Few- and Many-Fermion Problems (With 7 Figures)

Python software and data for the publication "Mitigating the barren plateau problem in linear optics" by Matthew D. Horner. To run this Python code, first install Aegiq's Lightworks and the fermion sampling extension. pip install lightworks pip install lightworks[fermionic] Notebooks This contains notebooks for various figures. Run each notebook to generate the data. Figure 2 - Barren plateau scaling of bosonic and fermionic linear optics. Figure 5 - Measurement-induced dual-valued phase shifter (DVPS). Figure 8 - False herald probasbility calculation for the DVPS Figure 9 - Cost landscape comparison. Figure 10 - Solving a random QUBO problem using gradient descent or Rotosolve for either bosonic or fermionic statistics. Figure 12 - Calculation of the Fourier modes in the QUBO cost landscape. Raw data This also contains raw data for Figure 2 - The barren plateau scaling figures stored in three .npz files Figure 5 - A set of pre-computed DVPS unitaries in a single .npz file Figure 9 - The raw cost landscape data in a single .npz file. Figure 12 - All subfigure data in 12 .txt files. This data is produced by the notebooks so is not necessary, but is included to save time. Scripts The scripts lightworks_optimiser_classes.py lightworks_qubo.py contain code for optimising via gradient descent and Rotosolve. These are called by the notebooks.Python software and data for the publication "Mitigating the barren plateau problem in linear optics" by Matthew D. Horner. To run this Python code, first install Aegiq's Lightworks and the fermion sampling extension. pip install lightworks pip install lightworks[fermionic] Notebooks This contains notebooks for various figures. Run each notebook to generate the data. Figure 2 - Barren plateau scaling of bosonic and fermionic linear optics. Figure 5 - Measurement-induced dual-valued phase shifter (DVPS). Figure 8 - False herald probasbility calculation for the DVPS Figure 9 - Cost landscape comparison. Figure 10 - Solving a random QUBO problem using gradient descent or Rotosolve for either bosonic or fermionic statistics. Figure 12 - Calculation of the Fourier modes in the QUBO cost landscape. Raw data This also contains raw data for Figure 2 - The barren plateau scaling figures stored in three .npz files Figure 5 - A set of pre-computed DVPS unitaries in a single .npz file Figure 9 - The raw cost landscape data in a single .npz file. Figure 12 - All subfigure data in 12 .txt files. This data is produced by the notebooks so is not necessary, but is included to save time. Scripts The scripts lightworks_optimiser_classes.py lightworks_qubo.py contain code for optimising via gradient descent and Rotosolve. These are called by the notebooks.

Sep 21, 20261 citation

Recent Advances in Description of Few Two-Component Fermions

O. I. Kartavtsev, A. V. Malykh

Overview of the recent advances in description of the few two-component fermions is presented. The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass $m$ and a distinct particle of mass $m_1$ : it turns out that two $L^P = 1^-$ three-body bound states emerge if mass ratio $m/m_1$ increases up to the critical value $μ_c \approx 13.607$ , above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for $m/m_1$ near $μ_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.Overview of the recent advances in description of the few two-component fermions is presented. The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass $m$ and a distinct particle of mass $m_1$: it turns out that two $L^P = 1^-$ three-body bound states emerge if mass ratio $m/m_1$ increases up to the critical value $μ_c \approx 13.607$, above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for $m/m_1$ near $μ_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.

arXiv:1211.5557Ядерная физикаJan 1, 20144 citations

A Solution to the Sign Problem Using a Sum of Controlled Few-Fermions

Wei, David H.

A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Then a universality is proven to assert that any bounded-error quantum polynomial time (BQP) algorithm can be encoded into a sum of controlled few-fermions and simulated efficiently using classical Monte Carlo. Therefore, BQP is precisely the same as the class of bounded-error probabilistic polynomial time (BPP), namely, BPP = BQP.A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Then a universality is proven to assert that any bounded-error quantum polynomial time (BQP) algorithm can be encoded into a sum of controlled few-fermions and simulated efficiently using classical Monte Carlo. Therefore, BQP is precisely the same as the class of bounded-error probabilistic polynomial time (BPP), namely, BPP = BQP.

arXiv:2208.13744Jun 8, 20220 citations

m

and a distinct particle of mass

m_1

: it turns out that two

L^P = 1^-

three-body bound states emerge if mass ratio

m/m_1

increases up to the critical value

μ_c \approx 13.607

, above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for

m/m_1

near $μ_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.