Simulating physical phenomena by quantum networks

2001/08/31 by Rolando D. Somma, R. Somma, G. Ortiz +6 · 379 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Creation and annihilation operators #Hamiltonian (control theory) #Isomorphism (crystallography) #Mathematics #Observable #Pauli exclusion principle #Physical system #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum mechanics #Theoretical physics #cond-mat #quant-ph

paper · pdf · doi:10.1103/physreva.65.042323

published in Physical Review A 65(4) (American Physical Society) · 44 pages, 15 psfigure

arxiv created 2001/08/31 · openalex publication_date 2002/04/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Physical systems, characterized by an ensemble of interacting constituents, can be represented and studied by different algebras of operators (observables). For example, a fully polarized electronic system can be studied by means of the algebra generated by the usual fermionic creation and annihilation operators or by the algebra of Pauli (spin-1/2) operators. The Jordan-Wigner isomorphism gives the correspondence between the two algebras. As we previously noted, similar isomorphisms enable one to represent any physical system in a quantum computer. In this paper we evolve and exploit this fundamental observation to simulate generic physical phenomena by quantum networks. We give quantum circuits useful for the efficient evaluation of the physical properties (e.g., the spectrum of observables or relevant correlation functions) of an arbitrary system with Hamiltonian H.

Citations

• Two-Bit Gates are Universal for Quantum Computation
• Expressing the operations of quantum computing in multiparticle geometric algebra
• Bose-Fermi transformation in three-dimensional space
• Elementary gates for quantum computation
• Quantum Algorithms Revisited
• Quantum algorithms for fermionic simulations

Cited by

• Theory of the Matchgate Commutant
• Measurement of linear response functions in Nuclear Magnetic Resonance
• Decomposition of high-rank factorized unitary coupled-cluster operators using ancilla and multiqubit controlled low-rank counterparts
• Estimating the Error of an Analog Quantum Simulator by Additional Measurements
• A proposal for using molecular spin qudits as quantum simulators of light–matter interactions
• Electromechanical quantum simulators
• Quantum optimal control with quantum computers: A hybrid algorithm featuring machine learning optimization
• Toward extracting scattering phase shift from integrated correlation functions on quantum computers
• Computational complexity in electronic structure
• Digital quantum simulation of beam splitters and squeezing with IBM quantum computers
• Operator locality in the quantum simulation of fermionic models
• Uranium in its natural compounds
• Simulating Hamiltonian Dynamics with a Truncated Taylor Series
• Computing n-time correlation functions without ancilla qubits
• Local spin operators for fermion simulations
• Dissipation-Induced Threshold on Integrability Footprints
• Higher order tensor factorizations for block encoding vibrational and vibronic Hamiltonians
• Fermion-to-qubit mappings with varying resource requirements for quantum simulation