A peer-reviewed result with an earlier history
On September 1, npj Quantum Information published a peer-reviewed experiment in which researchers prepared four 100-site states of a quantum spin-chain model on IBM superconducting hardware. Measurements revealed nonzero string order across as many as 20 sites, localized behavior at the chain's edges and qualitative patterns in entanglement spectra. Together, those probes supplied evidence that the hardware states retained the expected signatures of two symmetry-protected topological phases despite noise and imperfect gates.
The work was not first disclosed in September. George Pennington and five coauthors submitted its preprint to arXiv on March 6, 2026. The qualifying September event is publication of the version of record after peer review. Nor did the experiment establish quantum advantage. Its target states were first calculated using established classical tensor-network methods, and the same classical description enabled the researchers to compile unusually shallow circuits before sending them to the processor.
Order that cannot be diagnosed locally
The experiment studied the bond-alternating spin-1/2 Heisenberg chain, a one-dimensional model in which neighboring spins interact with alternating coupling strengths. Depending on those couplings, the chain can occupy distinct even-Haldane and odd-Haldane phases. Both are symmetry-protected topological phases. Unlike an ordinary magnet, whose order can be recognized from a local quantity such as magnetization, these phases require information spread across multiple sites to distinguish them.
That hidden structure makes the model a useful test for programmable quantum simulation. A device must prepare correlations over a large register and preserve enough of them for nonlocal measurements. The researchers selected four ground states, three from the even-Haldane phase and one from the odd-Haldane phase. The states were not simply copied from an exact formula. They represented different points in the model's phase diagram and had matrix-product-state bond dimensions between 19 and 40 before compression.
Classical calculations built the starting map
The preparation pipeline began with the density matrix renormalization group, or DMRG, a classical algorithm that efficiently describes many gapped one-dimensional systems. DMRG produced each ground state as a matrix product state. The team compressed those descriptions to smaller bond dimensions of five to eight while retaining at least 99.9 percent calculated fidelity, then used tensor-network approximate quantum compilation to optimize a brickwork circuit whose output matched each target.
This division of labor is central to the result. The classical computer supplied both the target and the optimization machinery. The quantum processor executed the resulting circuits and provided experimental measurements. The method is attractive because the chosen ground states have short-range correlations that a shallow nearest-neighbor circuit can represent. It does not remove the classical cost for models that tensor networks already handle well, and it may become harder for gapless states or systems with longer-range correlations.
The reported fidelities belong to compiled circuits
For the four target states, classical simulation calculated overlaps of 98.9, 98.9, 99.0 and 97.9 percent between the compiled circuit states and the original uncompressed DMRG ground states. Their CNOT depths were 18, 21, 21 and 39. The first three compilations reached their targets within hours. The deepest case required seven days of optimization and stopped at the lower overlap.
Those percentages are not physical fidelities measured after the circuits ran on noisy hardware. They quantify how accurately the ideal compiled circuits represented the classical targets before hardware errors were included. That is still important: a poor compilation would make the intended physics inaccessible even on a perfect device. But it cannot be used to claim that IBM's processor prepared a 100-qubit state with 97.9 to 99.0 percent end-to-end fidelity. The hardware evidence instead comes from selected observables.
Twenty-site strings exposed the phase pattern
The principal observable was string order, built from products of measurements across an extended section of the chain. The team measured even-length strings from two through 20 sites at five starting positions in the bulk, deliberately staying away from the first and last 20 sites to reduce edge effects. In an even-Haldane state, the expected even string-order signal remained nonzero through length 20 while the odd counterpart moved toward zero. The odd-Haldane state displayed the complementary pattern.
This is stronger than reporting a local magnetization or one convenient correlator. The signal followed the phase-dependent parity expected from theory at several positions and lengths. The hardware values obtained without zero-noise extrapolation, while still incorporating Pauli twirling and TREX, fell steadily as strings grew. The paper leaves unresolved whether accumulated readout error caused that decline or whether device noise physically erased some long-range order. Those no-ZNE data therefore demonstrate surviving order over the tested scale, not an unlimited correlation that remained constant throughout all 100 sites.
Edges and entanglement supplied separate tests
The odd-Haldane state should also contain spin-1/2 modes localized near the chain's ends. Hardware measurements found antiferromagnetic magnetization near those boundaries that decayed into the bulk. The extracted correlation length was 1.76 plus or minus 0.20 sites without zero-noise extrapolation and 1.81 plus or minus 0.21 with it, compared with 1.97 plus or minus 0.03 from DMRG and ideal compiled-circuit calculations. The string measurements extended about an order of magnitude farther than this edge length.
For a third diagnostic, the researchers reconstructed reduced density matrices for segments of up to six sites and examined their entanglement spectra. Alternating cuts produced patterns with one or two dominant eigenvalues in the arrangements expected for the two phases. The paper describes this agreement as qualitative. It explicitly stops short of proving exact eigenvalue degeneracy, because small reconstruction errors split values that theory predicts should coincide. Multiple compatible signatures strengthen the phase identification, but they do not turn a qualitative spectrum into a precision benchmark.
Error mitigation was part of the experiment
The raw circuit executions were supported by substantial statistical and error-mitigation machinery. For each string observable, the team used 10,000 shots, 100 Pauli-twirling randomizations and twirled readout-error extinction. It also used zero-noise extrapolation, running at several effective noise factors and fitting the results back toward a hypothetical zero-noise value. String order and edge magnetization were shown both with and without that extrapolation, allowing readers to see how much the processing changed the measured values.
Entanglement-spectrum tomography was more expensive because the number of Pauli observables grows as four to the number of reconstructed sites. Even after grouping compatible measurements, a six-site reconstruction required 206 groups rather than the full 4,096 individual strings. The authors used Pauli twirling and readout mitigation there but omitted zero-noise extrapolation because of the additional overhead. This uneven treatment matters when comparing diagnostics: none is a direct, complete measurement of the 100-qubit wavefunction, and each carries different noise assumptions.
A practical advance with a bounded domain
The useful progress is a preparation strategy that placed meaningful many-body structure across 100 physical qubits while keeping two-qubit depth below 40. Shallow compilation made it possible to ask several nonlocal questions of a noisy processor before errors overwhelmed every signal. The experiment also shows the value of checking one physical conclusion through string order, edge behavior and entanglement structure rather than treating a single favorable measurement as decisive. The authors have released associated code and data in a public repository.
The demonstrated method is best matched to gapped, one-dimensional systems with short-range correlations, precisely the regime where matrix product states and DMRG are effective classical tools. The paper does not show higher-dimensional scaling, gapless-state preparation, nonequilibrium dynamics or computational advantage. A consequential next step would use these prepared states as inputs for time evolution that becomes difficult to follow classically, while tracking how circuit depth and mitigation costs grow. For now, the result is substantial progress in programmable state preparation and quantum simulation, not evidence that the processor surpassed classical computation.