete demonstration that classical Pauli frame tracking plus parallelisation is worth roughly a 40% shorter schedule than sequential physical feed-forward on this processor.

Real-world applications:

• Quantum repeaters and network nodes. The experiment is explicitly motivated by repeaters, where entanglement must survive noisy processing at intermediate nodes. A shared multipartite resource that can be re-roled into different channel assignments is a candidate alternative to pre-allocated Bell pairs.

• Reconfigurable multichannel communication. Because sender and receiver roles are decided after resource preparation, a network could adapt channel assignments to demand rather than committing to a fixed pairing at distribution time.

• Quantum secret sharing. AME states connect directly to secret-sharing schemes, where authorised subsets must reconstruct a secret while unauthorised subsets learn nothing.

• Holographic quantum error correction. AME states serve as toy models of holographic codes relevant to black hole information puzzles, and the paper frames the experiment as an accessible experimental entry point to that line of work.

Industry relevance. The demonstration runs on IBM's cloud-accessible superconducting hardware with standard Qiskit tooling, so the schedule-shortening and decoder-selection lessons transfer directly to anyone building multi-round entanglement protocols on near-term processors. The results also give hardware teams concrete guidance: circuit depth and single-qubit gate count matter, but so do layout choice, coupler calibration and which DD sequence matches the idle-interval structure.

Future Directions

• Decoder selection as a hardware-aware problem. The authors argue future decoder choice should weigh logical circuit complexity alongside qubit connectivity, gate durations and the idle time each channel actually experiences, rather than depth alone.

• Interleaved benchmarking to control drift. Since data were collected over several days, they propose running different decoder, layout and DD combinations in interleaved runs within the same calibration sessions to reduce the influence of hardware drift.

• More rounds and larger AME resources. Extending the cascade would test how entanglement retention scales with circuit length and channel count, and would require assessing the sampling and readout-mitigation overhead of longer Bell-measurement histories.

• Remote-node parallel teleportation. Moving beyond a single processor, the paper points to optically linked trapped-ion modules as a promising platform, while flagging that distributing the AME resource intact and enabling joint receiver-side decoding remain open challenges. Connections to fusion-based quantum computation and loss-tolerant communication are also raised as untested possibilities.

Target Audience

Quantum communication researchers and experimentalists working on multipartite entanglement, entanglement distribution and repeater architectures; quantum error-correction researchers interested in the AME / [[5,1,3]] code connection; and quantum-hardware and compiler engineers who care about how circuit depth, layout selection, dynamical decoupling and mid-circuit feed-forward costs translate into measured fidelity on superconducting processors. Readers seeking an entry point to AME states will find the supplementary background helpful, but the main text presumes comfort with stabiliser formalism and fidelity estimation.

Authors’ abstract

The five-qubit Absolutely Maximally Entangled AME$(5,2)$ state, whose every pair of qubits is maximally mixed so that all its information lives in non-local correlations, could in principle serve as a single shared quantum networking resource for teleporting two unknown qubits in parallel (each via its own Bell measurement and Pauli correction). Nonetheless, its hardware implementations remain scarce despite its theoretical importance. Here, we demonstrate parallel teleportation based on a five-qubit absolutely maximally entangled state, AME$(5,2)$, on the superconducting processor ibm_pittsburgh. We construct three-qubit Clifford decoders that extract two Bell pairs using three logical two-qubit gates for each of 60 inequivalent sender-receiver assignments. Using parallelization and classical Pauli frame post-processing, we retain reference-receiver entanglement on both channels after three teleportation rounds. With XY4 dynamical decoupling and the lowest-cost decoder, the final entanglement fidelities are $0.704\pm0.028$ and $0.680\pm0.022$, where uncertainties are pointwise $99\%$ confidence-interval half-widths over eight trials. Their lower bounds exceed the separability threshold of $1/2$. The decoder with lower circuit depth generally retains higher mean fidelity, and XY4 generally improves on XX. These results establish a hardware demonstration of two-channel entanglement transmission through repeated AME-assisted teleportation and provide compact decoding circuits for reconfigurable multipartite communication.