How Far Can You Do Nothing On a Quantum Computer?

AI summary

Overview

• Research area: Quantum computing hardware characterization — spatial benchmarking of noisy intermediate-scale quantum (NISQ) processors using a communication-protocol-based test.
• Technical level: Intermediate. The protocol is conceptually simple (prepare, route out, undo, route back, measure), but the metrics, the prefix rule, and the statistical caveats assume familiarity with qubits, SWAP gates, connectivity graphs, and fidelity.
• Scope (one sentence): The paper applies the existing "do-nothing" state-transfer protocol as a route-resolved spatial probe on Rigetti's Cepheus-1-108Q and IBM's Heron-r2 processors (Fez, Kingston, Marrakesh), reporting two complementary quantities per initial qubit: the largest radius within which every evaluated shortest route passes an empirical 2/3 return-score cutoff, and the longest single successful route found.

What This Paper Is About

The authors ask a deliberately minimal question — "how far can you do nothing on a quantum computer?" — by preparing a state, shuttling it outward with SWAP gates, applying the inverse preparation, and shuttling it back to be measured. Any loss in the return score comes from the accumulated cost of routing: relaxation, dephasing, gate error, crosstalk, and state preparation and measurement effects. The goal is not to propose a new protocol but to use this deterministic, low-complexity task as a high-resolution spatial map that separates two different hardware properties: uniform reliability across all routes in a region, versus the existence of a few unusually good long routes.

Key Contributions

1. Route-resolved application of the do-nothing protocol across unrestricted chip regions. Earlier do-nothing evaluations were limited to coarse spatial segmentation of the tested QPUs; this work removes those topological constraints and maps unconstrained sections of the processor grid, and it is described as the first application of this specific evaluation on Rigetti's architecture alongside a comparison to IBM's different connectivity.

2. Two explicitly defined, complementary spatial metrics. The Maximal Isotropic Sub-star radius requires that every evaluated shortest route within that radius passes the empirical rule; the Maximal Successful Length records the longest individual route that does. The central novelty claimed is the separation of these two operationally different properties, together with explicit maps of the contributing qubits and couplers. The initial qubit plus all qubits within the isotropic radius is termed the Maximal Isotropic Sub-star.

3. A prefix-closed success rule with explicit statistical framing. A route counts as a "successful path" only if its own circuit and the circuit for every prefix from the same initial qubit each score above the cutoff. The cutoff is 2/3, with a binomial standard error near threshold of approximately 0.021 at 512 shots.

4. An explicit disclaimer about what the 2/3 number does and does not mean. The authors state that for this circuit ordering the comparison does not certify above-classical unknown-state transfer. Their illustration: if each transfer direction replaced its input with |0⟩⟨0|, the final return probability would be 1 for every U_rand even though no input information survived the outward trip. The classical average-fidelity bound of 2/3 is therefore used solely as an empirical classification rule.

Main Findings

• IBM Fez, qubit 140 (highlighted case): an isotropic radius of 10, meaning all evaluated shortest routes from that qubit within that radius pass the empirical prefix rule, and a successful route to qubit 23 at swap distance 27.

• IBM aggregate across evaluated initial qubits: mean isotropic radius approximately 7 and mean maximal successful length 21.8, versus 10 and 27 for qubit 140 — which the authors stress was selected after inspecting results as a deliberately high-performing illustrative case, not an average or pre-selected representative.

• Rigetti Cepheus-1-108Q (highlighted case): an isotropic radius of 1, with selected above-threshold routes reaching swap distance 8. Selected routes from qubits 107 and 67 satisfy the prefix rule through swap distances eight and six respectively.

• Zero isotropic radius is possible: for Rigetti initial qubit 40, the one-step routes to qubits 41 and 49 scored 245/512 and 313/512, both below 2/3. Routes to qubits 31 and 39 did pass the cutoff and belong to the successful-route set, but do not create an isotropic radius of one.

• Short distances are not automatically safe on Rigetti: some routes fall below the return-score cutoff even at short distances, including intra-chiplet routes from qubit 0.

