Bounding the computational power of bosonic systems

• URL: http://arxiv.org/abs/2503.03600v1
• Date: Wed, 05 Mar 2025 15:33:51 GMT
• Title: Bounding the computational power of bosonic systems
• Authors: Varun Upreti, Ulysse Chabaud,
• Abstract summary: We show that universal bosonic quantum computations can be simulated in exponential time on a classical computer.<n>We also present arguments supporting the plausibility of an exponential computational advantage of bosonic quantum computers over their discrete-variable counterparts.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as an exponentially greater complexity of state tomography [MMB+24] or a factoring algorithm in constant space [BCCRK24]. Yet, it remains unclear whether this structural difference of bosonic systems may also translate to a practical computational advantage over finite-dimensional quantum computers. Here we take a step towards answering this question by showing that universal bosonic quantum computations can be simulated in exponential time on a classical computer, significantly improving the best previous upper bound requiring exponential memory [CJMM24]. In complexity-theoretic terms, we improve the best upper bound on $\textsf{CVBQP}$ from $\textsf{EXPSPACE}$ to $\textsf{EXP}$. This result is achieved using a simulation strategy based on finite energy cutoffs and approximate coherent state decompositions. While we propose ways to potentially refine this bound, we also present arguments supporting the plausibility of an exponential computational advantage of bosonic quantum computers over their discrete-variable counterparts. Furthermore, we emphasize the role of circuit energy as a resource and discuss why it may act as the fundamental bottleneck in realizing this advantage in practical implementations.

Related papers

• Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets [4.289769713465494]
  This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms.<n>By integrating Singular Value Decomposition (SVD) into the process, the method achieves an operational depth of $O(n)$ with about $n$ ancilla qubits.<n>It allows for a deeper exploration of complex quantum states and phenomena, expanding the practical applications of quantum computing in physics and chemistry.
  arXiv  Detail & Related papers  (2025-02-13T04:55:51Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Evaluation of phase shifts for non-relativistic elastic scattering using quantum computers [39.58317527488534]
  This work reports the development of an algorithm that makes it possible to obtain phase shifts for generic non-relativistic elastic scattering processes on a quantum computer.
  arXiv  Detail & Related papers  (2024-07-04T21:11:05Z)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• Solving reaction dynamics with quantum computing algorithms [42.408991654684876]
  We study quantum algorithms for response functions, relevant for describing different reactions governed by linear response.<n>We focus on nuclear-physics applications and consider a qubit-efficient mapping on the lattice, which can efficiently represent the large volumes required for realistic scattering simulations.
  arXiv  Detail & Related papers  (2024-03-30T00:21:46Z)
• Efficient Representation of Gaussian Fermionic Pure States in Non-Computational Bases [0.0]
  This paper introduces an innovative approach for representing Gaussian fermionic states, pivotal in quantum spin systems and fermionic models. We focus on transitioning these states from the conventional computational (sigmaz) basis to more complex bases, such as (phi, fracpi2, alpha) We present a novel algorithm that not only simplifies the basis transformation but also reduces computational complexity.
  arXiv  Detail & Related papers  (2024-03-05T19:43:33Z)
• Towards Quantum Computational Mechanics [1.530480694206666]
  We show how quantum computing can be used to solve representative element volume (RVE) problems in computational homogenisation. Our quantum RVE solver attains exponential acceleration with respect to classical solvers.
  arXiv  Detail & Related papers  (2023-12-06T12:53:02Z)
• Low-rank tensor decompositions of quantum circuits [14.531461873576449]
  We show how MPOs can be used to express certain quantum states, quantum gates, and entire quantum circuits as low-rank tensors. This enables the analysis and simulation of complex quantum circuits on classical computers.
  arXiv  Detail & Related papers  (2022-05-19T22:09:15Z)
• No-signalling constrains quantum computation with indefinite causal structure [45.279573215172285]
  We develop a formalism for quantum computation with indefinite causal structures. We characterize the computational structure of higher order quantum maps. We prove that these rules, which have a computational and information-theoretic nature, are determined by the more physical notion of the signalling relations between the quantum systems.
  arXiv  Detail & Related papers  (2022-02-21T13:43:50Z)
• Quantum Causal Unravelling [44.356294905844834]
  We develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process. Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography.
  arXiv  Detail & Related papers  (2021-09-27T16:28:06Z)
• Computing Free Energies with Fluctuation Relations on Quantum Computers [0.0]
  We present an algorithm utilizing a fluctuation relation known as the Jarzynski equality to approximate free energy differences of quantum systems on a quantum computer. We successfully demonstrate a proof-of-concept of our algorithm using the transverse field Ising model on a real quantum processor.
  arXiv  Detail & Related papers  (2021-03-17T18:14:19Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Efficient simulatability of continuous-variable circuits with large Wigner negativity [62.997667081978825]
  Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures. We identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable. We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.
  arXiv  Detail & Related papers  (2020-05-25T11:03:42Z)

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.