• Corpus ID: 248887663

Saturation and recurrence of quantum complexity in random quantum circuits

  title={Saturation and recurrence of quantum complexity in random quantum circuits},
  author={Michał Oszmaniec and Michal Horodecki and Nicholas Hunter-Jones},
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applica-tions beyond quantum computing—in studying the dynamics of quantum many-body systems and the long-time properties of AdS black holes. In this context Brown and Susskind [1] conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating… 
1 Citations

Figures from this paper

Concentration of quantum equilibration and an estimate of the recurrence time
Jonathon Riddell, 2, ∗ Nathan J. Pagliaroli, † and Álvaro M. Alhambra ‡ Department of Physics & Astronomy, McMaster University, 1280 Main St. W., Hamilton ON L8S 4M1, Canada. Perimeter Institute for


Linear growth of quantum circuit complexity
The complexity of quantum states has become a key quantity of interest across various subfields of physics, from quantum computing to the theory of black holes. The evolution of generic quantum
Models of Quantum Complexity Growth
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
Entangling Power and Quantum Circuit Complexity.
  • J. Eisert
  • Physics, Computer Science
    Physical review letters
  • 2021
This work discusses a simple relationship when both the entanglement of a state and the cost of a unitary take small values, building on ideas on how values of entangling power of quantum gates add up, and proposes a continuous-variable small incremental entangling bound.
Improved spectral gaps for random quantum circuits: Large local dimensions and all-to-all interactions
The smallest non-trivial case exactly is solved exactly and numerics and Knabe bounds are combined to improve the constants involved in the spectral gap for small values of $t$ and a recursion relation for the spectral gaps involving an auxiliary random walk is proved.
Decoupling with Random Quantum Circuits
It is proved that random quantum circuits with O(n log2n) gates satisfy an essentially optimal decoupling theorem and can be implemented in depth O(log3n), which proves that decoupled can happen in a time that scales polylogarithmically in the number of particles in the system.
Convergence rates for arbitrary statistical moments of random quantum circuits.
We consider a class of random quantum circuits where at each step a gate from a universal set is applied to a random pair of qubits, and determine how quickly averages of arbitrary finite-degree
The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes
  • S. Aaronson
  • Physics
    Electron. Colloquium Comput. Complex.
  • 2016
The focus is quantum circuit complexity---i.e., the minimum number of gates needed to prepare a given quantum state or apply a given unitary transformation---as a unifying theme tying together several topics of recent interest in the field.
Second law of quantum complexity
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)
Quantum Entanglement Growth Under Random Unitary Dynamics
Characterizing how entanglement grows with time in a many-body system, for example after a quantum quench, is a key problem in non-equilibrium quantum physics. We study this problem for the case of
Exponential quantum speed-ups are generic
It is shown that for almost any sufficiently long quantum circuit one can construct a black-box problem which is solved by the circuit with a constant number of quantum queries, but which requires exponentially many classical queries, even if the classical machine has the ability to postselect.