Author: Denis Avetisyan
New research reveals that the complex process of SU(N) invariant two-body scattering can be remarkably simplified and expressed using a surprisingly compact quantum circuit.
This paper demonstrates that SU(N) scattering amplitudes can be constructed using only two involutive unitary gates, providing a fundamental link between quantum computation and particle physics.
Despite the complexity of calculating scattering amplitudes in quantum field theory, remarkably minimal structures can emerge when viewed through the lens of quantum computation. This is the central claim of ‘Quantum Computational Structure of $SU(N)$ Scattering’, where we demonstrate that all two-particle scattering processes governed by $SU(N)$ symmetry can be constructed using only two fundamental quantum gates—effectively, bit flips acting on internal quantum numbers. This finding suggests a surprisingly simple quantum circuit underlies fundamental interactions, raising the question of whether similar minimal representations exist for more complex scattering scenarios and higher-body interactions. Could this framework offer new insights into the underlying principles governing quantum dynamics?
The Entropic Cost of Scattering
Calculating the $SSMatrix$ is central to understanding particle interactions, yet traditional methods quickly become computationally prohibitive due to its factorial growth with particle number. This limitation hinders accurate modeling of complex physical systems, particularly those involving many-body interactions. Accurate $TwoParticleScattering$ descriptions require relativistic treatment via $RelativisticScattering$, demanding efficient computation. Non-relativistic approximations introduce inaccuracies at higher energies. Maintaining relativistic accuracy exacerbates the computational challenges. This inherent complexity arises from representing quantum states with $Qudit$ systems, which require exponential resources, underscoring the need for novel algorithms and hardware.
Quantum Computation: A Path Through Complexity
Quantum computation offers a powerful paradigm for complex simulations by leveraging quantum mechanics to encode and manipulate physical processes. Traditional methods struggle with the exponential scaling of resources required to model many-body quantum systems. At the heart of this approach are $UnitaryGate$ operations that manipulate $QuantumState$ vectors to simulate particle interactions. Efficient implementation and high fidelity of these gates are crucial for achieving speedups. $BlockEncoding$ efficiently represents unitary operations as low-rank matrices, reducing quantum resource requirements and facilitating complex simulations.
Efficient Representations: Minimizing Computational Debt
Recent advancements leverage techniques to efficiently represent and simulate complex quantum operations. The `LinearCombinationOfUnitaries` approach builds on `BlockEncoding` to express operations as weighted sums of simpler gates, reducing computational cost. Resource optimization is further achieved with `OneAncillaQubit`, minimizing qubit overhead in $SSMatrix$ calculations and allowing simulation of larger systems. Applying `PartialWaveExpansion` decomposes scattering amplitudes, revealing that any SU(N) invariant two-body scattering amplitude can be expressed using only 3 `UnitaryGate` operations – a fundamental limit on simulation complexity.
Symmetry as a Guiding Principle
Scattering amplitudes, fundamental to describing particle interactions, are governed by $SUNSymmetry$ and the broader concept of $SU(N)Invariance$. Exploiting this invariance simplifies calculations by reducing the number of independent amplitudes. A direct consequence is a remarkably compact representation of the $SSMatrix$, requiring only two unitary matrices instead of a vast number of parameters. This dimensionality reduction is analogous to efficient encoding in quantum information theory. The principles of symmetry, specifically as expressed through $RecouplingCoefficient$ within a $PartialWaveExpansion$, accelerate quantum simulations, allowing modeling of more complex systems.
The pursuit of minimal representations in quantum systems, as evidenced by this work on SU(N) scattering, echoes a fundamental principle: elegant solutions often lie at the core of complex phenomena. The demonstration that scattering amplitudes can be constructed from just two involutive unitary gates suggests an underlying simplicity within nature’s building blocks. This resonates with the inevitability of decay; systems strive for minimal energy states, and this circuit’s efficiency can be seen as a graceful aging of computational complexity. As Richard Feynman observed, “The first principle is that you must not fool yourself – and you are the easiest person to fool.” This research, by stripping away unnecessary operations, attempts precisely that – a refusal to be fooled by superficial complexity, revealing the bare essentials of quantum interaction.
What Lies Ahead?
The demonstration that SU(N) scattering—a cornerstone of particle interactions—can be recast within the constraints of merely two involutive unitary gates is not, perhaps, a simplification, but a relocation of complexity. The apparent minimality of the circuit structure does not erase the inherent latency in accessing the scattering amplitude; it merely shifts the burden. Uptime, after all, is temporary. The true challenge now lies not in further compressing the quantum circuit, but in understanding the limitations imposed by these fundamental gates themselves. What algorithmic landscapes are accessible only through this restricted gate set, and which remain forever beyond reach?
The work highlights a curious symmetry: the reduction of a continuous symmetry group—SU(N)—to a discrete set of operations. This suggests that many physical systems, seemingly defined by continuous parameters, may possess hidden, quantized underpinnings. The question then becomes: are these involutive gates a fundamental property of reality, or an artifact of the chosen representational framework? Stability, it must be remembered, is an illusion cached by time.
Future investigations should explore the scalability of this approach. While the two-body scattering case is elegantly resolved, extending this framework to multi-body interactions—where the combinatorial complexity explodes—will inevitably reveal the boundaries of this simplification. The focus must shift from seeking further compression to charting the inevitable decay of performance as complexity increases. Every request, after all, must pay the tax of latency.
Original article: https://arxiv.org/pdf/2511.10550.pdf
Contact the author: https://www.linkedin.com/in/avetisyan/
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2025-11-14 17:24