Two quasiparticles fired at each other on 42 qubits
The paper turns a quantum processor into a scattering experiment. The target is the one-dimensional Fermi-Hubbard model, a chain where fermions hop between neighbouring sites with amplitude J and pay an on-site interaction energy U when two occupy the same site. On the half-filled Mott background, the relevant charge excitations are the doublon (a site holding both spin species) and the holon (an empty site). The authors prepare one of each on opposite sides of a 21-site chain and steer them toward the centre.
The mapping is concrete: two neighbouring qubits form one Hubbard site, one qubit per spin orbital, so 21 sites occupy 42 qubits. A Jordan-Wigner transformation with a zigzag ordering keeps each Trotter step to nearest-neighbour gates. To give the quasiparticles definite direction, the evolution is split in two. For 0 < T ≤ 1, hopping toward the nearer chain edge is switched off, so each excitation becomes a directed wave packet; for 1 < T ≤ 4, all hopping is restored and the packets collide near the chain centre. The authors report that more than 93% of the packet weight sits in the leading component for T ≤ 4.
Because the initial Neel state is not the exact ground state, each measurement is paired with a reference run using the same circuit without the excitations, and the reference value is subtracted. Quantities carrying a Δ prefix are these background-subtracted values. This matters for reading every number below: the reported densities and probabilities are differences from a no-excitation baseline, not raw site occupations.
Interaction strength switches transmission to reflection
The central measured quantity is the doublon transmission probability T, defined at T = 3.2 as the fraction of the total doublon number found on the far side of the chain centre (sites i ≥ 11). It is a fraction of doublons, not of total charge, and it is evaluated at one fixed time shortly after the collision rather than integrated over the whole evolution.
Across U = 1 to 8, the experiment shows a crossover. At U = 1 the doublon and holon packets pass through each other and keep their directions; at U = 7 they are reflected back. The measured curve agrees with the Bethe-ansatz two-body result T(θ) = θ²/(1 + θ²), with θ = 2J(sin k₁ − sin k₂)/U, using the maximum relative group velocity c = 4J and no free parameters. Fitting the same form with c free gives c ≈ 3.6J, which the authors attribute to the packet carrying a spread of momenta around k = π/2, so the average relative velocity falls below the maximum.
The paper offers a mechanism for why strong interaction means reflection. For the doublon and holon to swap positions, the pair must pass through an intermediate configuration detuned by U, so the exchange amplitude is suppressed to order J²/U and the quasiparticles behave as hard-core objects. The authors also note that the outgoing packets show no noticeable speed change relative to the incoming ones, which they read as an elastic collision consistent with integrability of the one-dimensional Hubbard model.
A vanishing charge signal is not pair annihilation
At the intermediate value U = 3.5, the charge density of both packets nearly disappears after the collision. That is an ambiguous signature: it would also appear if the doublon and holon simply annihilated. The authors separate the two possibilities by measuring doublon density d_i = ⟨n_i↑ n_i↓⟩ and holon density h_i = ⟨(1 − n_i↑)(1 − n_i↓)⟩ independently.
The centre-of-mass trajectories decide the question. At U = 1 the doublon and holon centres cross; at U = 7 they turn back toward their starting sides; at U = 3.5 both centres stay near the chain centre while both distributions broaden. That is what a superposition of transmitted and reflected components, |ψ_out⟩ ∼ t|d_R h_L⟩ + r|d_L h_R⟩ with |t|² = T and |r|² = 1 − T, would produce: at T ≈ 1/2 each side holds comparable doublon and holon weight, and their opposite charges cancel.
A second check compares total charge Σ_i |Δ⟨n_i⟩| with total doublon number Σ_i Δd_i at T = 3.2. Total charge dips near U ≈ 3.5, but the doublon number rises monotonically with U. Recombination would reduce both together, so the monotonic doublon number rules out annihilation as the explanation for the charge dip.
