The author proposes a method to circumvent the challenging problems caused by the strong short-range repulsion in realistic atomic systems by introducing a softening and extrapolation approach. This method is then demonstrated in calculating the binding energies and scattering processes in weakly bound few-body atomic ${}^{4}$ He systems.''The author proposes a method to circumvent the challenging problems caused by the strong short-range repulsion in realistic atomic systems by introducing a softening and extrapolation approach. This method is then demonstrated in calculating the binding energies and scattering processes in weakly bound few-body atomic ${}^{4}$He systems.''

Physical Review AApr 13, 20223 citations

The Many-Body Problem

Daniel Charles Mattis

WORLD SCIENTIFIC eBooksMar 1, 1993156 citations

The Many-Body Problem

Taylor & Francis eBooksDec 31, 20040 citations

Nonperturbative k -body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins

Jacob Biamonte

An algebraic method has been developed which allows one to engineer several energy levels including the low-energy subspace of interacting spin systems. By introducing ancillary qubits, this approach allows $\mathit{k}$ -body interactions to be captured exactly using two-body Hamiltonians. Our method works when all terms in the Hamiltonian share the same basis and has no dependence on perturbation theory or the associated large spectral gap. Our methods allow problem instance solutions to be embedded into the ground energy state of Ising spin systems. Adiabatic evolution might then be used to place a computational system into its ground state.An algebraic method has been developed which allows one to engineer several energy levels including the low-energy subspace of interacting spin systems. By introducing ancillary qubits, this approach allows $\mathit{k}$-body interactions to be captured exactly using two-body Hamiltonians. Our method works when all terms in the Hamiltonian share the same basis and has no dependence on perturbation theory or the associated large spectral gap. Our methods allow problem instance solutions to be embedded into the ground energy state of Ising spin systems. Adiabatic evolution might then be used to place a computational system into its ground state.

arXiv:0801.3800Physical Review AMay 23, 2008120 citations

The Many-Body Problem

Jerome K. Percus

Interscience Publishers eBooksJan 1, 196313 citations

Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions

Motohiko Ezawa

Topological quantum computation by way of braiding of Majorana fermions is not universal quantum computation. There are several attempts to make universal quantum computation by introducing some additional quantum gates or quantum states. However, there is a serious problem in embedding an $M$ -qubit quantum gate in the $N$ -qubit system with $N>M$ . This is an inherent problem to the Majorana system, where quantum gates for logical qubits become nonlocal in terms of physical qubits in general because braiding operations preserve the fermion parity. For instance, the CZ gate could not be embedded in the three-qubit system. We overcome this embedding problem by introducing $2(N+1)$ -body interactions of Majorana fermions in the $N$ -qubit system. A universal set of quantum gates is constructed for $N$ logical qubits, leading to topological-nontopological hybrid universal quantum computation. It would be more robust than conventional universal quantum computation because the quantum gates generated by braiding are topologically protected.Topological quantum computation by way of braiding of Majorana fermions is not universal quantum computation. There are several attempts to make universal quantum computation by introducing some additional quantum gates or quantum states. However, there is a serious problem in embedding an $M$-qubit quantum gate in the $N$-qubit system with $N>M$. This is an inherent problem to the Majorana system, where quantum gates for logical qubits become nonlocal in terms of physical qubits in general because braiding operations preserve the fermion parity. For instance, the CZ gate could not be embedded in the three-qubit system. We overcome this embedding problem by introducing $2(N+1)$-body interactions of Majorana fermions in the $N$-qubit system. A universal set of quantum gates is constructed for $N$ logical qubits, leading to topological-nontopological hybrid universal quantum computation. It would be more robust than conventional universal quantum computation because the quantum gates generated by braiding are topologically protected.

arXiv:2304.06260Physical review. B./Physical review. BJul 9, 20245 citations

{}^{4}

He systems.''

\mathit{k}

-body interactions to be captured exactly using two-body Hamiltonians. Our method works when all terms in the Hamiltonian share the same basis and has no dependence on perturbation theory or the associated large spectral gap. Our methods allow problem instance solutions to be embedded into the ground energy state of Ising spin systems. Adiabatic evolution might then be used to place a computational system into its ground state.

M

-qubit quantum gate in the

N

-qubit system with

N>M

. This is an inherent problem to the Majorana system, where quantum gates for logical qubits become nonlocal in terms of physical qubits in general because braiding operations preserve the fermion parity. For instance, the CZ gate could not be embedded in the three-qubit system. We overcome this embedding problem by introducing

2(N+1)

-body interactions of Majorana fermions in the

N

-qubit system. A universal set of quantum gates is constructed for

N

logical qubits, leading to topological-nontopological hybrid universal quantum computation. It would be more robust than conventional universal quantum computation because the quantum gates generated by braiding are topologically protected.