Simulating physical phenomena by quantum networks

By Rolando D. Somma, G. Ortiz, James E. Gubernatis, Emanuel Knill, R. Laflamme. 2001

298 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3527b7d2cfc2684f0359812a9832feb6c577a570

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Simulating Hamiltonians in quantum networks: Efficient schemes and complexity bounds (2001, background): “Various schemes for constructing gate sequences which simulate the unitary evolution corresponding to a given Hamiltonian have been suggested (see e. g. [18, 23]).”
Simulating chemistry using quantum computers. (2010, methodology): “This problem can be solved by using the Jordan-Wigner transformation to enforce the correct commutation relations on the quantum computer (99,118,119,10).”
Toward the first quantum simulation with quantum speedup (2017, background): “havior of speciﬁc types of systems. Quantum computers presumably oﬀer an advantage for simulations of any system in which quantum mechanics plays a signiﬁcant role, including fermionic lattice models [63, 71, 72, 77], quantum chemistry [3–5, 36, 42, 62, 64, 76], and quantum ﬁeld theories [39–41]. Mu”
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity (2018, methodology): “…for performing a controlled indexed X l operation with L ¼ 11 possible targets. below, our approach for implementing SELECT will require that we have a circuit capable of selectively applying the Majorana fermion operator where the last equality holds under the Jordan-Wigner transformation [61].”
Scalable Quantum Simulation of Molecular Energies (2015, methodology): “Until this work, important aspects of scalable chemistry simulation such as the Jordan-Wigner transformation [40] or the Bravyi-Kitaev transformation [41,42] had never been used to represent a molecule in an experiment; however, prior experiments such as Ref.”
Quantum Simulation (2013, methodology): “In (Somma et al., 2002) it was shown how to obtain the energy spectrum of the Fermi-Hubbard Hamiltonian:”