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Experimental Comparison of Two Quantum Computing Architectures
N. M. Linke, D. Maslov, M. Roetteler, S. Debnath, C. Figgatt, K. A. Landsman, K. Wright, C. Monroe
TL;DR
The paper addresses how physical architecture affects identical quantum algorithms, comparing programmable five-qubit superconducting and trapped-ion systems. It maps composite gates and algorithms onto their respective native libraries and connectivity graphs, finding that connectivity matching and gate expressivity shape circuit performance and scaling considerations.
Problem
The study examines limited evidence about how qubit connectivity and physical architecture affect comparable quantum computations across different programmable platforms.
Method
The authors compare identical composite gates and algorithms on five-qubit superconducting and fully connected ion-trap systems after hardware-specific gate decomposition and optimization.
Results
Performance depends on circuit connectivity: the ion trap achieves 85.0(2)% for the full Toffoli versus 52.6(8)% for the superconducting system, while connectivity matching reduces algorithmic gate overhead.
Takeaways & Limitations
The results indicate that quantum hardware connectivity, gate expressivity, and circuit structure should be considered together when scaling quantum computers.
Takeaways & Limitations
The experiments use small five-qubit systems whose capabilities remain limited to demonstration algorithms and whose technologies face substantial large-scale control and connectivity challenges.
Abstract
from arXiv · showhide
We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programmed in a way that is blind to the underlying hardware, thus allowing the first comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that employ more connectivity clearly benefit from a better connected system of qubits. While the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that co-designing particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.
PHYSICAL SYSTEMS
The comparison uses two programmable five-qubit platforms with different connectivity and native gate libraries. Mapping identical circuits to each architecture shows that gate counts depend on connectivity matching and gate expressivity.
- Connectivity: The IBM hardware has star-shaped connectivity with four two-qubit interactions targeting the central qubit.The ion trap system is fully connected, whereas the IBM device's connectivity is limited.
- Scaling constraints: The superconducting architecture has practical scaling constraints, including control-wire routing and refrigerator heat-budget management.Alternative modular designs can improve connectivity but add substantial volume per qubit.
- Circuit mapping: Circuit mapping breaks algorithms into gates native to each platform and optimizes circuits to minimize operations.The trapped-ion circuits use an optimization protocol, while IBM experiments use CNOT+T/Z_a algebra with further manual optimization.
- Gate libraries: The ion trap uses an R/XX library, while the IBM device uses the Clifford+T library.The R/XX library offers greater overall expressive power, although Clifford+T was likely selected for didactic reasons.
- Connectivity: Two-qubit gate counts strongly depend on how the circuit matches the connectivity graph.LNN is as efficient as full connectivity for hidden shift, while the star-shaped system is more efficient for Bernstein-Vazirani.
Margolus and Toffoli Gate
The Margolus and Toffoli comparisons isolate how gate requirements and connectivity affect performance on the two five-qubit systems. The fully connected ion trap outperforms the star-shaped superconducting system, especially for the full Toffoli circuit.
- Margolus gate: The Margolus gate succeeds at 74.1(7)% on superconductors and 90.1(2)% on ions.Its entangling operations all connect to the same qubit, making it efficient on star-shaped connectivity.
- Toffoli gate: A Toffoli gate normally requires 6 CNOT gates, but five entangling gates suffice when a square root of CNOT is available.The trapped-ion XX gate provides this capability.
- Toffoli gate: The full Toffoli succeeds at 52.6(8)% on superconductors and 85.0(2)% on the ion trap.The ion implementation uses five two-qubit gates, while the star-shaped implementation requires seven additional two-qubit gates for SWAP operations.
- Toffoli gate: The full Toffoli uses the same three qubits as the Margolus implementation, keeping preparation and measurement errors comparable.The performance difference therefore accompanies the additional circuit operations and connectivity requirements.
Bernstein-Vazirani and Hidden Shift Algorithms
The Bernstein–Vazirani algorithm maps well onto the star-shaped superconducting architecture, whereas Hidden Shift requires interactions between disconnected qubit pairs. The fully connected ion-trap implementation consequently achieves higher reported success for both algorithms.
