Related papers: A way to solve BCS-type pairing model
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We…
We propose and implement an algorithm for solving an overdetermined system of partial differential equations in one unknown. Our approach relies on Bour-Mayer method to determine compatibility conditions via Jacobi-Mayer brackets. We solve…
Exploiting quantum properties to outperform classical ways of information-processing is an outstanding goal of modern physics. A promising route is quantum simulation, which aims at implementing relevant and computationally hard problems in…
We implement an algorithm which is aimed to reduce the number of basis states spanning the Hilbert space of quantum many-body systems. We test the efficiency of the procedure by working out and analyzing the spectral properties of strongly…
As is well known, the single level seniority model of pairing has been solved exactly since long using angular momentum algebra. It is shown that it can also be solved using the Dyson equation of standard many-body theory. The formalism…
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that play an important role in networking, computational biology, and biochemistry. We show an explicit construction…
The fundamental structure of the full set of solutions of the BCS $^3 P_2$ pairing problem in neutron matter is established. The relations between different spin-angle components in these solutions are shown to be practically independent of…
We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of $1/\sin^2$-type. The…
The continuous matrix product state (cMPS) ansatz is a promising numerical tool for studying quantum many-body systems in continuous space. Although it provides a clean framework that allows one to directly simulate continuous systems, the…
The BCS theory models electron correlations with pure zero-momentum pairs. Here we consider a family of pairing Hamiltonians, where the electron correlations are modelled with pure arbitrary-momentum pairs. We find all models in the family…
To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is…
Pairwise models like the Ising model or the generalized Potts model have found many successful applications in fields like physics, biology, and economics. Closely connected is the problem of inverse statistical mechanics, where the goal is…
For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a…
We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
The development of quantum algorithms and protocols calls for adequate modelling and verification techniques, which requires abstracting and focusing on the basic features of quantum concurrent systems, like CCS and CSP have done for their…
In this paper, we employ the bootstrap method, a technique that relies on consistency relations instead of direct diagonalization, to determine the expectation values in quantum many-body systems. We then use these values to assess the…
We present a novel method for solving eigenvalue problems on a quantum computer based on spectroscopy. The method works by coupling a "probe" qubit to a set of system simulation qubits and then time evolving both the probe and the system…
We identify a large class of quantum many-body systems that can be solved exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on arbitrary lattices. We show that the entire ground state manifold of such models can be…