A continuous process tensor is defined by embedding the discrete multi-partite Choi matrix of a quantum comb into bosonic Fock space, closing the gap between discrete and continuum descriptions of multi-time quantum processes.
Continuous Matrix Product States for Inhomogeneous Quantum Field Theories: a Basis-Spline Approach
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abstract
Continuous Matrix Product States (cMPS) are powerful variational ansatz states for ground states of continuous quantum field theories in (1+1) dimension. In this paper we introduce a novel parametrization of the cMPS wave function based on basis-spline functions, which we coin spline-based MPS (spMPS), and develop novel regauging techniques for inhomogeneous cMPS. We extend a recently developed ground-state optimization algorithm for translational invariant cMPS [M. Ganahl, J. Rinc\'on, G.Vidal. Phys.Rev.Lett. 118,220402 (2017)] to the case of inhomogeneous cMPS and, as proof-of-principle, use it to obtain the ground-state of a gas of Lieb-Liniger bosons in a periodic potential. The proposed method provides a first working implementation of a cMPS optimization for non-translational invariant continuous Hamiltonians.
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An operational continuum limit of quantum combs
A continuous process tensor is defined by embedding the discrete multi-partite Choi matrix of a quantum comb into bosonic Fock space, closing the gap between discrete and continuum descriptions of multi-time quantum processes.