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Quantifying Teleportation Overhead in Distributed Unitary Coupled-Cluster Ans\"atze
Grier M. Jones, Hassan Tariq Shafi, Zixuan Wang, Thomas Trenty, Zachary Vernec, Hans-Arno Jacobsen
TL;DR
Classical full configuration interaction becomes intractable as quantum-chemistry active spaces grow, while quantum algorithms remain constrained by qubit count and quality. The paper estimates teleportation-based distribution resources for three UCC ansätze on hydrogen chains, comparing naive partitions with TeleSABRE. Across the tested mappings and orderings, UpCCD scales most cleanly, UCCSD requires the largest resource budget, and TeleSABRE reduces Bell-pair costs by more than an order of magnitude versus naive layouts.
Problem
Classical full configuration interaction becomes intractable as active spaces grow, and quantum chemistry algorithms remain constrained by qubit count and quality.
Source: §I · p. 1Method
The study estimates teleportation-based resources for UpCCD, UpCCGSD, and UCCSD circuits on hydrogen chains, comparing naive partitions with TeleSABRE.
Source: §I · p. 1, §IV · p. 2Results
Across tested mappings and orderings, UpCCD had the cleanest scaling, UCCSD demanded the largest resource budget, and TeleSABRE reduced Bell-pair requirements by more than an order of magnitude versus naive orderings.
Source: §V · p. 3Takeaways & Limitations
Routing-aware methods such as TeleSABRE are necessary for realistic, substantially lower resource estimates of distributed execution than crossing-gate counts alone provide.
Source: §IV · p. 3The comparison covers hydrogen-chain simulations; generalization to other molecules and ansätze remains future work.
Source: §V · p. 3
Abstract
from arXiv · showhide
Distributed quantum computing (DQC) has been proposed as a way to scale quantum algorithms for practical applications beyond monolithic quantum processor architectures. Among these applications, quantum chemistry is widely regarded as one of the most promising use cases for quantum computing. In this work, we estimate the distributed-resource requirements of unitary coupled-cluster (UCC) ans\"atze for quantum chemistry, focusing on unitary coupled-cluster singles and doubles (UCCSD), unitary pair coupled-cluster doubles (UpCCD), and unitary pair coupled-cluster with generalized singles and doubles (UpCCGSD) circuits for hydrogen chains. We focus on a teleportation-based approach to DQC, quantitatively comparing a naive distribution method to the output of the TeleSABRE algorithm. For both approaches, we estimate the cost of handling nonlocal two-qubit gates across a fixed midpoint or quarter-point partition, reporting Bell-pair/classical-communication costs in teleportation. Across Jordan-Wigner and Bravyi-Kitaev, we find that UpCCD with spin-blocked Jordan-Wigner ordering gives the most favorable scaling, while UCCSD incurs substantially larger distributed-resource requirements.
I. INTRODUCTION
Classical full configuration interaction becomes intractable as active spaces grow, motivating approximate quantum-chemistry methods and approaches to hardware limits. This work estimates teleportation-based distribution costs for three UCC ansätze and compares naive partitions with TeleSABRE.
I. INTRODUCTION
- Active spaces beyond (22, 22) make full configuration interaction computationally intractable on classical hardware.An active space is denoted by (Ne, No), the numbers of electrons and spatial orbitals.Source: §I · p. 1
- The study compares Bell-pair estimates for naive partitions and TeleSABRE across UpCCD, UpCCGSD, and UCCSD on two coupled 120-qubit square-lattice QPUs.The prior circuit-cutting study found prohibitive sampling overhead for most UCC-derived ansätze.Source: §I · p. 1
- Naive partitioning gives similar results across fermion-to-qubit mappings except for UCCSD, while TeleSABRE greatly reduces Bell-pair requirements compared with naive layouts.The authors report similar scaling for half and quarter partitions.Source: §I · p. 1
A. Quantum Chemistry
The section motivates unitary coupled-cluster methods as alternatives to less tractable or less reliable approaches and distinguishes the UCC variants considered. It frames their wavefunctions through electronic excitations and specifies how the three ansätze restrict those excitations.
A. Quantum Chemistry
- Full configuration interaction captures the exact energy in a one-particle basis but is generally intractable as system size grows; truncated CI can have convergence and size-extensivity problems.Hartree–Fock, a common starting point, fails to capture electron-correlation energy.Source: A. Quantum Chemistry · p. 2
- UCC defines an ansatz wavefunction by applying e^(T−T†) to the Hartree–Fock reference, with T a linear combination of electronic excitations.The paper presents UCC as an alternative to truncated CI variants.Source: A. Quantum Chemistry · p. 2
- UCCSD includes single and double excitations, UpCCD restricts doubles to paired α and β spins in the same spatial orbital, and UpCCGSD combines singles with generalized spin-paired doubles.UpCCGSD generalizes the excitation summation over a general set of orbitals.Source: A. Quantum Chemistry · p. 2
B. Quantum Teleportation Protocols
Distributed quantum computing uses state and gate teleportation for non-local operations between QPUs. Both rely on shared Bell pairs, local operations, classical communication, and measurement-conditioned corrections, but differ in what is transferred and what operation is implemented.
