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arXiv:2402.08969 · Physics Letters B

Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers

Weijie Du, James P. Vary

Published May 9, 2025• 4 citations
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Abstract

We present a novel input scheme for general second-quantized Hamiltonians of relativistic or non-relativistic many-fermion systems. This input scheme incorporates the fermionic anticommutation relations, particle number variations, and respects the symmetries of the Hamiltonian. Based on our input scheme, we propose a hybrid quantum-classical framework for spectral calculations on future quantum hardwares. We provide explicit circuit designs and the associated gate cost. We demonstrate our hybrid framework by solving the low-lying spectra of 42 Ca and 46 Ca. Our input scheme provides new pathways to solving the spectra and dynamics of the relativistic and nonrelativistic many-fermion systems via first-principles approaches.

DOI
10.1016/j.physletb.2025.139548

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We develop a novel, systematic input scheme for many-boson Hamiltonians in order to solve field theory problems within the light-front Hamiltonian formalism via quantum computing. We present our discussion of this input scheme based on the light-front Hamiltonian of the two-dimensional ${\ensuremath{\phi}}^{4}$ theory. In our input scheme, we employ a set of quantum registers, where each register encodes the occupation of a distinct boson mode as binaries. We squeeze the boson operators of each mode and present the Hamiltonian in terms of unique combinations of the squeezed-boson operators. We design the circuit modules for these unique combinations. Based on these circuit modules, we block encode the many-boson Hamiltonian utilizing the idea of quantum walk. For demonstration purposes, we present the spectral calculations of the Hamiltonian utilizing the hybrid quantum-classical symmetry-adapted quantum Krylov subspace diagonalization algorithm based on our input scheme, where the quantum computations are performed with the IBM qiskit quantum simulator. The results of the hybrid calculations agree with exact results. We can incorporate the input scheme in this work with the input scheme for many-fermion Hamiltonians; they jointly offer new pathways to solving the structure and dynamics of more general field theory problems on future fault-tolerant quantum computers.
Response functions are key observables for probing the structure and dynamics of many-body systems. We introduce and demonstrate a quantum-classical framework for computing response functions of general many-fermion systems that also provides the full bound-state spectrum. The framework employs the Lorentz integral transform and a new Hamiltonian input scheme that enables practical and scalable circuit constructions for general many-fermion Hamiltonians. Within this framework, we develop a hybrid strategy to evaluate the Lorentz integral and propose three protocols to extract response functions and bound-state structural information. As a demonstration, we apply the method to 19O{}^{19}\mathrm{O}19O with realistic internucleon interactions, computing both the bound-state spectrum and the response function. We envision that our approach will open new avenues for exploring the structure and dynamics of a broad class of many-body systems across diverse fields.
Systematic input scheme of many-boson Hamiltonians with applications to the two-dimensional ϕ4ϕ^4ϕ4 theory
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We propose a framework for computing the structure and dynamics for second-quantized many-nucleon Hamiltonians on quantum computers. We develop an oracle-based Hamiltonian input model that computes the many-nucleon states and nonzero Hamiltonian matrix elements of the many-nucleon system. With our Fock-state based input model, we show how to implement the sparse matrix simulation algorithms to calculate the dynamics of the second-quantized many-nucleon Hamiltonian. Based on the dynamics simulation methods, we also present the methodology for structure calculations of the many-nucleon system. In this work, we provide an explicit circuit design of our input model of the second-quantized Hamiltonian within a direct encoding scheme that maps the occupation of each available single-particle state in the many-nucleon state to the state of specific qubit in a quantum register. We analyze our method and provide the asymptotic cost in computing resources for structure and dynamics calculations of many-nucleon systems. For pedagogical purposes, we demonstrate our input model with two model problems in restricted model spaces.
Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem, for instance, the development of variational quantum algorithms. A recent work by Huggins et al. [1] reports a novel candidate, i.e. a quantum-classical hybrid Monte Carlo algorithm with a reduced bias in comparison to its fully-classical counterpart. In this paper, we propose a family of scalable quantum-assisted Monte Carlo algorithms where the quantum computer is used at its minimal cost and still can reduce the bias. By incorporating a Bayesian inference approach, we can achieve this quantum-facilitated bias reduction with a much smaller quantum-computing cost than taking empirical mean in amplitude estimation. Besides, we show that the hybrid Monte Carlo framework is a general way to suppress errors in the ground state obtained from classical algorithms. Our work provides a Monte Carlo toolkit for achieving quantum-enhanced calculation of fermion systems on near-term quantum devices.