REVIEW 6 cited by
Local random quantum circuits form approximate designs on arbitrary architectures
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
We consider random quantum circuits (RQC) on arbitrary connected graphs whose edges determine the allowed $2$-qudit interactions. Prior work has established that such $n$-qudit circuits with local dimension $q$ on 1D, complete, and $D$-dimensional graphs form approximate unitary designs, that is, they generate unitaries from distributions close to the Haar measure on the unitary group $U(q^n)$ after polynomially many gates. Here, we extend those results by proving that RQCs comprised of $O(\mathrm{poly}(n,k))$ gates on a wide class of graphs form approximate unitary $k$-designs. We prove that RQCs on graphs with spanning trees of bounded degree and height form $k$-designs after $O(|E|n\,\mathrm{poly}(k))$ gates, where $|E|$ is the number of edges in the graph. Furthermore, we identify larger classes of graphs for which RQCs generate approximate designs in polynomial circuit size. For $k \leq 4$, we show that RQCs on graphs of certain maximum degrees form designs after $O(|E|n)$ gates, providing explicit constants. We determine our circuit size bounds from the spectral gaps of local Hamiltonians. To that end, we extend the finite-size (or Knabe) method for bounding gaps of frustration-free Hamiltonians on regular graphs to arbitrary connected graphs. We further introduce a new method based on the Detectability Lemma for determining the spectral gaps of Hamiltonians on arbitrary graphs. Our methods have wider applicability as the first method provides a succinct alternative proof of [Commun. Math. Phys. 291, 257 (2009)] and the second method proves that RQCs on any connected architecture form approximate designs in quasi-polynomial circuit size.
Forward citations
Cited by 6 Pith papers
-
Random unitary circuits with constant spectral gap
Constant-depth brickwork random unitary circuits and random Pauli rotations on n qubits have constant spectral gap, independent of n and uniform over all unitary representations.
-
iSWAP maximises the second-moment spectral gap in random quantum circuits
iSWAP gates maximise the second-moment spectral gap of random two-local quantum circuits on every connected graph with at least three qubits, for Hermitian gate ensembles.
-
Apparent Universal Behavior in Second Moments of Random Quantum Circuits
Most random circuit geometries form approximate 2-designs in O(log n) depth with explicit constants; bridge/lollipop graphs need Ω(n²) gates, and 10-20 layers suffice for 50-qubit near-random circuits.
-
Quantum State Design and Emergent Confinement Mechanism in Measured Tensor Network States
Random matrix product states, when partially measured, produce projected ensembles whose randomness is governed by confined domain walls, with exact frame-potential formulas for two circuit architectures.
-
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.
-
Entanglement asymmetry dynamics in random quantum circuits
Subsystem entanglement asymmetry in random unitary circuits relaxes on the scrambling time for subsystems smaller than half the system, growing linearly with size in local circuits and logarithmically in non-local cir...
Discussion (0). Continue with ORCID to comment.