Every Classical Sampling Circuit is a Quantum Sampling Circuit

• URL: http://arxiv.org/abs/2109.04842v1
• Date: Fri, 10 Sep 2021 12:52:23 GMT
• Title: Every Classical Sampling Circuit is a Quantum Sampling Circuit
• Authors: Steven Herbert
• Abstract summary: This note introduces "Q-marginals", which are quantum states encoding some probability distribution. It shows that these can be prepared directly from a classical circuit sampling for the probability distribution of interest.
• Score: 0.8122270502556371
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This note introduces "Q-marginals", which are quantum states encoding some probability distribution in a manner suitable for use in Quantum Monte Carlo Integration (QMCI), and shows that these can be prepared directly from a classical circuit sampling for the probability distribution of interest. This result is important as the quantum advantage in Monte Carlo integration is in the form of a reduction in the number of uses of a quantum state encoding the probability distribution (in QMCI) relative to the number of samples that would be required in classical MCI -- hence it only translates into a computational advantage if the number of operations required to prepare this quantum state encoding the probability distribution is comparable to the number of operations required to generate a classical sample (as the Q-marginal construction achieves).

Related papers

• Quantum state preparation for bell-shaped probability distributions using deconvolution methods [0.0]
  We present a hybrid classical-quantum approach to load quantum data. We use the Jensen-Shannon distance as the cost function to quantify the closeness of the outcome from the classical step and the target distribution. The output from the deconvolution step is used to construct the quantum circuit required to load the given probability distribution.
  arXiv  Detail & Related papers  (2023-10-08T06:55:47Z)
• Accelerating variational quantum Monte Carlo using the variational quantum eigensolver [0.0]
  Variational Monte Carlo (VMC) methods are used to sample classically from distributions corresponding to quantum states. We propose replacing this initial distribution with samples produced using a quantum computer.
  arXiv  Detail & Related papers  (2023-07-15T05:45:55Z)
• QAOA-MC: Markov chain Monte Carlo enhanced by Quantum Alternating Operator Ansatz [0.6181093777643575]
  We propose the use of Quantum Alternating Operator Ansatz (QAOA) for quantum-enhanced Monte Carlo. This work represents an important step toward realizing practical quantum advantage with currently available quantum computers.
  arXiv  Detail & Related papers  (2023-05-15T16:47:31Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Protocols for classically training quantum generative models on probability distributions [17.857341127079305]
  Quantum Generative Modelling (QGM) relies on preparing quantum states and generating samples as hidden - or known - probability distributions. We propose protocols for classical training of QGMs based on circuits of the specific type that admit an efficient gradient. We numerically demonstrate the end-to-end training of IQP circuits using probability distributions for up to 30 qubits on a regular desktop computer.
  arXiv  Detail & Related papers  (2022-10-24T17:57:09Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Quantum-enhanced Markov chain Monte Carlo [0.22166578153935784]
  We introduce a quantum algorithm to sample from distributions that pose a bottleneck in several applications. In each step, the quantum processor explores the model in superposition to propose a random move, which is then accepted or rejected by a classical computer. We find that this quantum algorithm converges in fewer iterations than common classical MCMC alternatives on relevant problem instances.
  arXiv  Detail & Related papers  (2022-03-23T15:50:12Z)
• Learnability of the output distributions of local quantum circuits [53.17490581210575]
  We investigate, within two different oracle models, the learnability of quantum circuit Born machines. We first show a negative result, that the output distributions of super-logarithmic depth Clifford circuits are not sample-efficiently learnable. We show that in a more powerful oracle model, namely when directly given access to samples, the output distributions of local Clifford circuits are computationally efficiently PAC learnable.
  arXiv  Detail & Related papers  (2021-10-11T18:00:20Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems [69.33243249411113]
  We show that Pauli errors incur the lowest sampling overhead among a large class of realistic quantum channels. We conceive a scheme amalgamating QEM with quantum channel coding, and analyse its sampling overhead reduction compared to pure QEM.
  arXiv  Detail & Related papers  (2020-12-15T15:51:27Z)

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.