Semicoherent Symmetric Quantum Processes: Theory and Applications

• URL: http://arxiv.org/abs/2403.05470v2
• Date: Wed, 30 Oct 2024 15:20:02 GMT
• Title: Semicoherent Symmetric Quantum Processes: Theory and Applications
• Authors: Yan Wang, Sarah Chehade, Eugene Dumitrescu,
• Abstract summary: We consider the interplay between the $varepsilon$-approximate processes and the exact symmetries in a semicoherent context. Our work paves the way for a deeper understanding and greater appreciation of how symmetries can be used to control quantum dynamics.
• Score: 3.6190123930006317
• License:
• Abstract: Discovering pragmatic and efficient approaches to construct $\varepsilon$-approximations of quantum operators such as real (imaginary) time-evolution propagators in terms of the basic quantum operations (gates) is challenging. Prior $\varepsilon$-approximations are invaluable, in that they enable the compilation of classical and quantum algorithm modeling of, e.g., dynamical and thermodynamic quantum properties. In parallel, symmetries are powerful tools concisely describing the fundamental laws of nature; the symmetric underpinnings of physical laws have consistently provided profound insights and substantially increased predictive power. In this work, we consider the interplay between the $\varepsilon$-approximate processes and the exact symmetries in a semicoherent context -- where measurements occur at each logical clock cycle. We draw inspiration from Pascual Jordan's groundbreaking formulation of nonassociative, but commutative, symmetric algebraic form. Our symmetrized formalism is then applied in various domains such as quantum random walks, real-time evolutions, variational algorithm ansatzes, and efficient entanglement verification. Our work paves the way for a deeper understanding and greater appreciation of how symmetries can be used to control quantum dynamics in settings where coherence is a limited resource.

Related papers

• Strong symmetries in collision models and physical dilations of covariant quantum maps [0.0]
  Covariant or weakly symmetric quantum maps play a key role in defining quantum evolutions. This work explores how weak symmetries of quantum maps manifest in their dilations.
  arXiv  Detail & Related papers  (2024-10-22T11:28:36Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Physical consequences of gauge optimization in quantum open systems evolutions [44.99833362998488]
  We show that gauge transformations can be exploited, on their own, to optimize practical physical tasks. First, we describe the inherent structure of the underlying symmetries in quantum Markovian dynamics. We then analyze examples of optimization in quantum thermodynamics.
  arXiv  Detail & Related papers  (2024-07-02T18:22:11Z)
• Efficient quantum algorithms for testing symmetries of open quantum systems [17.55887357254701]
  In quantum mechanics, it is possible to eliminate degrees of freedom by leveraging symmetry to identify the possible physical transitions. Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures. We develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers.
  arXiv  Detail & Related papers  (2023-09-05T18:05:26Z)
• A Bottom-up Approach to Constructing Symmetric Variational Quantum Circuits [0.0]
  We show how to construct symmetric quantum circuits using representation theory. We show how to derive the particle-conserving exchange gates, which are commonly used in constructing hardware-efficient quantum circuits.
  arXiv  Detail & Related papers  (2023-08-17T10:57:15Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Efficient classical algorithms for simulating symmetric quantum systems [4.416367445587541]
  We show that classical algorithms can efficiently emulate quantum counterparts given certain classical descriptions of the input. Specifically, we give classical algorithms that calculate ground states and time-evolved expectation values for permutation-invariantians specified in the symmetrized Pauli basis.
  arXiv  Detail & Related papers  (2022-11-30T13:53:16Z)
• Quantum Simulation of Conformal Field Theory [77.34726150561087]
  We describe a quantum algorithm to simulate the dynamics of conformal field theories. A full analysis of the approximation errors suggests near-term applicability.
  arXiv  Detail & Related papers  (2021-09-29T06:44:33Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• 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)
• Symmetries of quantum evolutions [0.5735035463793007]
  Wigner's theorem establishes that every symmetry of quantum state space must be either a unitary transformation, or an antiunitary transformation. We show that it is impossible to extend the time reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem implies that any time symmetric formulation of quantum theory must either restrict the set of the allowed evolutions, or modify the operational interpretation of quantum states and processes.
  arXiv  Detail & Related papers  (2021-01-13T09:47:32Z)

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.