We give an efficient classical algorithm that recovers the distribution of a non-interacting fermion state over the computational basis. For a system of $n$ non-interacting fermions and $m$ modes, we show that $O(m^2 n^4 \log(m/\delta)/ \varepsilon^4)$ samples and $O(m^4 n^4 \log(m/\delta)/ \varepsilon^4)$ time are sufficient to learn the original distribution to total variation distance $\varepsilon$ with probability $1 - \delta$ . Our algorithm empirically estimates the one- and two-mode correlations and uses them to reconstruct a succinct description of the entire distribution efficiently.We give an efficient classical algorithm that recovers the distribution of a non-interacting fermion state over the computational basis. For a system of $n$ non-interacting fermions and $m$ modes, we show that $O(m^2 n^4 \log(m/\delta)/ \varepsilon^4)$ samples and $O(m^4 n^4 \log(m/\delta)/ \varepsilon^4)$ time are sufficient to learn the original distribution to total variation distance $\varepsilon$ with probability $1 - \delta$. Our algorithm empirically estimates the one- and two-mode correlations and uses them to reconstruct a succinct description of the entire distribution efficiently.

Feb 20, 20211 citation

Interacting Composite Fermions

Chia‐Chen Chang

Jun 22, 20060 citations

Tensor Product State Capacity of Non-interacting Fermion Quantum Channel

彭永刚 PENG Yong-gang, 巩龙 GONG Long-yan

The physical model of non-interacting fermion quantum channel is proposed by fermionic linear optics.Based on covariance matrix property of even Gaussian state and majorization theory,a formula of fermion quantum channel minimum output entropy for even Gaussian input state is deduced.A output entropy correspondence between Gaussian state and even Gaussian state is established by adding one extra fermionic mode to n-qubit fermion system.A formula of tensor product state capacity for non-interacting fermion channel is deduced according this output entropy correspondence and under assumption that minimum output entropy is achieved on a Gaussian input state.For fermionic channel correct of proposed minimum output entropy formula is confirmed by the iterative minimization algorithm of output entropy.The numerical results is that for non-interacting fermion noisy quantum channel the proposed formula agrees with the numerical results with a precision about 10e-9.The physical model of non-interacting fermion quantum channel is proposed by fermionic linear optics.Based on covariance matrix property of even Gaussian state and majorization theory,a formula of fermion quantum channel minimum output entropy for even Gaussian input state is deduced.A output entropy correspondence between Gaussian state and even Gaussian state is established by adding one extra fermionic mode to n-qubit fermion system.A formula of tensor product state capacity for non-interacting fermion channel is deduced according this output entropy correspondence and under assumption that minimum output entropy is achieved on a Gaussian input state.For fermionic channel correct of proposed minimum output entropy formula is confirmed by the iterative minimization algorithm of output entropy.The numerical results is that for non-interacting fermion noisy quantum channel the proposed formula agrees with the numerical results with a precision about 10e-9.

ACTA PHOTONICA SINICAJan 1, 20110 citations

Interacting Fermions in 2 Dimensions

Vincent Rivasseau

Lecture notes in physicsJan 1, 20060 citations

Composite-fermionization of bosons in rapidly rotating atomic traps

Chia‐Chen Chang, Nicolas Regnault, Th. Jolicœur +1 more

The non-perturbative effect of interaction can sometimes make interacting bosons behave as though they were free fermions. The system of neutral bosons in a rapidly rotating atomic trap is equivalent to charged bosons coupled to a magnetic field, which has opened up the possibility of fractional quantum Hall effect for bosons interacting with a short range interaction. Motivated by the composite fermion theory of the fractional Hall effect of electrons, we test the idea that the interacting bosons map into non-interacting spinless fermions carrying one vortex each, by comparing wave functions incorporating this physics with exact wave functions available for systems containing up to 12 bosons. We study here the analogy between interacting bosons at filling factors $\nu=n/(n+1)$ with non-interacting fermions at $\nu^*=n$ for the ground state as well as the low-energy excited states and find that it provides a good account of the behavior for small $n$ , but interactions between fermions become increasingly important with $n$ . At $\nu=1$ , which is obtained in the limit $n\rightarrow \infty$ , the fermionization appears to overcompensate for the repulsive interaction between bosons, producing an {\em attractive} interactions between fermions, as evidenced by a pairing of fermions here.The non-perturbative effect of interaction can sometimes make interacting bosons behave as though they were free fermions. The system of neutral bosons in a rapidly rotating atomic trap is equivalent to charged bosons coupled to a magnetic field, which has opened up the possibility of fractional quantum Hall effect for bosons interacting with a short range interaction. Motivated by the composite fermion theory of the fractional Hall effect of electrons, we test the idea that the interacting bosons map into non-interacting spinless fermions carrying one vortex each, by comparing wave functions incorporating this physics with exact wave functions available for systems containing up to 12 bosons. We study here the analogy between interacting bosons at filling factors $\nu=n/(n+1)$ with non-interacting fermions at $\nu^*=n$ for the ground state as well as the low-energy excited states and find that it provides a good account of the behavior for small $n$, but interactions between fermions become increasingly important with $n$. At $\nu=1$, which is obtained in the limit $n\rightarrow \infty$, the fermionization appears to overcompensate for the repulsive interaction between bosons, producing an {\em attractive} interactions between fermions, as evidenced by a pairing of fermions here.

Jan 1, 20051 citation

Uniform non-interacting gas of fermions

Luca Salasnich

Springer eBooksJan 1, 20200 citations

We give an efficient classical algorithm that recovers the distribution of a non-interacting fermion state over the computational basis. For a system of

n

non-interacting fermions and

m

modes, we show that

O(m^2 n^4 \log(m/\delta)/ \varepsilon^4)

samples and

O(m^4 n^4 \log(m/\delta)/ \varepsilon^4)

time are sufficient to learn the original distribution to total variation distance

\varepsilon

with probability

1 - \delta

. Our algorithm empirically estimates the one- and two-mode correlations and uses them to reconstruct a succinct description of the entire distribution efficiently.

\nu=n/(n+1)

with non-interacting fermions at

\nu^*=n

for the ground state as well as the low-energy excited states and find that it provides a good account of the behavior for small

n

, but interactions between fermions become increasingly important with

n

. At

\nu=1

, which is obtained in the limit

n\rightarrow \infty

, the fermionization appears to overcompensate for the repulsive interaction between bosons, producing an {\em attractive} interactions between fermions, as evidenced by a pairing of fermions here.