Universal Early-Time Growth in Quantum Circuit Complexity

• URL: http://arxiv.org/abs/2406.12990v2
• Date: Sat, 12 Oct 2024 08:31:06 GMT
• Title: Universal Early-Time Growth in Quantum Circuit Complexity
• Authors: S. Shajidul Haque, Ghadir Jafari, Bret Underwood,
• Abstract summary: We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times. We are able to extract the early-time behavior and dependence on the lattice spacing of complexity of field theories in the limit, demonstrating how this approach applies to systems that have been previously difficult to study using existing techniques for quantum circuit complexity.
• Score: 0.0
• License:
• Abstract: We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times, independent of any choices of the fundamental gates or cost metric. Deviations from linear early-time growth arise from the commutation algebra of the gates and are manifestly negative for any circuit, decreasing the linear growth rate and leading to a bound on the growth rate of complexity of a circuit at early times. We illustrate this general result by applying it to qubit and harmonic oscillator systems, including the coupled and anharmonic oscillator. By discretizing free and interacting scalar field theories on a lattice, we are also able to extract the early-time behavior and dependence on the lattice spacing of complexity of these field theories in the continuum limit, demonstrating how this approach applies to systems that have been previously difficult to study using existing techniques for quantum circuit complexity.

Related papers

• Upper bounds on quantum complexity of time-dependent oscillators [0.0]
  An explicit formula for an upper bound on the quantum complexity of a harmonic oscillator Hamiltonian with time-dependent frequency is derived. This result aligns with the gate complexity and earlier studies of de Sitter complexity. It provides a proof of concept for the application of Nielsen complexity in cosmology, together with a systematic setting in which higher-order terms can be included.
  arXiv  Detail & Related papers  (2024-07-01T18:00:03Z)
• Experimental Implementation of Noncyclic and Nonadiabatic Geometric Quantum Gates in a Superconducting Circuit [14.92931729758348]
  We experimentally implement a set of noncyclic and nonadiabatic geometric quantum gates in a superconducting circuit. Our results provide a promising routine to achieve fast, high-fidelity, and error-resilient quantum gates.
  arXiv  Detail & Related papers  (2022-10-07T04:56:58Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Out-of-time-order correlator in the quantum Rabi model [62.997667081978825]
  We show that out-of-time-order correlator derived from the Loschmidt echo signal quickly saturates in the normal phase. We show that the effective time-averaged dimension of the quantum Rabi system can be large compared to the spin system size.
  arXiv  Detail & Related papers  (2022-01-17T10:56:57Z)
• Operator Complexity for Quantum Scalar Fields and Cosmological Perturbations [0.0]
  We study the complexity of the unitary evolution of quantum cosmological perturbations in de Sitter space. The complexity of cosmological perturbations scales as the square root of the (exponentially) growing volume of de Sitter space.
  arXiv  Detail & Related papers  (2021-10-15T20:37:36Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Complexity and Floquet dynamics: non-equilibrium Ising phase transitions [0.0]
  We study the time-dependent circuit complexity of the periodically driven transverse field Ising model. In the high-frequency driving limit the system is known to exhibit non-equilibrium phase transitions governed by the amplitude of the driving field.
  arXiv  Detail & Related papers  (2020-08-31T19:13:03Z)
• Quantum Chaos on Complexity Geometry [3.800391908440439]
  We show that complexity can exhibit exponential sensitivity in response to perturbations of initial conditions for chaotic systems. We show that the complexity linear response matrix gives rise to a spectrum that fully recovers the Lyapunov exponents in the classical limit.
  arXiv  Detail & Related papers  (2020-04-07T15:53:57Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.