Quantum simulations of quantum chromodynamics (QCD) require a representation of gauge fields and fermions on the finitely many degrees of freedom available on a quantum computer. We introduce a truncation of lattice QCD coupled to staggered fermions that includes (i) a local Krylov truncation that generates allowed basis states; (ii) a maximum allowed electric energy per link; (iii) a limit on the number of fermions per site; and (iv) a truncation in the large N_c scaling of Hamiltonian matrix elements. Explicit truncated Hamiltonians for 1+1D and 2+1D lattices are given, and numerical simulations of string-breaking dynamics are performed.Quantum simulations of quantum chromodynamics (QCD) require a representation of gauge fields and fermions on the finitely many degrees of freedom available on a quantum computer. We introduce a truncation of lattice QCD coupled to staggered fermions that includes (i) a local Krylov truncation that generates allowed basis states; (ii) a maximum allowed electric energy per link; (iii) a limit on the number of fermions per site; and (iv) a truncation in the large N_c scaling of Hamiltonian matrix elements. Explicit truncated Hamiltonians for 1+1D and 2+1D lattices are given, and numerical simulations of string-breaking dynamics are performed.

hep-latCross-listedarXiv:2602.02344Feb 3, 20260 citations

Trapped-ion quantum simulation of (1+1)D SU(2) lattice gauge theory via loop-string-hadron formulation

Toshiaki Kaji, Jesse R. Stryker, Yutaro Iiyama +4 more

We present a quantum simulation of the SU(2) lattice gauge theory in 1+1 dimensions with one flavor of fermions, performed using the trapped-ion Quantinuum System Model H2. This work is based on the loop-string-hadron (LSH) formulation of the gauge theory, and is distinguished by using qubits to represent both bosonic-gauge and fermionic-matter degrees of freedom. Furthermore, we access the $j=1$ electric-flux sector beyond the $j_{\max}=1/2$ truncation commonly used in SU(2) quantum simulations. To that end, we digitize an electric-field degree of freedom using a multiqubit register for representing the bosonic quantum number. Our simulation therefore synthesizes several key ingredients relevant to quantum simulations in higher spatial dimensions, in particular explicit local gauge-field degrees of freedom represented here by a multiqubit bosonic register, while relying solely on circuit-construction optimizations that are expected to scale polynomially with lattice size. This work demonstrates that modern quantum hardware is increasingly able to accommodate the features of complicated but physically important lattice gauge theories while successfully reproducing the expected Trotterized dynamics.We present a quantum simulation of the SU(2) lattice gauge theory in 1+1 dimensions with one flavor of fermions, performed using the trapped-ion Quantinuum System Model H2. This work is based on the loop-string-hadron (LSH) formulation of the gauge theory, and is distinguished by using qubits to represent both bosonic-gauge and fermionic-matter degrees of freedom. Furthermore, we access the $j=1$ electric-flux sector beyond the $j_{\max}=1/2$ truncation commonly used in SU(2) quantum simulations. To that end, we digitize an electric-field degree of freedom using a multiqubit register for representing the bosonic quantum number. Our simulation therefore synthesizes several key ingredients relevant to quantum simulations in higher spatial dimensions, in particular explicit local gauge-field degrees of freedom represented here by a multiqubit bosonic register, while relying solely on circuit-construction optimizations that are expected to scale polynomially with lattice size. This work demonstrates that modern quantum hardware is increasingly able to accommodate the features of complicated but physically important lattice gauge theories while successfully reproducing the expected Trotterized dynamics.

hep-latCross-listedarXiv:2610.24091Oct 20, 20260 citations

Duality and Quantum Mechanics

J. M. Isidro

This Festschrift in honour of J. A. de Azcarraga gives an introduction to the concept of duality, i.e., to the relativity of the notion of a quantum, in the context of the quantum mechanics of a finite number of degrees of freedom. Although the concept of duality arises in string and M--theory, Vafa has argued that it should also have a counterpart in quantum mechanics, before moving on to second quantisation, fields, strings and branes. We illustrate our analysis with the case when classical phase space is complex projective space, but our conclusions can be generalised to other complex, symplectic phase spaces, both compact and noncompact.This Festschrift in honour of J. A. de Azcarraga gives an introduction to the concept of duality, i.e., to the relativity of the notion of a quantum, in the context of the quantum mechanics of a finite number of degrees of freedom. Although the concept of duality arises in string and M--theory, Vafa has argued that it should also have a counterpart in quantum mechanics, before moving on to second quantisation, fields, strings and branes. We illustrate our analysis with the case when classical phase space is complex projective space, but our conclusions can be generalised to other complex, symplectic phase spaces, both compact and noncompact.

arXiv:quant-ph/0310092Oct 14, 20031 citation

The Variety of Finite Fermion Systems and Their Basic Properties

Joachim Alexander Maruhn, P.‐G. Reinhard, E. Suraud

Springer eBooksNov 12, 20090 citations

j=1

electric-flux sector beyond the

j_{\max}=1/2

truncation commonly used in SU(2) quantum simulations. To that end, we digitize an electric-field degree of freedom using a multiqubit register for representing the bosonic quantum number. Our simulation therefore synthesizes several key ingredients relevant to quantum simulations in higher spatial dimensions, in particular explicit local gauge-field degrees of freedom represented here by a multiqubit bosonic register, while relying solely on circuit-construction optimizations that are expected to scale polynomially with lattice size. This work demonstrates that modern quantum hardware is increasingly able to accommodate the features of complicated but physically important lattice gauge theories while successfully reproducing the expected Trotterized dynamics.