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A formal analysis is conducted on the exactness of various forms of unitary coupled cluster (UCC) theory based on particle-hole excitation and de-excitation operators. Both the conventional single exponential UCC parameterization and a disentangled (factorized) version are considered. We formulate a differential cluster analysis to determine the UCC amplitudes corresponding to a general quantum state. The exactness of conventional UCC (ability to represent any state) is explored numerically and it is formally shown to be determined by the structure of the critical points of the UCC exponential mapping. A family of disentangled UCC wave functions are shown to exactly parameterize any state, thus showing how to construct Trotter-error-free parameterizations of UCC for applications in quantum computing. From these results, we derive an exact disentangled UCC parameterization that employs an infinite sequence of particle-hole or general one- and two-body substitution operators.
We present a coupled cluster and linear response theory to compute properties of many-electron systems at non-zero temperatures. For this purpose, we make use of the thermofield dynamics, which allows for a compact wavefunction representation of the
A variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are pre-computed and
A full coupled-cluster expansion suitable for sparse algebraic operations is developed by expanding the commutators of the Baker-Campbell-Hausdorff series explicitly for cluster operators in binary representations. A full coupled-cluster reduction th
We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behaviour of a coupled cluster wavefunction representation we propos
The coupled cluster iteration scheme is analysed as a multivariate discrete-time map using nonlinear dynamics and synergetics. The nonlinearly coupled set of equations to determine the cluster amplitudes are driven by a fraction of the entire set of