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arXiv:2507.10777 · New Journal of Physics

Entanglement and magic on the light-front

Sam Alterman, Peter J. Love

Published Mar 1, 2026• 1 citation
arXivHTMLPDF

Abstract

Abstract In the light-front (LF) formulation of quantum field theory (QFT), physics is formulated from the perspective of a massless observer necessarily traveling at the speed of light. The LF formulation provides an alternative computational approach to lattice gauge theory, and has recently been investigated as a future application of quantum computers. A natural question is how quantum resources such as entanglement and contextuality amongst physical qubits in the laboratory are utilized in LF simulations of QFTs. We use the (1+1) D transverse-field Ising model to explore this question. We derive the LF energy operator that generates the LF dynamics of the system, which is distinct from the instant-form (IF) Hamiltonian. We find that while the eigenstates of the IF Hamiltonian exhibit pairwise entanglement between positive and negative momenta in IF momentum-space, the eigenstates of the LF Hamiltonian are separable in LF momentum-space. We then calculate the momentum-space magic of the IF-momentum-space ground state and show that it always requires more magic to prepare than the LF-momentum-space ground state. At the quantum critical point, corresponding to a massless free fermion, both LF and IF ground states are stabilizers, but the LF ground state is separable in LF momentum-space while the IF ground state is a product of maximally entangled pairs in IF momentum-space. These results show that quantum resources such as entanglement and magic are utilized differently by quantum simulations formulated in LF and IF, and that the simplicity of the LF ground state results in fewer required quantum resources.

