Quantum magic is a fundamental resource that quantifies to what extent quantum states can be efficiently simulated on a classical computer. We study it for states constructed from the Sachdev-Ye-Kitaev (SYK) Hamiltonian with $N$ Majoranas by the fermionic anti-flatness (FAF). We show analytically that, in the large $N$ limit, the quantum magic of pure Kourkoulou-Maldacena (KM) states, dual to a quantum black hole with an end-of-world particle behind the horizon, is linear in $N$ with a slope, depending on the black hole temperature, that can be tuned between zero and $1/2$. By contrast, the FAF of Gaussian states evolved in real time with the SYK Hamitonian approaches $\approx N/2$ exponentially at a rate given by a multiple of the leading Ruelle-Pollicot resonance. Subleading corrections in $N$ for SYK energy eigenstates, computed numerically for $N \leq 54$ by combining Krylov subspace with GPU acceleration techniques, decay exponentially with $N$, but power-law if the SYK couplings are sparsified, and are order of magnitude larger for states close to the ground state, a region with an established gravity analogue. Our results offer new insights about the relation between quantum information, quantum chaos and low-dimension quantum gravity.
This work introduces a unified measure, the magic R\'enyi entropy (MRE), to quantify computational resources in spins, bosons, and fermions on an equal footing and shows that the MRE is a resource monotone under stabilizer and Gaussian protocols involving measurements and feedforward operations.
We present a recipe for simulating one-dimensional quantum systems for low and high energies with $L$ qubits within the framework of first quantisation. Assuming a minimum grid spacing $\Delta L$ in the finite-difference method, the generalised uncertainty principle (GUP) is derived analytically and shows distinct properties for low- and high-energy quantum systems. In the low-energy regime, the GUP approaches to the standard Heisenberg uncertainty principle (HUP) for $ \Delta L \ll \hbar$. However, for finite $\Delta L \neq 0$, the GUP mathematically provides three different regions dependent on the average momentum and suggests that a wavefunction can exhibit a single-point localisation at the finite momentum uncertainty due to lack of grid resolution. We then derive a new expression for the high-energy momentum and focus on two specific cases relevant to relativistic aspects. First, if the HUP is relaxed and the high-energy momentum is matched to the special-relativistic one, the resulting GUP predicts the existence of a minimum length with non-zero mass for high energy despite the continuous limit $\Delta L = 0$. Second, enforcing consistency with the HUP allows the recovery of a canonical high-energy representation with no minimum length. But this requirement brings incompatibility with the special-relativistic momentum and suggests a modified energy-momentum equation. Therefore, we believe that the proposed momentum formulation provides a novel pathway to investigate quantum gravity phenomena for high energy using quantum simulation tools.
Jack Keable-Elliott, David J. Bacon, A. Burbanks et al.· 0 citations
We perform an extensive analysis of the quantum correlations carried by the qubit-qubit-qutrit pure state arising in the decay of a massive scalar into a fermion-antifermion pair and a massive gauge boson, $H \to f \bar f V$, specialising to the Higgs boson decay $h \to \tau^- \tau^+ Z$. Working with the exact tree-level spin state and its systematic expansion around the massless-fermion limit, we obtain analytic control over the entire phase space: the bipartite entanglement measures, the genuine $2 \otimes 2 \otimes 3$ entanglement structure (the Miyake classification), as well as the Bell-inequality violations and the non-stabiliserness (magic) are all mapped and reproduced by compact formulas. The bipartite measures exhibit a monogamy-like trade-off between the fermion pair and the fermion-boson pairs. The state is genuinely $2 \otimes 2 \otimes 3$ entangled over almost the entire phase space, most strongly in the collinear regions. We derive, for the first time, semi-analytical expressions for the tight $4 \times 4 \times 2$ Bell inequalities of the $2 \otimes 2 \otimes 3$ system, generalising the optimisation previously available only for three qubits, and find that the local-hidden-variable bound is violated over the entire phase space, reaching within a few per cent of the quantum bound at the upper endpoint of the di-tau mass spectrum. We further extend the stabiliser R\'enyi entropy and the non-local magic to systems with unequal local dimensions, and show that the near-endpoint state carries almost exactly one bit of non-local magic, which peaks at $\log_2 \frac{27}{7} \simeq 1.95$ in the collinear regions. The differential decay rate concentrates precisely in the most nonclassical region of the phase space.