- Bernstein–Vazirani: 72.8(5)% versus 85.1(1)%: Bernstein–Vazirani single-shot success was lower on the star-shaped superconducting system than on the fully connected ion trap.The oracle’s CNOT gates all target the ancilla, matching the star-shaped architecture.
- Bernstein–Vazirani: The Bernstein–Vazirani oracle encodes the unknown bit string c in a pattern of CNOT gates targeting the ancilla qubit.The algorithm finds c in a single shot and resembles a parity-check circuit used in error correction.
- Hidden Shift: The Hidden Shift algorithm determines an n-bit hidden shift s with one oracle query for the selected bent-function class, while classical algorithms require Ω(2n) queries.The supplied passage states the quantum single-query result and begins the classical-query comparison; the exponent formatting is preserved as given.
- Hidden Shift: 35.1(6)% versus 77.1(2)%: Hidden Shift fidelity was lower on the superconducting device than on the fully connected ion-trap system.The circuit uses gates between two disconnected qubit pairs, creating a six-two-qubit-gate overhead for the star-shaped architecture.
- Error interpretation: The measured error trends were broadly consistent with the models, with systematic errors better predicting the superconducting system while ion-trap performance fell between the models.The superconducting Hidden Shift result was the only example identified as significantly lower, possibly due to inhomogeneous device errors.
OUTLOOK
The comparison highlights architecture-level factors that influence quantum-circuit performance and scaling, while emphasizing unresolved physical-scaling challenges.
- OUTLOOK: 72.8(5)% and 85.1(1)% are the average Bernstein-Vazirani success probabilities for the superconductor and ion trap systems, respectively.The figure compares all possible 4-bit oracle parameters on star-shaped and fully connected systems.
- OUTLOOK: 35.1(6)% and 77.1(2)% are the average Hidden Shift success probabilities for the superconducting and ion trap systems, respectively.The comparison covers all possible 4-bit shifted oracle functions on both systems.
- OUTLOOK: Higher absolute fidelities and coherence times were observed in the trapped ion system, while the superconducting system had higher clock speeds.The paper cautions that these metrics are moving targets because both technologies are advancing rapidly.
- OUTLOOK: Circuit performance and time to solution depend critically on architectural restrictions, qubit connectivity, gate reconfigurability, and gate expressivity.The paper argues that these attributes become increasingly important as quantum systems scale.
- OUTLOOK: Even with 5-qubit systems, co-designing the connectivity graph with a circuit’s structure and choosing an expressive gate library affect computational efficiency.This conclusion links hardware connectivity and gate-library design to the efficiency of implemented computations.
- OUTLOOK: How leading quantum technologies will be connected and reconfigured at large scales remains an open question.The paper identifies control complexity and potential cross-talk as major scaling challenges, including difficult wiring and routing in superconducting designs.
- OUTLOOK: Table II compares observed success probabilities with random and systematic gate-error propagation models parameterized by gate number and gate and readout errors.The models use gate count N and readout error for M qubits to estimate overall error.
- OUTLOOK: Fully connected ion-trap architectures may not scale to arbitrarily large qubit numbers because collective motional modes can spectrally overlap.The passage notes that full connectivity between 20−100 trapped-ion qubits appears possible and discusses modular scaling approaches.
APPENDIX
The appendix provides numerical input/output matrices for gate and algorithm experiments conducted on the superconducting and trapped-ion systems.
- APPENDIX: Appendix tables highlight nominal target populations and use a 0 to 0.1 bar scale for error populations to emphasize systematic error patterns.The target populations have nominal unit probabilities.
- APPENDIX: The Margolis and Toffoli appendix matrices show numerical 3-qubit input/output results for both quantum computers.The Margolis results occupy the top two panels and the Toffoli results the bottom two panels.
- APPENDIX: The Bernstein-Vazirani appendix matrix shows numerical 4-qubit input/output results for the superconductor and ion trap systems.The superconductor results are shown on top and the ion trap results on the bottom.
- APPENDIX: The Hidden Shift appendix matrix shows numerical 4-qubit input/output results for the superconductor and ion trap systems.The figure corresponds to the Hidden Shift results in the main text.