Design boosters: from constant-time quantum chaos to $\infty$-designs and beyond

• URL: http://arxiv.org/abs/2511.08543v1
• Date: Wed, 12 Nov 2025 02:04:01 GMT
• Title: Design boosters: from constant-time quantum chaos to $\infty$-designs and beyond
• Abstract summary: We give the first rigorous example of unitary dynamics generating a state such that, projection at very early (constant) times can boost design randomness.<n>We show that, even though a state generated by such dynamics at constant time only forms a $k=mathcalO(1)$ design, the projected ensemble is Haar-random (or a $k'=infty$ design) in the thermodynamic limit.
• Score: 0.9332987715848714
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study a counterintuitive property of 'conditioning' on the result of measuring a subsystem of a quantum state: such conditioning can boost design quality, at the cost of increased system size. We work in the setting of deep thermalization from many-body physics: starting from a bipartite state on a global system $(A,B)$ drawn from a $k$-design, we measure system $B$ in the computational basis, keep the outcome and examine the state that remains in system $A$, approximating the overall ensemble (the 'projected ensemble') by a $k'$-design. We ask: how does the design quality change due to this procedure, or how does $k'$ compare to $k$? We give the first rigorous example of unitary dynamics generating a state such that, projection at very early (constant) times can boost design randomness. These dynamics are those of quantum chaos, modeled by the evolution of a Hamiltonian drawn from the Gaussian Unitary Ensemble (GUE). We show that, even though a state generated by such dynamics at constant time only forms a $k=\mathcal{O}(1)$ design, the projected ensemble is Haar-random (or a $k'=\infty$ design) in the thermodynamic limit (i.e. when $N_B=\infty$). This phenomenon persists even with weaker and more physically realistic assumptions; our results can be appropriately applied to non-GUE Hamiltonians that nevertheless show likely chaotic signatures in their eigenbases. Moreover, we show that with no assumption on how the global state was generated, a $k$-design experiences a degradation in design quality to $k' = \lfloor k/2 \rfloor$. This improves upon best prior results on the deep thermalization of designs. Together, our contributions argue for design boosting as a result of chaos and showcase a novel mechanism to generate good designs.