• A visible boundary on Fez: no evaluated successful path from qubit 140 includes the coupler between qubits 102 and 103, which identifies a boundary in the observed route map without isolating an error in that coupler from the rest of the circuit.

• Prefix rule can disqualify an apparently strong start qubit: on Fez, qubit 0 dominates at extended swap distances beyond 23, but many shorter intermediate paths — particularly between swap distances 9 and 23 — fell below the cutoff, so the prefix-closed constraint excluded the affected long routes.

• Near-threshold sensitivity: for Fez qubit 140, the mean return score is below 2/3 at every evaluated swap distance from 23 to 32, and also at distance 21 before rising above it at 22; at distance 21, fourteen of the 25 evaluated route circuits were above 2/3. The authors note that routes only a few percentage points from the cutoff are boundary-sensitive.

• Reported contrast, not a ranking: within the two highlighted cases, Fez qubit 140 attains a larger isotropic radius and longer identified route than the best displayed Rigetti initial qubit, but the data support a contrast between uniform reliability and routing flexibility rather than a platform-wide superiority claim.

• Idealized summary from Table 1: IBM (Fez) — Max Isotropic Radius 10, Max Successful Distance 27, best long path 140 → 23. Rigetti Cepheus-1-108Q — Max Isotropic Radius 1, Max Successful Distance 8, best long path 107 → 75 and 67. The table aggregates over routes from qubit 140 for IBM and qubit 107 for Rigetti.

Methodology in Plain English

The work qubit starts in |0⟩ and a random unitary U_rand prepares |ψ⟩. A sequence of SWAP gates carries that state outward along a shortest topological path to a destination qubit, where the inverse U_rand† is applied. The state is then routed back along the same kind of path and measured. If it returns cleanly, most shots read 0; the estimated return score is simply the number of zero outcomes divided by 512. The swap distance is the number of SWAPs used to reach the furthest point.

Initial qubits were chosen to capture different chip regions. On Rigetti, four qubits were used (0, 40, 67 and 107): two central and two at opposite peripheral corners. On IBM, with a larger experimental budget, eight initial qubits were used — four central and four at the corners. All transfer used shortest topological paths only, and each circuit ran 512 shots.

A route is labelled successful only if its own circuit and every shorter prefix from the same initial qubit each exceed 2/3. Because Rigetti offers far more alternative routes, the authors used a staged, cost-saving search there: all paths up to swap distance 4 were evaluated first, and only passing routes were extended to length 8 and then 10; at L = 10 all remaining return scores fell below the cutoff, ending the experiment. On IBM Fez, the smaller number of shortest paths under heavy-hex connectivity plus a different cloud pricing model allowed full-depth execution of all routes without staging. The authors are explicit that the staged strategy is a search heuristic, not a proof that performance degrades monotonically with path length, and that the resulting Rigetti longest route is not asserted to be the architecture-wide longest possible route.

Two architectural details matter for interpretation. Cepheus-1-108Q is built from twelve 9-qubit chiplets in a three-by-four grid, joined by inter-module couplers (IMCs) that may act differently on quantum information than intra-chiplet couplers; routes crossing IMC boundaries probe this, but the experiment does not separately identify an individual coupler's contribution. IBM's heavy-hex lattice gives each qubit at most three direct neighbours, which means fewer routing alternatives.

Why This Matters

• Impact on research: Standard metrics like Quantum Volume produce one chip-wide score, and randomized benchmarking produces averaged gate error rates; neither isolates spatial routing constraints, directional dependencies, or topological overhead. This paper shows that a single average can conceal the difference between "every route here works" and "one lucky long route works," which matters for noise-aware qubit placement and routing and for interpreting benchmark results whose underlying information is increasingly hard to read.

