Stochastic emulation of quantum algorithms

• URL: http://arxiv.org/abs/2109.07777v1
• Date: Thu, 16 Sep 2021 07:54:31 GMT
• Title: Stochastic emulation of quantum algorithms
• Authors: Daniel Braun and Ronny M\"uller
• Abstract summary: We introduce higher-order partial derivatives of a probability distribution of particle positions as a new object that shares basic properties of quantum mechanical states needed for a quantum algorithm. We prove that the propagation via the map built from those universal maps reproduces up to a prefactor exactly the evolution of the quantum mechanical state. We implement several well-known quantum algorithms, analyse the scaling of the needed number of realizations with the number of qubits, and highlight the role of destructive interference for the cost of emulation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two qubits at the same time. The former aspect renders the direct classical simulation of quantum algorithms difficult. Here we introduce higher-order partial derivatives of a probability distribution of particle positions as a new object that shares these basic properties of quantum mechanical states needed for a quantum algorithm. Discretization of the positions allows one to represent the quantum mechanical state of $n_\text{bit}$ qubits by $2(n_\text{bit}+1)$ classical stochastic bits. Based on this, we demonstrate many-particle interference and representation of pure entangled quantum states via derivatives of probability distributions and find the universal set of stochastic maps that correspond to the quantum gates in a universal gate set. We prove that the propagation via the stochastic map built from those universal stochastic maps reproduces up to a prefactor exactly the evolution of the quantum mechanical state with the corresponding quantum algorithm, leading to an automated translation of a quantum algorithm to a stochastic classical algorithm. We implement several well-known quantum algorithms, analyse the scaling of the needed number of realizations with the number of qubits, and highlight the role of destructive interference for the cost of the emulation. Foundational questions raised by the new representation of a quantum state are discussed.

Related papers

• Efficient Quantum Pseudorandomness from Hamiltonian Phase States [41.94295877935867]
  We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem. We show that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We show that our assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives.
  arXiv  Detail & Related papers  (2024-10-10T16:10:10Z)
• Enhanced quantum state transfer: Circumventing quantum chaotic behavior [35.74056021340496]
  We show how to transfer few-particle quantum states in a two-dimensional quantum network. Our approach paves the way to short-distance quantum communication for connecting distributed quantum processors or registers.
  arXiv  Detail & Related papers  (2024-02-01T19:00:03Z)
• Quantum simulation of excited states from parallel contracted quantum eigensolvers [5.915403570478968]
  We show that a ground-state contracted quantum eigensolver can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two excited-state CQEs that perform the excited-state calculation while inheriting many of the remarkable features of the original ground-state version of the algorithm.
  arXiv  Detail & Related papers  (2023-11-08T23:52:31Z)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• 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)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Quantum algorithms for estimating quantum entropies [6.211541620389987]
  We propose quantum algorithms to estimate the von Neumann and quantum $alpha$-R'enyi entropies of an fundamental quantum state. We also show how to efficiently construct the quantum entropy circuits for quantum entropy estimation using single copies of the input state.
  arXiv  Detail & Related papers  (2022-03-04T15:44:24Z)
• Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer [0.0]
  Neutral atom hyperfine qubits provide inherent scalability due to their identical characteristics, long coherence times, and ability to be trapped in dense multi-dimensional arrays. We demonstrate several quantum algorithms on a programmable gate model neutral atom quantum computer in an architecture based on individual addressing of single atoms with tightly focused optical beams scanned across a two-dimensional array of qubits.
  arXiv  Detail & Related papers  (2021-12-29T15:02:43Z)
• Automatic quantum circuit encoding of a given arbitrary quantum state [0.0]
  We propose a quantum-classical hybrid algorithm to encode a given arbitrarily quantum state onto an optimal quantum circuit. The proposed algorithm employs as an objective function the absolute value of fidelity $F = langle 0 vert hatmathcalCdagger vert Psi rangle$. We experimentally demonstrate that a quantum circuit generated by the AQCE algorithm can indeed represent the original quantum state reasonably on a noisy real quantum device.
  arXiv  Detail & Related papers  (2021-12-29T12:33:41Z)
• Q-means using variational quantum feature embedding [0.9572675949441442]
  The objective of the Variational circuit is to maximally separate the clusters in the quantum feature Hilbert space. The output of the quantum circuit are characteristic cluster quantum states that represent a superposition of all quantum states belonging to a particular cluster. The gradient of the expectation value is used to optimize the parameters of the variational circuit to learn a better quantum feature map.
  arXiv  Detail & Related papers  (2021-12-11T13:00:51Z)
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator [41.74498230885008]
  We demonstrate a programmable quantum simulator based on deterministically prepared two-dimensional arrays of neutral atoms. We benchmark the system by creating and characterizing high-fidelity antiferromagnetically ordered states. We then create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation.
  arXiv  Detail & Related papers  (2020-12-22T19:00:04Z)

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.