Simulation of linear non-Hermitian boundary-value problems with quantum singular value transformation

• URL: http://arxiv.org/abs/2212.09113v1
• Date: Sun, 18 Dec 2022 15:46:13 GMT
• Title: Simulation of linear non-Hermitian boundary-value problems with quantum singular value transformation
• Authors: I. Novikau, I. Y. Dodin, and E. A. Startsev
• Abstract summary: We propose a quantum algorithm for simulating dissipative waves in inhomogeneous linear media as a boundary-value problem. We construct a quantum circuit that models the propagation of electromagnetic waves in a one-dimensional system with outgoing boundary conditions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a quantum algorithm for simulating dissipative waves in inhomogeneous linear media as a boundary-value problem. Using the so-called quantum singular value transformation (QSVT), we construct a quantum circuit that models the propagation of electromagnetic waves in a one-dimensional system with outgoing boundary conditions. The corresponding measurement procedure is also discussed. Limitations of the QSVT algorithm are identified in connection with the large condition numbers that the dispersion matrices exhibit at weak dissipation.

Related papers

• Quantum linear algebra for disordered electrons [0.0]
  We describe how to use quantum linear algebra to simulate a physically realistic model of disordered non-interacting electrons on exponentially many lattice sites. We overcome this by simulating an exponentially large disorder instance using a block-encoded hopping matrix of physical form. Key physical quantities, including the reduced density matrix, Green's function, and local density of states, can then be computed using quantum singular value transformation, quantum amplitude estimation, and trace estimation.
  arXiv  Detail & Related papers  (2024-11-01T08:00:10Z)
• Locally purified density operators for noisy quantum circuits [17.38734393793605]
  We show that mixed states generated from noisy quantum circuits can be efficiently represented by locally purified density operators (LPDOs) We present a mapping from LPDOs of $N$ qubits to projected entangled-pair states of size $2times N$ and introduce a unified method for managing virtual and Kraus bonds.
  arXiv  Detail & Related papers  (2023-12-05T16:10:30Z)
• Quantum simulation of Maxwell's equations via Schr\"odingersation [27.193565893837356]
  We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schr"odingersation approach. Instead of qubits, the quantum algorithms can also be formulated in the continuous variable quantum framework.
  arXiv  Detail & Related papers  (2023-08-16T14:52:35Z)
• Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr\"odinger Equation [56.9919517199927]
  "Wasserstein Quantum Monte Carlo" (WQMC) uses the gradient flow induced by the Wasserstein metric, rather than Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.
  arXiv  Detail & Related papers  (2023-07-06T17:54:08Z)
• Decoherence quantification through commutation relations decay for open quantum harmonic oscillators [2.0508733018954843]
  We consider the exponentially fast decay in the two-point commutator matrix of the system variables as a manifestation of quantum decoherence. These features are exploited as nonclassical resources in quantum computation and quantum information processing technologies.
  arXiv  Detail & Related papers  (2022-08-04T08:57:31Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Quantum computing critical exponents [0.0]
  We show that the Variational Quantum-Classical Simulation algorithm admits a finite circuit depth scaling collapse when targeting the critical point of the transverse field Ising chain. The order parameter only collapses on one side of the transition due to a slowdown of the quantum algorithm when crossing the phase transition.
  arXiv  Detail & Related papers  (2021-04-02T17:38:20Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)

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.