Quantum Chaos and Circuit Parameter Optimization

Kim, Joon-Ho; Oz, Yaron; Rosa, Dario

doi:10.48550/arxiv.2201.01452

Cited by 2 publications

(4 citation statements)

References 38 publications

(68 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We gathered data from the JLQCD collaboration described in [48]. This data is obtained from numerical simulations on a Euclidean 16 3 × 32 space-time lattice at β = 2.30, with a lattice spacing a ∼ 0.12 fm, via two different algorithms, namely domain wall and overlap fermions. From those two algorithms the 50 smallest eigenvalues of the overlap Dirac operator with a total number of configurations of about n conf.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…This procedure applies to the bulk of the spectrum. The spacing distribution continues to be a popular tool in today's applications, ranging from quantum spin chains [2], quantum circuits [3], chemical isotopes [4] and graphene [5] to classical integrable systems [6] and theoretical studies [7], which are all from past year. We refer to [1,8] for a list of more topics and references therein.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk

Akemann

Gorski

Kieburg

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The local spectral statistics of random matrices forms distinct universality classes, strongly depending on the position in the spectrum. Surprisingly, the spacing between consecutive eigenvalues at the spectral edges has received little attention, where the density diverges or vanishes, respectively. This different behaviour is called hard or soft edge. We show that the spacings at the edges are almost indistinguishable from the spacing in the bulk of the spectrum. We present analytical results for consecutive spacings between the $k$th and $(k + 1)$st smallest eigenvalues in the chiral Gaussian unitary ensemble, both for finite- and large-$n$. The result depends on the number of the generic zero modes $\nu$ and the number of flavours $N_f$ , which are given in terms of characteristic polynomials, as motivated by Quantum Chromodynamics (QCD). We find that the convergence in $n$ is very rapid. The same can be said separately about the limit $k\to\infty$ (limit to the bulk) and $\nu\to\infty$ (limit to the soft edge). Interestingly, the Wigner surmise is a very good approximation for all these cases and, apart from $k = 1$, shows a deviation below one percent. These findings are corroborated with Monte-Carlo simulations. We finally compare for $k = 1$ with data from QCD on the lattice, being in this symmetry class.

show abstract

Section: Acknowledgmentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk

Akemann

Gorski

Kieburg

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…Such decrease in the largest eigenvalue of ρ A is displayed in the min-entropy curve. We note this spectral change of ρ A can be a contributing factor for the emergence of the random matrix behavior of ρ A , studied elsewhere [50]. Note that while the min-entropy can provide a diagnostic for effective VQA optimization, this is not the case with the max-entropy.…”

Section: A3 the Syk Modelmentioning

confidence: 72%

“…Third, the layered circuit defines a discrete dynamical system. We would like to investigate the appearance of quantum chaos in the circuit wavefunction, such as the emergence of random matrix ensemble for the reduced density matrix [48] and the operator spreading [49], relating them to the efficient VQA optimization [50]. Fourth, it is crucial to investigate the implication of entanglement diagnostics with specialized optimizers for quantum circuits, such as quantum natural gradient descent or non-gradient-based methods.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Entanglement diagnostics for efficient VQA optimization

Kim¹,

Oz²

2022

J. Stat. Mech.

View full text Add to dashboard Cite

We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient variational quantum/classical computations. We establish a robust connection between entanglement measures and optimization accuracy by solving two eigensolver problems for Ising Hamiltonians with nearest-neighbor and long-range spin interactions. As the circuit depth affects the average entanglement of random circuit states, the entanglement diagnostics can identify a high-performing depth range for optimization tasks encoded in local Hamiltonians. We argue, based on an eigensolver problem for the Sachdev–Ye–Kitaev model, that entanglement alone is insufficient as a diagnostic to the approximation of volume-law entangled target states and that a large number of circuit parameters is needed for such an optimization task.

show abstract

Quantum Chaos and Circuit Parameter Optimization

Cited by 2 publications

References 38 publications

Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk

Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk

Entanglement diagnostics for efficient VQA optimization

Contact Info

Product

Resources

About