DOI
10.1088/1367-2630/ae4fea

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Abstract In the light-front (LF) formulation of quantum field theory (QFT), physics is formulated from the perspective of a massless observer necessarily traveling at the speed of light. The LF formulation provides an alternative computational approach to lattice gauge theory, and has recently been investigated as a future application of quantum computers. A natural question is how quantum resources such as entanglement and contextuality amongst physical qubits in the laboratory are utilized in LF simulations of QFTs. We use the (1+1) D transverse-field Ising model to explore this question. We derive the LF energy operator that generates the LF dynamics of the system, which is distinct from the instant-form (IF) Hamiltonian. We find that while the eigenstates of the IF Hamiltonian exhibit pairwise entanglement between positive and negative momenta in IF momentum-space, the eigenstates of the LF Hamiltonian are separable in LF momentum-space. We then calculate the momentum-space magic of the IF-momentum-space ground state and show that it always requires more magic to prepare than the LF-momentum-space ground state. At the quantum critical point, corresponding to a massless free fermion, both LF and IF ground states are stabilizers, but the LF ground state is separable in LF momentum-space while the IF ground state is a product of maximally entangled pairs in IF momentum-space. These results show that quantum resources such as entanglement and magic are utilized differently by quantum simulations formulated in LF and IF, and that the simplicity of the LF ground state results in fewer required quantum resources.
We present a quantum algorithm for simulation of quantum field theory in the light-front formulation and demonstrate how existing quantum devices can be used to study the structure of bound states in relativistic nuclear physics. Specifically, we apply the Variational Quantum Eigensolver algorithm to find the ground state of the light-front Hamiltonian obtained within the Basis Light-Front Quantization (BLFQ) framework. The BLFQ formulation of quantum field theory allows one to readily import techniques developed for digital quantum simulation of quantum chemistry. This provides a method that can be scaled up to simulation of full, relativistic quantum field theories in the quantum advantage regime. As an illustration, we calculate the mass, mass radius, decay constant, electromagnetic form factor, and charge radius of the pion on the IBM Vigo chip. This is the first time that the light-front approach to quantum field theory has been used to enable simulation of a real physical system on a quantum computer.
Entanglement and non-stabilizerness (magic) quantify two distinct departures of quantum systems from classical description: the former measures non-local correlations, while the latter measures the deviation from stabilizer states that can be efficiently simulated classically. Understanding magic in physically relevant quantum field theories is essential for identifying where quantum advantage may be realized in the early fault-tolerant quantum computing era. We calculate the gauge-invariant entanglement entropy and stabilizer Rényi entropy of the ground state of the (1+1)-dimensional SU(2) lattice gauge theory formulated in a dressed-site basis that enforces Gauss's law exactly. Using tensor networks, we obtain results for system sizes up to L=100L=100L=100 (300 qubits). We find a crossover denoted by g⋆g_{\star}g⋆​ where the ground state passes from a more magic-rich regime into a regime with less magic; this is also tracked by the sharpest change of both the entanglement entropy and lattice particle density. Our large-scale study of non-stabilizerness and entanglement entropy in a non-Abelian lattice gauge theory with matter provides new insight into the interplay of magic and entanglement in gauge theories, both of which are relevant for classical and early fault-tolerant quantum simulations.
Quantum chromodynamics (QCD) describes the structure of hadrons such as the proton at a fundamental level. The precision of calculations in QCD limits the precision of the values of many physical parameters extracted from collider data. For example, uncertainty in the parton distribution function is the dominant source of error in the WWW mass measurement at the Large Hadron Collider. Improving the precision of such measurements is essential in the search for new physics. Quantum simulation offers an efficient way of studying quantum field theories (QFTs) such as QCD nonperturbatively. Previous quantum algorithms for simulating QFTs have qubit requirements that are well beyond the most ambitious experimental proposals for large-scale quantum computers. Can the qubit requirements for such algorithms be brought into range of quantum computation with several thousand logical qubits? We show how this can be achieved by using the light-front formulation of quantum field theory. This work was inspired by the similarity of the light-front formulation to quantum chemistry, first noted by Wilson [Nucl. Phys. B, Proc. Suppl. 17, 82 (1990)].
The interplay between quantum orientation entanglement and Wigner rotation plays a fundamental role in understanding the behavior of spin angular momentum in quantum states. To analyze the quantum orientation entanglement of the relativistic helicity states interpolating between the Jacob-Wick helicity and the light-front helicity, we examine the relative angle between the particle's momentum direction and the spin orientation for the interpolating helicity states. For this analysis, we introduce a novel method for expanding the interpolating helicity states in terms of the Jacob-Wick helicity. The corresponding probabilistic coefficients follow the structure of the Wigner d-matrix elements, which we use for the interpretation of the quantum orientation entanglement manifested in the angular distributions of the interpolating scattering helicity amplitudes. As an explicit demonstration, we compute the interpolating helicity amplitudes for the pair production of spin-1 (vector) particles in the annihilation of two spin-0 (scalar) particles, focusing primarily on their contact interaction. In particular, we identify the critical interpolation angle that bifurcates the dynamical branches between the instant-form dynamics and the light-front dynamics and discuss the underlying orientation entanglement in the interpolating helicity amplitudes.
In distributed fault-tolerant quantum computing, entanglement and magic are essential resources for quantum communication and universal fault-tolerant computation, respectively. Although they are usually treated as distinct resource currencies, whether they admit a unified resource-theoretic description remains an open question. Here, we introduce the distributed resource theory of entanglement and magic (DREAM). In this framework, the free states are convex mixtures of product local stabilizer states, and the free operations are local stabilizer circuits assisted by classical communication (LSCC). We show that DREAM contains nontrivial resource states that are neither entanglement nor magic, so it is strictly richer than treating the two resources independently. Surprisingly, such resources can enable the teleportation of magic states between distant parties without consuming entanglement, revealing a counterintuitive form of resource teleportation mediated entirely by separable states. We further generalize this result to quantum networks and investigate general quantum-state teleportation under LSCC. We show that the shared resource under DREAM is closely related to the teleportation capability, quantified by the magic of the teleported state. Our work establish a systematic framework for studying distributed quantum resources and uncover intrinsic relations among distinct resources within a unified resource theory.
Magic, a quantum resource distinct from entanglement, measures departure from states stabilized by products of Pauli operators. Such stabilizer states can be maximally entangled yet admit efficient classical description: quantum advantage requires magic. We develop a powerful framework to evaluate the degree of magic in generic many-body states. We use it to study the fate of magic under thermal and dynamical evolution. In the transverse field Ising model, we find a thermal sudden death of magic that saturates with system size, and occurs after the death of entanglement. We reach similar conclusions in generic spin chains, and in the Kitaev quantum spin liquid on the honeycomb lattice, where the threshold shows an intricate dependence on subregion shape. We then study how magic equilibrates after a quantum quench. In quenches of generic spin chains, the magic of a subregion typically dies before entanglement, contrary to thermal trajectories. An explanation is given in terms of the geometry of non-magical states. As a third type of trajectory, we examine the fate of magic with separation with an appropriate notion of non-local magic and establish a sudden death. Finally, we show how to experimentally witness a volume law of frame-robust magic in quantum materials by using neutron scattering.