A four-qubit universe: validated digital simulation of 1+1D lattice QED quenches on IBM Kingston

Abstract

Baseline-validated digital quantum simulation of four-site Schwinger-model quench dynamics and background-field response on IBM Kingston Field Value Author Amit Brahmbhatt Affiliation Quantum Clarity LLC ORCID 0009-0003-5882-8476 Report date 2026-09-25 Version 1.2 Resource type Technical report / computational research record Abstract We report a validation-led digital quantum simulation of real-time dynamics in a four-site lattice Schwinger model, a (1+1)-dimensional formulation of quantum electrodynamics [1]. The study had three stages executed on the IBM Quantum processor ibm_kingston. First, an 18-PUB control experiment tested previously proposed “anomaly” observables against independently calculated noiseless baselines. Hardware agreed with the correct baselines to a maximum absolute deviation of 0.084, whereas the discarded analytic expectations differed by as much as 1.062. This negative result established that the earlier apparent anomalies were baseline errors rather than evidence of new physics. Second, we prepared the bare staggered vacuum on four qubits and evolved it under a Gauss-law-reduced Schwinger Hamiltonian with open boundaries, lattice spacing a=1, fermion mass m=0.5, and gauge coupling g=1. A nine-time-point quench reproduced the predicted non-monotonic staggered-magnetization trajectory. The maximum absolute hardware deviation was 0.262 from the noiseless first-order Trotter circuit and 0.240 from exact evolution; the largest deviations occurred in the deepest circuits. Third, we scanned a background-field parameter alpha over five values and six times. The hardware qualitatively reproduced both preregistered trends: increasing field suppressed the early-time rise of the pair-density proxy, while stronger fields sustained a larger late-time density. A repeated zero-field subset agreed across two jobs within 0.036 at every shared time. The three jobs comprised 57 circuits/PUBs, 116,736 requested shots, and 38 seconds of reported QPU usage. These results demonstrate an end-to-end workflow for small lattice-gauge simulations on noisy hardware: correct the classical baseline first, verify two independent Hamiltonian constructions, quantify Trotter error before submission, audit several days of backend-calibration history, freeze the selected physical qubit path into every hardware script, and interpret only features that survive those controls. A five-day, 12-hour-cadence audit selected ibm_kingston path [107,106,105,117]; the same mapping was then used for the control, zero-field quench, and field scan. The experiment does not measure the continuum Schwinger tunneling rate, probe electron substructure, or establish new particle physics. Keywords: Schwinger model; lattice gauge theory; quantum simulation; IBM Quantum; Qiskit; real-time dynamics; digital quantum simulation; background electric field; NISQ; validation Plain-language summary The Schwinger model is a simplified version of quantum electrodynamics in one space dimension and one time dimension. It is often used as a compact testbed for studying how matter and electric fields interact. Here, four qubits represented four points on a tiny spatial lattice. The qubits began in a simple “empty” reference pattern. Quantum gates then approximated how that state would change under the model. We measured a quantity called staggered magnetization. In this encoding, a value of -1 is the starting vacuum pattern; movement toward zero indicates more pair-like fermionic excitations on the lattice. This is an indirect model observable, not a detector counting real electrons and positrons. Three hardware jobs were used. The first was a sanity check. It showed that an earlier apparent anomaly came from incorrect expected formulas, not from the quantum processor. The second job then reproduced the predicted rise, partial return, and renewed rise of the excitation proxy after a sudden quench. The third changed a background-field parameter and found the same two qualitative effects predicted before hardware execution: stronger field slightly suppressed the early response but sustained much more excitation at later times. Before spending QPU time, we also examined five days of IBM calibration records at 12-hour intervals. Rather than choosing the least busy machine or trusting one favorable calibration, a script compared connected four-qubit paths using two-qubit-gate quality, readout quality, coherence relative to expected idle exposure, and stability over time. It selected the connected Kingston path [107,106,105,117]. We then locked the four model sites to those four physical qubits in all three hardware jobs. This made the hardware choice part of the experimental protocol rather than an after-the-fact explanation of the results. The important result is not a discovery of new physics. It is that a carefully validated, four-qubit lattice-field calculation retained its principal dynamical features on a real superconducting quantum processor despite gate noise. The work also illustrates why simulation baselines and negative controls must be established before interpreting unusual hardware output. 