B. Quantum Teleportation Protocols
- State and gate teleportation are the two main primitives for non-local operations in distributed quantum computing.They use shared Bell pairs, local operations, classical communication, and measurement-conditioned corrections.Source: B. Quantum Teleportation Protocols · p. 2
- Gate teleportation implements a controlled-unitary gate without direct physical interaction between QPUs.It enables non-local gate implementation through the teleportation protocol.Source: B. Quantum Teleportation Protocols · p. 2
- State teleportation is an identity at the operator level, but moves qubit-state information between QPUs and changes which local gates are available afterward.Source: B. Quantum Teleportation Protocols · p. 2
C. TeleSABRE
Compilation maps circuit wires to physical qubits and routes operations to respect distributed-system connectivity. TeleSABRE extends SABRE with a heuristic, look-ahead approach that jointly optimizes local swaps and inter-core teleportations.
C. TeleSABRE
- Qubit layout fixes the mapping of circuit wires to physical qubits, while routing rewrites the circuit to satisfy the system’s connectivity.The need is acute when all-to-all circuit connectivity exceeds intra-QPU and inter-QPU connectivity.Source: C. TeleSABRE · p. 2
- TeleSABRE extends SABRE from monolithic to distributed quantum computing, where QPUs connect through entanglement-generation channels for teleportation.Source: C. TeleSABRE · p. 2
- TeleSABRE uses greedy look-ahead to jointly optimize intra-core swaps and inter-core teleportations, prioritizing less expensive intra-core operations.Source: C. TeleSABRE · p. 2
III. COMPUTATIONAL WORKFLOW
The workflow compiles three UCC ansätze for hydrogen chains under JW and BK mappings, then estimates resources using TeleSABRE. Memory and routing-search limits restrict some ansatz and chain-length combinations.
III. COMPUTATIONAL WORKFLOW
- UpCCGSD, UpCCD, and UCCSD circuits are generated in Tequila and considered under both Jordan-Wigner and Bravyi-Kitaev mappings.Compilation is abstract-level and not distribution-aware; arbitrary-angle rotations make resource estimates independent of circuit parameter choices.Source: §III · p. 2
- TeleSABRE uses default settings with up to 100,000 routing iterations across 100 attempts and a weighted 20-gate lookahead heuristic.Layouts are dynamically initialized using round-robin and Hungarian matching; multi-core constraints use edge weighting, full-core penalties, passing-core teleportation, and deadlock resolution capped at 1,000 steps.Source: §III · p. 2
- Memory limits UCCSD estimates beyond H18 for both strategies and TeleSABRE estimates for UpCCGSD beyond H26.Naive UpCCGSD estimates extend to H50; its TeleSABRE limit is attributed to rapid routing-search-space growth for its denser two-qubit gate structure.Source: §III · p. 2
IV. RESULTS AND DISCUSSION
The study compares naive midpoint and quarter-point partitions with TeleSABRE routing for hydrogen-chain circuits. UpCCD has the lowest naive Bell-pair requirements, while TeleSABRE reshapes encoding-dependent resource trends and reports substantially lower Bell-pair budgets than naive orderings.
IV. RESULTS AND DISCUSSION
- UpCCD requires the fewest naive-partition Bell pairs, from 4 for H2 under JW to 2508 for H50 under BK.UCCSD has the steepest increase in gate crossings; UpCCGSD falls between UpCCD and UCCSD, while the UpCCD crossing count is consistent across partition counts and encodings.Source: §IV · p. 3, Figure 1 · p. 3
- Under TeleSABRE, qubit and Bell-pair counts grow more slowly than SWAP and gate counts, and JW and BK resource trends track closely.UpCCD’s four reported metrics scale similarly across the evaluated range; UpCCGSD has substantially larger absolute resource requirements at higher chain lengths and was evaluated only through H26.Source: §IV · p. 3, Figure 2 · p. 3
- TeleSABRE reduces the required Bell-pair budget by more than an order of magnitude compared with naive orderings.The routed resource estimates include SWAPs, total gates, qubits, and Bell pairs for UpCCD and UpCCGSD under JW and BK.Source: §IV · p. 3, Figure 2 · p. 3
- For UpCCGSD, BK requires more Bell pairs than JW at H10, a comparable number at H18, and fewer at H26, unlike the naive ordering trend.Naive partition crossing counts provide an upper bound on gate teleportations, so routing-aware estimates are needed for realistic distributed-resource estimates.Source: §IV · p. 3
V. OUTLOOK AND CONCLUSIONS
Across the tested hydrogen-chain circuits, UpCCD has the cleanest scaling and UCCSD the largest resource budget. TeleSABRE reduces Bell-pair budgets by more than an order of magnitude versus naive orderings, while generalization beyond hydrogen chains remains future work.
V. OUTLOOK AND CONCLUSIONS
- UpCCD offers the cleanest scaling across tested mapping and ordering schemes, while UCCSD demands the largest resource budget.TeleSABRE consistently reduces required Bell-pair budgets by more than an order of magnitude compared with naive orderings.Source: §V · p. 3
- The comparison covers hydrogen-chain simulations only; generalization to other molecules and larger active spaces is left for future work.Planned extensions include additional ansätze under TeleSABRE and evaluation of accuracy-per-resource trade-offs.Source: §V · p. 3