Michał Banacki, Misaki Ohta, Abhyoudai S. Shaleena et al.· 0 citations
Maximally mixed state spectral sampling is an unbiased quantum algorithm that allows for extraction of a finite-resolution spectral distribution from a Hamiltonian over potentially the entire allowed range of energies. We show how it may be focused on any desired area of the spectrum in order to learn about the full \textit{fingerprint} of the model of interest: from its ground state phenomena such as quantum criticality, obtained from the lowest lying energies, to its thermalization behavior, obtained from the mid-spectrum. We demonstrate this technique specifically on a $(1+1)d$ non-Abelian $SO(3)$ gauge theory, providing a comprehensive analysis of the steps necessary for performing this algorithm, as well as what is possible in the near-term with superconducting quantum hardware, performing simulations with circuits that are $78$ two-qubit gates deep. We show how this algorithm is able to take advantage of emerging dynamical circuit capabilities in near-term hardware to roughly halve the number required qubits, as well as how quantum readout error mitigation is trivial for this method. Along the way, we propose a novel strategy for compiling the controlled-time evolutions needed for spectral sampling by means of Pauli-frame optimizations. We illustrate two physical applications of quantum spectral sampling -- disordered many-body transitions, and mid-spectrum densities of states -- and what postprocessing steps they require beyond the Fourier outputs of the algorithm.
Graham Van Goffrier, Debasish Banerjee, Bipasha Chakraborty et al.· 0 citations
A central question in quantum information theory is the circuit complexity of states arising from standard many-body models. We study this question for quantum $p$-spin glasses, random Hamiltonians whose interactions act on $p$-tuples of qubits through Pauli strings. Anschuetz, Gamarnik, and Kiani (arXiv:2404.07231) showed that the optimum energy is separated from the best energy achievable by product states. This leaves open whether shallow circuits can close the gap, since even depth-one circuits can generate entanglement. We show that the entanglement needed to close the product-state gap cannot be generated at shallow depth. When the average interaction degree grows with $n$, we prove that, for all sufficiently large fixed $p$, any circuit preparing an $n$-qubit state whose normalized energy is within a fixed positive constant of the optimum must have depth $\Omega_p(\log n)$. In the bounded-average-degree regime, we prove a fixed-depth obstruction: for every fixed $D$, a sufficiently large degree prefactor rules out depth-$D$ preparation of near-ground states. Both results hold uniformly over circuits with an arbitrary number of ancilla qubits. Our results give an obstruction in the spirit of the No Low-Energy Trivial States problem of Freedman and Hastings (arXiv:1301.1363), but for random quantum spin glasses rather than code-based Hamiltonians such as those of Anshu, Breuckmann, and Nirkhe (arXiv:2206.13228), whose ground states admit polynomial-size preparation circuits. This setting opens a probabilistic route to NLTS-like questions: we recast state-preparation lower bounds for random quantum Hamiltonians as uniform control of Gaussian processes indexed by shallow circuits.
Open-system descriptions are typically introduced by coupling a quantum system to an external environment. Here we show that a closed interacting many-body system can itself generate a controlled non-Markovian quantum channel acting on a reduced nonlinear qubit through finite-size corrections to a nonlinear mean-field limit. We demonstrate this using the Kitagawa-Ueda one-axis twisting model, $H=\chi J_z^2$, a paradigmatic model of collective spin dynamics, spin squeezing, and two-component Bose-Einstein condensates. Although the large-$N$ regime of this model has been extensively studied, the conventional fixed-$\chi$ scaling does not yield a nontrivial dynamical large-$N$ limit. In this paper, we investigate a complementary large-$N$ formulation obtained from the double limit $N\rightarrow\infty$ and $\chi\rightarrow O(g/N)$, where $g$ is a coupling constant. We derive the leading finite-$N$ corrections to this limit and show that they correspond to an emergent non-Markovian dephasing process, producing a Gaussian decay of the Bloch-vector coherence with characteristic timescale $t_\varphi\geq\sqrt{N}/(2g)$. Exact finite-$N$ calculations demonstrate that this effective open-system description becomes quantitatively accurate for systems containing on the order of one hundred qubits. The resulting framework provides a microscopic realization of non-Markovian dephasing generated intrinsically by a closed many-body system and enables efficient simulation of collective quantum dynamics beyond unitary mean-field theory. These results link the long-studied phenomenon of phase diffusion in atomic ensembles and Bose-Einstein condensates to the growing effort to characterize non-Markovian, beyond-Lindblad noise in quantum computing hardware, providing a rare case in which such a noise channel is derived from microscopic dynamics rather than fit phenomenologically.
Gregory T. Carroll, Michael R. Geller, A. Erpenbeck· 0 citations