The paper decomposes dynamical Lie algebras of XY-mixer topologies and demonstrates warm-starting QAOA via pre-training on restricted generators to improve convergence on constrained optimization problems.
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Unitary designs from statistical mechanics in random quantum circuits
11 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Random quantum circuits are proficient information scramblers and efficient generators of randomness, rapidly approximating moments of the unitary group. We study the convergence of local random quantum circuits to unitary $k$-designs. Employing a statistical mechanical mapping, we give an exact expression of the distance to forming an approximate design as a lattice partition function. In the statistical mechanics model, the approach to randomness has a simple interpretation in terms of domain walls extending through the circuit. We analytically compute the second moment, showing that random circuits acting on $n$ qudits form approximate 2-designs in $O(n)$ depth, as is known. Furthermore, we argue that random circuits form approximate unitary $k$-designs in $O(nk)$ depth and are thus essentially optimal in both $n$ and $k$. We can show this in the limit of large local dimension, but more generally rely on a conjecture about the dominance of certain domain wall configurations.
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Perturbed random Floquet-Clifford circuits exhibit operator-space fragmentation into wall-separated sectors for p < 1, yielding exact local integrals of motion, tunable operator spreading length, an entanglement bottleneck, and a pre-RMT fragmentation timescale at p = 1.
Two constructions yield strong unitary k-designs and pseudorandom unitaries on D-dimensional grids with provably optimal depth.
The arrow of time exhibits nonanalytic behavior at the critical point of measurement-induced phase transitions, with an identified critical exponent, in an exactly solved model of random quantum circuits with non-projective measurements.
In random quantum automaton ensembles, the subsystem symmetrization scale depends on the initial state's participation entropy, and the onset of U(1) entanglement asymmetry coincides with the onset of subsystem coherence.
Quantum information lifetime scales exponentially with system size under continuous monitoring via mid-circuit measurements, proven analytically for Haar random unitaries and confirmed numerically and experimentally, unlike the linear scaling without monitoring.
Late-time ensembles in chaotic systems with symmetries match Haar-random statistics for typical product states but follow constrained ensembles for atypical low-variance initial states.
QCNNs are classically simulable via Pauli shadows on low-bodyness subspaces of locally-easy datasets, with explicit simulation demonstrated up to 1024 qubits for phases of matter classification.
Conservation laws in quantum circuits and Hamiltonians replace logarithmic coherence saturation with slow hydrodynamic relaxation globally and produce algebraic peak-time growth locally, unlike ergodic cases.
Non-Abelian symmetries and unentangled initial states block full Haar randomization in unitary quantum dynamics, leaving finite deviations in late-time entanglement entropy.
The k-commutant of free fermions is the Grassmannian manifold of fermionic Gaussian states on 2k sites, exposing a real-replica space duality.
citing papers explorer
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The Lie Algebra of XY-mixer Topologies and Warm Starting QAOA for Constrained Optimization
The paper decomposes dynamical Lie algebras of XY-mixer topologies and demonstrates warm-starting QAOA via pre-training on restricted generators to improve convergence on constrained optimization problems.
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Operator space fragmentation in perturbed Floquet-Clifford circuits
Perturbed random Floquet-Clifford circuits exhibit operator-space fragmentation into wall-separated sectors for p < 1, yielding exact local integrals of motion, tunable operator spreading length, an entanglement bottleneck, and a pre-RMT fragmentation timescale at p = 1.
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Arts & crafts: Strong random unitaries and geometric locality
Two constructions yield strong unitary k-designs and pseudorandom unitaries on D-dimensional grids with provably optimal depth.
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Arrow of Time as an indicator of Measurement-Induced Phase Transitions
The arrow of time exhibits nonanalytic behavior at the critical point of measurement-induced phase transitions, with an identified critical exponent, in an exactly solved model of random quantum circuits with non-projective measurements.
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Entanglement Asymmetry in Random Quantum Automata
In random quantum automaton ensembles, the subsystem symmetrization scale depends on the initial state's participation entropy, and the onset of U(1) entanglement asymmetry coincides with the onset of subsystem coherence.
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Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics
Quantum information lifetime scales exponentially with system size under continuous monitoring via mid-circuit measurements, proven analytically for Haar random unitaries and confirmed numerically and experimentally, unlike the linear scaling without monitoring.
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Late-time ensembles of quantum states in quantum chaotic systems
Late-time ensembles in chaotic systems with symmetries match Haar-random statistics for typical product states but follow constrained ensembles for atypical low-variance initial states.
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Quantum Convolutional Neural Networks are Effectively Classically Simulable
QCNNs are classically simulable via Pauli shadows on low-bodyness subspaces of locally-easy datasets, with explicit simulation demonstrated up to 1024 qubits for phases of matter classification.
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Coherence dynamics in quantum many-body systems with conservation laws
Conservation laws in quantum circuits and Hamiltonians replace logarithmic coherence saturation with slow hydrodynamic relaxation globally and produce algebraic peak-time growth locally, unlike ergodic cases.
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Quantum state randomization constrained by non-Abelian symmetries
Non-Abelian symmetries and unentangled initial states block full Haar randomization in unitary quantum dynamics, leaving finite deviations in late-time entanglement entropy.
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Geometry of Free Fermion Commutants
The k-commutant of free fermions is the Grassmannian manifold of fermionic Gaussian states on 2k sites, exposing a real-replica space duality.