1. Research objective and scope The project asked whether a small, gate-based quantum processor could reproduce controlled real-time features of an interacting lattice gauge theory after a sudden quench, and whether those features changed predictably when a background electric-field parameter was varied. The final investigation addressed three questions: Baseline validity: Did the original electron-probe expectations survive exact, noiseless reconstruction? Zero-field quench: Could ibm_kingston reproduce the predicted non-monotonic evolution of a four-site Schwinger-model pair-density proxy? Background-field response: Could the processor preserve the predicted early- and late-time field-dependent trends without increasing the entangling-gate count? The scope is deliberately narrow. This is a finite, four-site digital simulation at dimensionless parameters, not a continuum extrapolation. It measures dynamics of an encoded model, not physical pair production in the IBM device. 2. Model and observable We used the staggered-fermion Hamiltonian for the Schwinger model with open boundaries. Gauss's law was used to eliminate explicit gauge-link degrees of freedom, leaving a spin Hamiltonian suitable for qubits. Hamiltonian: H(α) = [1/(2a)] · Σ(n = 0 to N − 2) [σₙ⁺σₙ₊₁⁻ + σₙ⁻σₙ₊₁⁺] + (m/2) · Σ(n = 0 to N − 1) (−1)ⁿσₙᶻ + (ag²/2) · Σ(n = 0 to N − 2) (Lₙ + α)² where Lₙ = Σ(k = 0 to n) [σₖᶻ + (−1)ᵏ]/2 The parameters used in every Schwinger run were: Lattice size: N=4 sites mapped to four qubits. Boundary condition: Open. Lattice spacing: a=1. Mass: m=0.5. Gauge coupling: g=1.0. Initial state: Bare staggered vacuum |1,0,1,0> in Qiskit qubit order. Background field: alpha=0 for the main quench; alpha={0,0.5,1.0,1.5,2.0} for the scan. The measured observable was staggered magnetization: M(t) = (1/N) · Σ(n = 0 to N − 1) (−1)ⁿ⟨σₙᶻ(t)⟩ For the prepared bare vacuum, M(0)=-1. Movement toward zero corresponds to increased occupation relative to that reference and is used here as a pair-density proxy. Because the initial state is not generally the interacting ground state, the observed dynamics combine quench energy, interactions, finite-size effects, and the background field. Consequently, the scan is interpreted as field reshaping of quench-induced pair-like dynamics, not as a direct measurement of the continuum Schwinger tunneling law. 3. Validation-first methodology 3.1 Reconstructing the original control baselines Before running the lattice-gauge model, the earlier electron-probe circuits were rebuilt in noiseless Qiskit Aer statevector simulation. This exposed three problems: An ad hoc formula predicted nonzero correlators where the simulated circuit predicted zero. A presumed random bit-match ratio of 0.5 was actually 0.0873 for the specified noiseless circuit. A tomography string-ordering error targeted qubits 3 and 2 rather than qubits 0 and 1 because Qiskit Pauli labels are little-endian; the error created a spurious -1 value in one YZ channel. A corrected hardware control then compared Kingston measurements with the reconstructed noiseless values. This step changed the interpretation from “possible anomaly” to a conventional null result before any Schwinger-model claim was made. 3.2 Independent Hamiltonian checks The zero-field Hamiltonian was constructed twice: as a dense matrix from tensor products of single-site operators; and independently as a SparsePauliOp. The two constructions agreed to machine precision (max|dH|=0). For the field-dependent model, the independent constructions agreed after removal of a physically irrelevant identity contribution, which changes only the global phase. The checks also caught and corrected: a Qiskit little-endian initial-state ordering error; a Q_j^2 expansion error in the electric term; label indices incorrectly treated as qubit indices in the field scan; and incorrect coefficients in a hand-simplified field-dependent expansion. 3.3 Exact and Trotter baselines Exact time evolution was obtained by diagonalizing the finite Hamiltonian. Digital circuits used first-order Trotterization. One-body Z terms were implemented as RZ rotations. Terms acting on the same qubit pair were exponentiated jointly and decomposed into two-qubit gates; every synthesized two-qubit unitary was checked to fidelity greater than 1-10^-9 against its target matrix. Combining the XX+YY interaction on each bond reduced the logical two-qubit cost at t=4 from 144 to 80 CX gates. A second-order formula was tested but was less favorable in the selected time-step regime. The chosen zero-field operating point used eight first-order steps at t=4, with a maximum noiseless magnetization error of 0.0552 relative to exact evolution. For the 30-point field grid, th