• Real-world applications:

  • Compiler and transpiler design: distinguishing regions of uniform reliability from regions with a few good long paths informs qubit mapping and SWAP-insertion strategies.
  • Hardware selection and procurement: teams choosing between cloud-accessible devices can compare spatial reliability profiles rather than a single headline number.
  • Calibration monitoring: the return-score-versus-distance profile provides a simple diagnostic of combined T₁ relaxation, T₂ dephasing, and crosstalk, and can be repeated as a temporal snapshot to detect drift.
  • Algorithm placement: a control qubit that must travel to a distant register and return can be placed using the isotropic-radius map rather than guesswork.

• Industry relevance: The study directly compares a multi-chiplet superconducting architecture (Rigetti's modular tiling approach, which is a scalable manufacturing strategy but introduces inter-module couplers with potentially different noise profiles) against IBM's monolithic heavy-hex layout. The authors thank IBM Quantum and Rigetti Computing for low-level qubit and coupler control on their cloud platforms, which was essential to the design and execution of the work.

Future Directions

• Extend to multi-qubit protocols. The broader Benchmarking via Protocols framework includes teleportation, superdense coding, and transmission of entangled pairs; applying route-resolved spatial analysis to these is named as the natural next step.
• Un-staged, exhaustive routing on Rigetti. The staged search means longer-distance Rigetti statistics are conditioned on survival through the filter, and the reported longest route is not an architecture-wide maximum; a full-depth sweep would test how much is missed.
• Symmetric sampling for fair cross-platform comparison. The IBM and Rigetti route populations were generated by different search procedures, and the highlighted initial qubits are not a symmetric random sample; the authors explicitly present the IBM–Rigetti comparison as illustrative rather than an unbiased ranking.
• Toward certification rather than classification. A genuine classical-threshold claim for any protocol in the suite would require a bound valid for that protocol's actual circuit, input ensemble, and measured observable, plus control of finite-shot uncertainty — none of which the present return-score analysis supplies. Related open questions include the unspecified preparation-unitary distribution and the number of independent preparations per route, which the retained records do not document.

Target Audience

Quantum hardware researchers and benchmarking specialists; compiler and transpiler engineers who need spatial noise maps for qubit placement and routing; experimentalists characterizing superconducting multi-chiplet and heavy-hex architectures; and readers interested in protocol-based, hardware-agnostic benchmarking of NISQ devices. The paper is also useful for those who want a clear worked example of how a familiar number like 2/3 can be used as an empirical cutoff without being misread as a proof of quantum advantage — the authors are unusually explicit that their return score is not, in general, the fidelity of the transferred state with the unknown input. Readers seeking a definitive vendor comparison, a new protocol, or a public data and code repository will not find one here: the authors state that no such repository or complete circuit-and-analysis archive is provided, and they list five limitations, including that every hardware result is a temporal snapshot exposed to calibration drift.

Authors’ abstract

We present a route-resolved comparative assessment of Rigetti's Cepheus-1-108Q and IBM Heron-r2 processors using the established do-nothing state-transfer protocol. Rather than proposing a new protocol, we use this deterministic, low-complexity task as a high-resolution spatial probe. For each evaluated initial qubit, we report two complementary quantities: the largest tested radius within which every evaluated shortest route satisfies the operational success rule, and the longest successful route identified within the evaluated route family. To address the question "How far can you do-nothing on a quantum computer?", we prepare a quantum state, route it outward using SWAP gates, apply the inverse preparation at the destination, and route it back for measurement. We compare the measured probability of returning $0$ with the empirical cutoff $2/3$. For this circuit ordering, that comparison does not certify above-classical unknown-state transfer. While this trivial state-transfer protocol serves as the most intuitive baseline, actively preserving a quantum state across a physical lattice proves to be a non-trivial task that exposes the information to cumulative relaxation, dephasing, and environmental cross-talk. In the highlighted IBM QPU case, we identify an isotropic radius of 10 and a successful path of swap distance 27, whereas the highlighted Rigetti Cepheus case exhibits an isotropic radius of 1 but selected above-threshold routes reaching swap distance 8. These results reveal a sharp distinction between uniform spatial reliability and best-route performance. The presented quantities are empirical and conditional on the evaluated route families, finite-shot decision rule, calibration state, and execution time; they are not architecture-wide constants.