Entanglement is inferred from number fluctuation
The entanglement claim rests on a different observable than the transmission probability. The authors infer it from particle-number fluctuation, quantified by a number entropy S_num defined in their equation (4), and they report that S_num and the entanglement reach a maximum at U/J = 4, the point where transmission and reflection weights are comparable.
The paper is explicit about what this does and does not establish. The measured data show the presence of the two components and their relative weights, but do not directly confirm coherence between them. The reading as a coherent superposition rests on two things: the time evolution is unitary, and the observed U dependence follows the predicted form of equation (2). The authors state that an additional interference experiment on the wave function after the collision could confirm it once longer simulation times become accessible.
This is the boundary that most changes how the result should be cited. The scattering-probability measurement is a direct hardware comparison with the Bethe-ansatz S-matrix; the entanglement statement is an inference from number fluctuation plus the assumption of unitary evolution, not a tomographic reconstruction of the post-collision state.
The doublon-doublon control shows no interaction dependence
The control experiment collides two doublons instead of a doublon and a holon. The paper reports that this collision shows neither the interaction dependence nor the number fluctuation seen in the doublon-holon case, which the authors describe as expected for indistinguishable particles.
The contrast is what makes the doublon-holon result interpretable. The interaction-dependent crossover and the number fluctuation appear specifically when the two colliding objects are distinguishable charge excitations with opposite charge, and they are absent in the same hardware when the two objects are identical. Without this control, a U-dependent signal in the doublon-holon run could be attributed to device behaviour rather than to quasiparticle scattering.
Error handling sets how much the agreement means
The comparison with theory is only as strong as the error budget behind it. Qubits and couplers exceeding calibration thresholds for readout and CZ error are excluded as a hard constraint, and Bell-state fidelity tests on the remaining couplers select the 42-qubit chain. Each data point uses 70,000 shots split across 70 Pauli twirling instances, combined with dynamical decoupling and readout twirling, which approximately convert coherent gate and asymmetric readout errors into stochastic bit-flip channels.
Post-processing then uses symmetries of the problem. Total particle number is conserved and known for the initial state, so the measured total-number distribution is fitted to estimate a uniform bit-flip probability p, which is used to restore noiseless expectation values. The combined inversion and particle-hole symmetry IC is also exploited, with excitations and symmetrization defined over the first 20 sites so the length is even. The authors report that adding the extinction step of dividing by γ_q changed the mitigated observables only marginally.
Two further constraints bound the simulation. Trotterization is capped at N = 20 steps with a two-qubit circuit depth of 5N + 2, and the time mesh is refined around the collision to reduce late-time Trotter error. The authors compare against MPS-based TEBD tensor-network simulations and describe the agreement as sufficient to distinguish the different dynamical behaviours, which is a weaker standard than quantitative agreement at every point.
What the platform adds beyond a scattering matrix
The paper's own framing of the advance is specific: the ability to create quasiparticles of a chosen flavour on demand and program their motion and interactions makes a digital quantum processor a toolset for probing the entanglement structure generated by quasiparticle scattering. The measured transmission probability is presented as the first such measurement of Hubbard-model quasiparticles on quantum hardware, agreeing with the Bethe-ansatz S-matrix without free parameters.
The most decision-relevant split in the paper is therefore between two claims of different strength. The U-dependent transmission curve, the elastic character of the collision, and the doublon-doublon control form a hardware measurement compared against an exact two-body result. The entanglement interpretation is a superposition inferred from a vanishing charge signal, broadening centre-of-mass distributions, and a number-entropy maximum near U/J = 4, with coherence left to a future interference experiment. Readers weighing this work should treat the scattering-matrix agreement as the established result and the entanglement generation as a well-motivated inference whose direct confirmation the authors themselves defer.
Sources used in this answer
An entangling Hubbard quasiparticle collider on a digital quantum processor
A doublon-holon collision on 42 qubits of ibm boston yields a doublon transmission probability matching the parameter-free Bethe-ansatz S-matrix, with entanglement inferred from particle-number fluctuation and absent in a doublon-doublon control.