Holographic complexity measures show universal linear growth followed by late-time saturation, proven necessary and sufficient via pole structures in the energy basis using the residue theorem, arising from random matrix statistics.
hub Canonical reference
The Second Law of Quantum Complexity
Canonical reference. 83% of citing Pith papers cite this work as background.
13
Pith papers citing it
Background
83% of classified citations
abstract
We give arguments for the existence of a thermodynamics of quantum complexity that includes a "Second Law of Complexity". To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of $K$ qubits, and the positional entropy of a related classical system with $2^K$ degrees of freedom. We also argue that the kinetic entropy of the classical system is equivalent to the Kolmogorov complexity of the quantum Hamiltonian. We observe that the expected pattern of growth of the complexity of the quantum system parallels the growth of entropy of the classical system. We argue that the property of having less-than-maximal complexity (uncomplexity) is a resource that can be expended to perform directed quantum computation. Although this paper is not primarily about black holes, we find a surprising interpretation of the uncomplexity-resource as the accessible volume of spacetime behind a black hole horizon.
hub tools
citation-role summary
background 6
citation-polarity summary
roles
background 6representative citing papers
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
SYK disorder is shown to be an approximate unitary k-design for poly(N) k; under the planted-SYK hardness conjecture this yields gravitationally pseudorandom unitaries, implying cryptographic censorship in JT gravity with the regularized maximal geodesic length as distinguisher.
Exact Krylov correlators in sl(2,R) models are proportional to radial momenta in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
Quantum complexity measures applied to the Schwinger model reveal nonlocal correlations along the string and show that entanglement and magic give complementary views of string formation and breaking.
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.
The study demonstrates that long-range couplings and heterogeneous degree distributions in Ising spin networks on path, Erdős–Rényi, and Watts–Strogatz topologies accelerate quantum information scrambling and chaos, diagnosed via OTOCs, tripartite information, Krylov complexity, and spectral form fa
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
In holographic Schwinger pair production, the excess capacity of entanglement is √λ(d−2)/(d−1)³ — positive for d>2, zero for d=2 — so the produced pair carries nonlocal magic for d>2.
A timelike quantum focusing conjecture implies a complexity-based quantum strong energy condition and a complexity bound analogous to the covariant entropy bound for suitable codimension-0 field theory complexity measures.
Post-selection probability and fidelity of bidirectional teleportation are expressed via the Loschmidt echo, revealing initial-state dependence of fidelity and stability of probability in integrable models.
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
citing papers explorer
-
Universal Time Evolution of Holographic and Quantum Complexity
Holographic complexity measures show universal linear growth followed by late-time saturation, proven necessary and sufficient via pole structures in the energy basis using the residue theorem, arising from random matrix statistics.
-
Generalized Complexity Distances and Non-Invertible Symmetries
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
-
Pseudorandom Dynamics in the SYK Model and Cryptographic Censorship in JT Gravity
SYK disorder is shown to be an approximate unitary k-design for poly(N) k; under the planted-SYK hardness conjecture this yields gravitationally pseudorandom unitaries, implying cryptographic censorship in JT gravity with the regularized maximal geodesic length as distinguisher.
-
Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity
Exact Krylov correlators in sl(2,R) models are proportional to radial momenta in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
-
The Quantum Complexity of String Breaking in the Schwinger Model
Quantum complexity measures applied to the Schwinger model reveal nonlocal correlations along the string and show that entanglement and magic give complementary views of string formation and breaking.
-
Searching for emergent spacetime in spin glasses
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
-
Bridging Krylov Complexity and Universal Analog Quantum Simulator
Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.
-
Topological Control of Quantum Chaos Diagnostics: OTOCs, Spectral Statistics, and Information Scrambling in Ising Model
The study demonstrates that long-range couplings and heterogeneous degree distributions in Ising spin networks on path, Erdős–Rényi, and Watts–Strogatz topologies accelerate quantum information scrambling and chaos, diagnosed via OTOCs, tripartite information, Krylov complexity, and spectral form fa
-
Fortuity and Complexity in a Simple Quark Model
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
-
Nonlocal Nonstabilizerness from Holographic Schwinger Pair Production
In holographic Schwinger pair production, the excess capacity of entanglement is √λ(d−2)/(d−1)³ — positive for d>2, zero for d=2 — so the produced pair carries nonlocal magic for d>2.
-
A Timelike Quantum Focusing Conjecture
A timelike quantum focusing conjecture implies a complexity-based quantum strong energy condition and a complexity bound analogous to the covariant entropy bound for suitable codimension-0 field theory complexity measures.
-
Post-Selection Probability and Fidelity of Bidirectional Teleportation
Post-selection probability and fidelity of bidirectional teleportation are expressed via the Loschmidt echo, revealing initial-state dependence of fidelity and stability of probability in integrable models.
-
Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.