Quantum State Preparation via Nested Entanglement

• URL: http://arxiv.org/abs/2502.02784v1
• Date: Wed, 05 Feb 2025 00:03:05 GMT
• Title: Quantum State Preparation via Nested Entanglement
• Abstract summary: We develop a representation of an n-qubit register that parameterizes its statevector as a series of nested entanglements.<n>It also allows for a straightforward treatment of pure state separability.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We develop a representation of an n-qubit register that parameterizes its statevector as a series of nested entanglements. We show that the recursive substructure of this representation provides a natural framework for automating the construction of quantum circuits for state preparation. It also allows for a straightforward treatment of pure state separability. We discuss a novel derivation of uniformly controlled rotations and the quantum Fourier transform within this representation, and consider the effects of single-qubit basis changes on its overall structure. We end with a discussion of the apparent connection between the compressibility of the state description in this representation, and the circuit complexity required to prepare it.

Related papers

• Spin-coherent quantum designs [0.0]
  We show that the canonical finite coherent-state formula reconstructs every operator in the rank-$S$ sector exactly if and only if the sampling points form a spherical $(2J+S)$-design.<n>We derive practical protocols for estimating moments of spin operators from these constructions, with direct applications to polarimetry, magnetometry, and quantum state tomography.
  arXiv  Detail & Related papers  (2026-08-11T18:00:06Z)
• A collider as a quantum computer [3.2802588232371277]
  We reformulate scattering at the level of the process itself by representing helicity transition matrices as quantum circuits.<n>Within this framework, an example of the process $e+e-to +-$ is shown, which decomposes into unitary and non-unitary components.<n>This representation reorganizes the amplitude into distinct operational elements, providing a perspective in which collider processes can be viewed as constrained quantum circuits.
  arXiv  Detail & Related papers  (2026-05-07T20:15:42Z)
• Engineering Perfect State Transfer Graphs via Givens Transformations [42.27843435279468]
  Perfect quantum state transfer is achievable in different settings, including linear qubit chains, bi-dimensional arrays, ladders, etc.<n>We present a scheme based on the Givens Transformations to analyse and obtain a class of qubit graphs that possess perfect quantum state transmission.
  arXiv  Detail & Related papers  (2026-04-02T21:40:06Z)
• Structure-Fair Quantum Circuit Complexity: An Auditable Information-Theoretic Lower Bound [0.2606834301724095]
  This paper introduces the Reference-Contingent Complexity (RCC), an information-theoretic measure calibrated by the available quantum operations.<n>Our central result is a key theorem that rigorously proves the RCC serves as a lower bound for the complexity of any universal quantum circuit.<n>This work provides a "ruler" for quantum technology that is structure-fair and enables cross-platform comparison.
  arXiv  Detail & Related papers  (2025-09-20T14:58:34Z)
• Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware [42.52549987351643]
  Quantum homogenization is a reservoir-based quantum state approximation protocol.<n>We extend the standard quantum homogenization protocol to the dynamically-equivalent ($mathttSWAP$)$alpha$ formulation.<n>We show that our proposed protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable.
  arXiv  Detail & Related papers  (2024-12-19T05:50:54Z)
• Achieving the volume-law entropy regime with random-sign Dicke states [0.5991851254194096]
  We show that the complexity of real-valued wave functions can be accurately tuned by introducing a random-sign structure. The practical realization of these random-sign Dicke states is possible on different physical platforms with shallow quantum circuits.
  arXiv  Detail & Related papers  (2024-04-23T13:50:07Z)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Quantum state tomography with disentanglement algorithm [0.0]
  We use variational quantum circuits to disentangle the quantum state to a product of computational zero states. Inverse evolution of the zero states reconstructs the quantum state up to an overall phase. Our method is universal and imposes no specific ansatz or constrain on the quantum state.
  arXiv  Detail & Related papers  (2023-10-10T03:11:12Z)
• Sufficient condition for universal quantum computation using bosonic circuits [44.99833362998488]
  We focus on promoting circuits that are otherwise simulatable to computational universality. We first introduce a general framework for mapping a continuous-variable state into a qubit state. We then cast existing maps into this framework, including the modular and stabilizer subsystem decompositions.
  arXiv  Detail & Related papers  (2023-09-14T16:15:14Z)
• Quantum process tomography of continuous-variable gates using coherent states [49.299443295581064]
  We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
  arXiv  Detail & Related papers  (2023-03-02T18:08:08Z)
• Real quantum operations and state transformations [44.99833362998488]
  Resource theory of imaginarity provides a useful framework to understand the role of complex numbers. In the first part of this article, we study the properties of real'' (quantum) operations in single-party and bipartite settings. In the second part of this article, we focus on the problem of single copy state transformation via real quantum operations.
  arXiv  Detail & Related papers  (2022-10-28T01:08:16Z)
• Harmonic flow field representations of quantum bits and gates [0.0]
  We describe a general procedure for mapping $n$-qubit states to 2D vector fields. Elementary qubits are identified with localized defects in 2D harmonic vector fields. We show that separable states appear as highly symmetric flow configurations, making them both dynamically and visually distinct from entangled states.
  arXiv  Detail & Related papers  (2022-01-30T10:18:58Z)
• Quantum Circuits in Additive Hilbert Space [0.0]
  We show how conventional circuits can be expressed in the additive space and how they can be recovered. In particular in our formalism we are able to synthesize high-level multi-controlled primitives from low-level circuit decompositions. Our formulation also accepts a circuit-like diagrammatic representation and proposes a novel and simple interpretation of quantum computation.
  arXiv  Detail & Related papers  (2021-11-01T19:05:41Z)
• 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)
• Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
  The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy. In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
  arXiv  Detail & Related papers  (2020-07-31T19:23:26Z)

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.