Related papers: Saturation and recurrence of quantum complexity in…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
The circuit complexity of time-evolved pure quantum states grows linearly in time for an exponentially long time. This behavior has been proven in certain models, is conjectured to hold for generic quantum many-body systems, and is believed…
Recently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. The latter refers to a sudden change in a…
For chaotic quantum dynamics modeled by random unitary circuits, we study the complexity of reduced density matrices of subsystems as a function of evolution time where the initial global state is a product pure state. The state complexity…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
We study the growth and saturation of Krylov spread (K-) complexity under random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, K-complexity grows linearly before saturating at a late-time value of…
We study the quantum complexity of time evolution in large-$N$ chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
We establish a direct connection between spread complexity and quantum circuit complexity by demonstrating that spread complexity emerges as a limiting case of a circuit complexity framework built from two fundamental operations:…
Characterizing the quantum complexity of local random quantum circuits is a very deep problem with implications to the seemingly disparate fields of quantum information theory, quantum many-body physics and high energy physics. While our…
We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results…
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…
The holographic complexity of a static spherically symmetric black hole, defined as the volume of an extremal surface, grows linearly with time at late times in general relativity. The growth comes from a region at a constant transverse…
It has been recently proposed that the naive semiclassical prediction of non-unitary black hole evaporation can be understood in the fundamental description of the black hole as a consequence of ignorance of high-complexity information.…
Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the…
The complexity of a quantum gate, defined as the minimal number of elementary gates to build it, is an important concept in quantum information and computation. It is shown recently that the complexity of quantum gates built from random…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By…