Digital quantum simulations of scattering in quantum field theories using W states

TL;DR

This work demonstrates a practical pathway to simulating real-time scattering in quantum field theories on near-term quantum hardware. By combining a constant-depth W-state wavepacket initialization with symmetry-preserving energy minimization via ADAPT-VQE, the authors prepare accurate single-particle wavepackets across multiple lattice QFTs. They implement a 1D Ising field theory scattering on IBM’s 104-qubit device, observe inelastic 11 12 production through skewness in energy density, and validate the approach against MPS benchmarks while detailing extensive error mitigation strategies. The results mark a significant step toward near-term quantum advantage in non-equilibrium QFT dynamics and lay groundwork for higher-dimensional extensions and more complex scattering phenomena.

Abstract

High-energy particle collisions can convert energy into matter through the inelastic production of new particles. Quantum computers are an ideal platform for simulating the out-of-equilibrium dynamics of collisions and the formation of subsequent many-particle states. In this work, evidence for inelastic particle production is observed in one-dimensional Ising field theory using IBM's quantum computers. The scattering experiment is performed on 104 qubits of ibm_marrakesh and uses up to 5,589 two-qubit gates to access the post-collision dynamics. An outgoing heavy particle produced in the collision is identified from the skewness of the measured energy density. Integral to this computation is a new quantum algorithm for preparing the initial state (wavepackets) of a quantum field theory scattering simulation. This method efficiently prepares wavepackets by extending recent protocols for creating W states with mid-circuit measurement and feedforward. The required circuit depth is independent of wavepacket size and spatial dimension, representing a superexponential improvement over previous methods. Our wavepacket preparation algorithm can be applied to a wide range of lattice models and is demonstrated in one-dimensional Ising field theory, scalar field theory, the Schwinger model and two-dimensional Ising field theory.

Figures (31)

• Figure 1: Wavepacket preparation using W states and symmetry-preserving energy minimization. Left: due to translational invariance, the Hamiltonian decomposes into blocks $\hat{H}_{k}$, each with definite momentum $k$. The lowest-energy state in each block corresponds to the single-particle momentum eigenstate $|\psi_k\rangle$. Higher-energy states can be interpreted as multiple particles with total momentum $k$ (or heavier single-particle states not shown). Right: quantum circuits that prepare the target wavepacket $|\psi_{\text{wp}}\rangle$. First, the state $|W(k_0)\rangle$ is prepared with a constant-depth circuit using MCM-FF (step 1). This initial state has the momentum content of the target wavepacket but incorrectly contains higher-energy components. Next, the energy is minimized using circuits that are translationally invariant, real, and conserve other system-specific symmetries (step 2). These constraints preserve the momentum content of $|W(k_0)\rangle$ while projecting the wavefunction onto the desired single-particle states. The energy minimum corresponds to $|\psi_{\text{wp}}\rangle$.
• Figure 2: Low-energy vs. high-energy collisions. A heatmap of the energy density throughout the scattering process as a function of lattice position $n$ and time $t$. Propagating particles are identified as beams of energy with a constant velocity. Left: the elastic scattering of two light $|1\rangle$ particles (blue), $11\to11$. Right: the inelastic process $11\to12$ that produces a heavy $|2\rangle$ particle (red).
• Figure 3: a) The $L=104$ qubit layout used on ibm_marrakesh. b) The structure of the quantum circuits used to simulate scattering in Ising field theory. The colors indicate the qubits used in the lattice-to-device mapping. The energy minimization circuit $\hat{U}(\vec{\theta}_*)$ creates wavepackets when acting on $|W(\pm k_0)\rangle$. The circuit $\hat{U}_2(t)$ implements time evolution with second-order Trotterization.
• Figure 4: Simulations of inelastic particle production in one-dimensional Ising field theory. a) The energy density $E_n$ throughout the scattering process obtained with a MPS circuit simulator on a $L=256$ lattice. b) Results from simulations of scattering using $L=104$ qubits of ibm_marrakesh for a selection of times depicted in a). The wavepackets are initialized at $t_0=0$ and collide around $t_1=8.25$. Outgoing particles begin to form at $t_2=16.5$ and $t_3=24.75$. The asymmetry of the energy density in each "bump" signals the formation of the $|2\rangle$ particle produced in the inelastic process $11\to12$. The y-axis range at each time is different to clearly show the features of the energy density. The initial wavepacket parameters are $k_0=0.32\pi$ and $\sigma_{}=0.13$, and each wavepacket is supported on $d \gtrsim 21$ sites. A Trotter step size of $\delta t=1/16$ is used to evolve the system in a) and $\delta t=0.55$ is used in b).
• Figure 5: Asymmetry in the post-collision and single-particle energy densities. The regions of positive energy density the left half of the lattice in the $11\to12$ scattering process (left column) and in the $1\to1$ process of single particle propagation (right column). Results at times $t_2$ and $t_3$ obtained from ibm_marrakesh and MPS are shown. The skewness of the energy density, $\gamma$, is computed by considering points in an interval determined by an energy cutoff (black dotted line). The uncertainty in $\gamma$ comes from varying the energy cutoff as described in Methods \ref{['sec:skew']}, and from statistical error. The skewness is increased in the $11\to12$ energy density compared to $1\to1$ due to the inelastic production of the heavy $|2\rangle$ particle. The simulation parameters are the same as in Fig. \ref{['fig:ibm_results']}b).