Quantum chaos is central to understanding quantum dynamics and is crucial for generating random quantum states, a key resource for quantum information tasks. In this work, we introduce a new class of quantum many-body dynamics, termed pseudochaotic dynamics. Although distinct from chaotic dynamics, out-of-time-ordered correlators, the key indicators of quantum chaos, fail to distinguish them. Moreover, pseudochaotic dynamics generates pseudorandom states that are computationally indistinguishable from Haar-random states. We construct pseudochaotic dynamics by embedding a smaller k-qubit subsystem into a larger n-qubit system. We demonstrate that a subsystem of size $k=\omega (\log n)$ is sufficient to induce pseudochaotic behavior in the entire n-qubit system. Furthermore, we construct a quantum circuit exhibiting pseudochaotic dynamics and demonstrate that it generates pseudorandom states within ${{{\rm{polylog}}}}(n)$ depth. In summary, our results constitute the discovery of new quantum dynamics that are computationally indistinguishable from genuine quantum chaos, which provides efficient routes to generate useful pseudorandom states. Recent work introduced pseudorandom quantum states, indistinguishable from truly random states by any polynomial-time algorithm. Here the authors propose pseudochaotic many-body dynamics, which is indistinguishable from chaotic dynamics and can generate pseudorandom states using polylogarithmic-depth circuits.Quantum chaos is central to understanding quantum dynamics and is crucial for generating random quantum states, a key resource for quantum information tasks. In this work, we introduce a new class of quantum many-body dynamics, termed pseudochaotic dynamics. Although distinct from chaotic dynamics, out-of-time-ordered correlators, the key indicators of quantum chaos, fail to distinguish them. Moreover, pseudochaotic dynamics generates pseudorandom states that are computationally indistinguishable from Haar-random states. We construct pseudochaotic dynamics by embedding a smaller k-qubit subsystem into a larger n-qubit system. We demonstrate that a subsystem of size $$k=\omega (\log n)$$ is sufficient to induce pseudochaotic behavior in the entire n-qubit system. Furthermore, we construct a quantum circuit exhibiting pseudochaotic dynamics and demonstrate that it generates pseudorandom states within $${{{\rm{polylog}}}}(n)$$ depth. In summary, our results constitute the discovery of new quantum dynamics that are computationally indistinguishable from genuine quantum chaos, which provides efficient routes to generate useful pseudorandom states. Recent work introduced pseudorandom quantum states, indistinguishable from truly random states by any polynomial-time algorithm. Here the authors propose pseudochaotic many-body dynamics, which is indistinguishable from chaotic dynamics and can generate pseudorandom states using polylogarithmic-depth circuits.

arXiv:2410.21268Nature CommunicationsJul 23, 20252 citations

Simulation of the quantum dynamics of indistinguishable bosons with the method of coupled coherent states

James A. Green, Dmitrii V. Shalashilin

Computer simulations of many-body quantum dynamics of indistinguishable particles is a challenging task for computational physics. In this paper we demonstrate that the method of coupled coherent states (CCS) developed previously for multidimensional quantum dynamics of distinguishable particles can be used to study indistinguishable bosons in the second-quantization formalism. To prove its validity, the technique termed here coupled coherent states for indistinguishable bosons (CCSB) is tested on two model problems. The first is a system-bath problem consisting of a tunneling mode coupled to a harmonic bath, previously studied by CCS and other methods in distinguishable representation in 20 dimensions. The harmonic bath is comprised of identical oscillators, and may be second quantized for use with CCSB, so that this problem may be thought of as a bosonic bath with an impurity. The cross-correlation function for the dynamics of the system and Fourier transform spectrum compare extremely well with a benchmark calculation, which none of the prior methods of studying the problem achieved. The second model problem involves 100 bosons in a shifted harmonic trap. Breathing oscillations in the one-body density are calculated and shown to compare favorably to a multiconfigurational time-dependent Hartree for bosons calculation, demonstrating the applicability of the method as a new formally exact way to study the quantum dynamics of Bose-Einstein condensates.Computer simulations of many-body quantum dynamics of indistinguishable particles is a challenging task for computational physics. In this paper we demonstrate that the method of coupled coherent states (CCS) developed previously for multidimensional quantum dynamics of distinguishable particles can be used to study indistinguishable bosons in the second-quantization formalism. To prove its validity, the technique termed here coupled coherent states for indistinguishable bosons (CCSB) is tested on two model problems. The first is a system-bath problem consisting of a tunneling mode coupled to a harmonic bath, previously studied by CCS and other methods in distinguishable representation in 20 dimensions. The harmonic bath is comprised of identical oscillators, and may be second quantized for use with CCSB, so that this problem may be thought of as a bosonic bath with an impurity. The cross-correlation function for the dynamics of the system and Fourier transform spectrum compare extremely well with a benchmark calculation, which none of the prior methods of studying the problem achieved. The second model problem involves 100 bosons in a shifted harmonic trap. Breathing oscillations in the one-body density are calculated and shown to compare favorably to a multiconfigurational time-dependent Hartree for bosons calculation, demonstrating the applicability of the method as a new formally exact way to study the quantum dynamics of Bose-Einstein condensates.

arXiv:1811.06293Physical Review AJul 10, 20198 citations

Indistinguishable Quantum Particles

Lecture notes in physics. M, MonographsJan 1, 19970 citations

Quantum Statistics from Indistinguishability

Andrei Yu. Khrennikov

Springer eBooksJan 1, 20230 citations

k=\omega (\log n)

is sufficient to induce pseudochaotic behavior in the entire n-qubit system. Furthermore, we construct a quantum circuit exhibiting pseudochaotic dynamics and demonstrate that it generates pseudorandom states within

{{{\rm{polylog}}}}(n)

depth. In summary, our results constitute the discovery of new quantum dynamics that are computationally indistinguishable from genuine quantum chaos, which provides efficient routes to generate useful pseudorandom states. Recent work introduced pseudorandom quantum states, indistinguishable from truly random states by any polynomial-time algorithm. Here the authors propose pseudochaotic many-body dynamics, which is indistinguishable from chaotic dynamics and can generate pseudorandom states using polylogarithmic-depth circuits.