Related papers

• State $k$-designs from Hamiltonian evolution [6.563118819518117]
  We study the generation of state $k$-designs from time evolution under a fixed Hamiltonian.<n>Remarkably, we show that time evolution under a simple nonintegrable mixed-field Ising Hamiltonian can generate approximate state $k$-designs with high precision.
  arXiv  Detail & Related papers  (2026-07-20T22:04:54Z)
• Holographic Quantum Transformer: A Generalist Neuro-Symbolic Architecture for Solving Frustrated Systems via Generative Attention [27.340988892399512]
  We introduce the Holographic Quantum Transformer (HQT), a physics-inspired generative architecture that leverages global self-attention to resolve non-local entanglement patterns.<n>Our results establish generative attention as a scalable paradigm for transferable quantum simulation.
  arXiv  Detail & Related papers  (2026-07-01T03:50:13Z)
• Effective Dimension Governs Generalization in Quantum Kernel Vision Models [31.082191748525137]
  We show that entanglement structure and quantum noise are two knobs that move $d_rm eff$.<n>Amplitude damping contracts $d_rm eff$ and lifts test accuracy by up to $+13%$ along an inverted-U sweet spot.
  arXiv  Detail & Related papers  (2026-06-18T12:55:59Z)
• Strong random unitaries and fast scrambling [37.03163411089211]
  We show that strong unitary designs can form in circuit depth $O(log2 n)$ in circuits composed of independent two-qubit Haar-random gates.<n>Our results provide an operational proof of the fast scrambling conjecture from black hole physics.
  arXiv  Detail & Related papers  (2025-09-30T14:23:46Z)
• Gain on ground state of quantum system for truly $\mathcal{PT}$ symmetry [15.84033037381773]
  For a truly $mathcalPT$-symmetric quantum system, the conventional non-Hermitian Hamiltonian is $H = Omegasigma_x -igamma|1ranglelangle1| + igamma|0ranglelangle0|.<n>We propose a pathway to efficiently construct truly $mathcalPT$-symmetric quantum devices, offering a powerful platform for engineering quantum resources vital for quantum information technology applications.
  arXiv  Detail & Related papers  (2025-07-30T14:47:50Z)
• Computational Complexity of Non-Hermitian Quantum Systems [0.0]
  conditional time evolutions arise when a quantum system is monitored and one postselects on a measurement record.<n>We establish an approximate equivalence between post-selection and arbitrary non-Hermitian Hamiltonians.<n>Non-Hermitian physics neither guarantees a quantum advantage nor precludes efficient classical simulation.
  arXiv  Detail & Related papers  (2025-06-03T22:35:28Z)
• Random ensembles of symplectic and unitary states are indistinguishable [0.0]
  A unitary state $t$-designs are obtained by evolving some reference pure state with unitaries from an ensemble that forms a design over the unitary group $mathbbU(d)$. We study whether Haar random symplectic states -- i.e., states obtained by evolving some reference state with unitaries sampled according to the Haar measure over $mathbbSP(d/2)$ -- form unitary state $t$-designs.
  arXiv  Detail & Related papers  (2024-09-24T23:12:18Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Projected state ensemble of a generic model of many-body quantum chaos [0.0]
  The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design.
  arXiv  Detail & Related papers  (2024-02-26T19:00:00Z)
• Robust Causal Bandits for Linear Models [20.028245872662843]
  Sequential design of experiments for optimizing a reward function in causal systems can be effectively modeled by the sequential design of interventions in causal bandits (CBs) This paper addresses the robustness of CBs to such model fluctuations. Cumulative regret is adopted as the design criteria, based on which the objective is to design a sequence of interventions that incur the smallest cumulative regret with respect to an oracle aware of the entire causal model and its fluctuations.
  arXiv  Detail & Related papers  (2023-10-30T17:58:01Z)
• Unitary k-designs from random number-conserving quantum circuits [0.0]
  Local random circuits scramble efficiently and accordingly have a range of applications in quantum information and quantum dynamics. We show that finite moments cannot distinguish the ensemble that local random circuits generate from the Haar ensemble on the entire group of number-conserving unitaries.
  arXiv  Detail & Related papers  (2023-06-01T18:00:00Z)
• Self-healing of Trotter error in digital adiabatic state preparation [52.77024349608834]
  We prove that the first-order Trotterization of a complete adiabatic evolution has a cumulative infidelity that scales as $mathcal O(T-2 delta t2)$ instead of $mathcal O(T2delta t2)$ expected from general Trotter error bounds. This result suggests a self-healing mechanism and explains why, despite increasing $T$, infidelities for fixed-$delta t$ digitized evolutions still decrease for a wide variety of Hamiltonians.
  arXiv  Detail & Related papers  (2022-09-13T18:05:07Z)
• Boundary time crystals in collective $d$-level systems [64.76138964691705]
  Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
  arXiv  Detail & Related papers  (2021-02-05T19:00:45Z)
• Universal tripartite entanglement in one-dimensional many-body systems [0.0]
  We introduce two related non-negative measures of tripartite entanglement $g$ and $h$. We prove structure theorems which show that states with nonzero $g$ or $h$ have nontrivial tripartite entanglement.
  arXiv  Detail & Related papers  (2020-11-24T02:59:14Z)
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism [0.0]
  This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe. We use the $Out-of-Time Ordered correlation (OTOC)$ functions for probing the random behaviour of the universe both at early and the late times.
  arXiv  Detail & Related papers  (2020-09-08T16:10:52Z)
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms [105.54048699217668]
  A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
  arXiv  Detail & Related papers  (2020-08-03T18:00:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.