Quantum circuit to estimate pi using quantum amplitude estimation

• URL: http://arxiv.org/abs/2008.02623v2
• Date: Wed, 21 Oct 2020 00:51:53 GMT
• Title: Quantum circuit to estimate pi using quantum amplitude estimation
• Authors: Takuma Noto
• Abstract summary: The proposed quantum circuit to estimate pi is based on the Monte Carlo method, quantum amplitude estimation, and quantum squarer. By applying the quantum squarer using QFT, the circuit was implemented in $ 4n + 1 $ qubits at $ 22n $ sampling.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This study presents a quantum circuit for estimating the pi value using arithmetic circuits and by quantum amplitude estimation. We review two types of quantum multipliers and propose quantum squaring circuits based on the multiplier as basic arithmetic circuits required for performing quantum computations. The squarer realized by a quantum adder with the gate size of $ O(n) $ requires $ O(n^2) $ gates and at least one ancillary qubits, while that realized by using quantum Fourier transform (QFT) requires $ O(n^3) $ gates without ancillary qubit. The proposed quantum circuit to estimate pi is based on the Monte Carlo method, quantum amplitude estimation, and quantum squarer. By applying the quantum squarer using QFT, the circuit was implemented in $ 4n + 1 $ qubits at $ 2^{2n} $ sampling. The proposed method was demonstrated using a quantum computer simulator with $ n $ being varied from 2 to 6, and the obtained result was compared with the one obtained by performing a classical calculation.

Related papers

• Exponential separation in quantum query complexity of the quantum switch with respect to simulations with standard quantum circuits [1.151731504874944]
  We prove that the action of the quantum switch on two $n$-qubit quantum channels cannot be simulated deterministically. This demonstrates an exponential separation in quantum query complexity of indefinite causal order compared to standard quantum circuits.
  arXiv  Detail & Related papers  (2024-09-27T03:18:28Z)
• Efficient implementation of discrete-time quantum walks on quantum computers [0.0]
  We propose an efficient and scalable quantum circuit implementing the discrete-time quantum walk (DTQW) model. For $t$ time-steps of the DTQW, the proposed circuit requires only $O(n2 + nt)$ two-qubit gates compared to the $O(n2 t)$ of the current most efficient implementation.
  arXiv  Detail & Related papers  (2024-02-02T19:11:41Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Variational-quantum-eigensolver-inspired optimization for spin-chain work extraction [39.58317527488534]
  Energy extraction from quantum sources is a key task to develop new quantum devices such as quantum batteries. One of the main issues to fully extract energy from the quantum source is the assumption that any unitary operation can be done on the system. We propose an approach to optimize the extractable energy inspired by the variational quantum eigensolver (VQE) algorithm.
  arXiv  Detail & Related papers  (2023-10-11T15:59:54Z)
• Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians [0.8009842832476994]
  We propose a method for constructing $textttPREPARE$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry. The $textttPREPARE$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes.
  arXiv  Detail & Related papers  (2023-08-26T05:32:38Z)
• 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)
• QuEst: Graph Transformer for Quantum Circuit Reliability Estimation [32.89844497610906]
  Python library called TorchQuantum can construct, simulate, and train PQC for machine learning tasks. We propose to leverage a graph transformer model to predict noise impact on circuit fidelity. Compared with circuit simulators, the predictor has over 200X speedup for estimating the fidelity.
  arXiv  Detail & Related papers  (2022-10-30T02:35:31Z)
• Halving the cost of quantum multiplexed rotations [0.0]
  We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls. Our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations.
  arXiv  Detail & Related papers  (2021-10-26T06:49:44Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• QUANTIFY: A framework for resource analysis and design verification of quantum circuits [69.43216268165402]
  QUANTIFY is an open-source framework for the quantitative analysis of quantum circuits. It is based on Google Cirq and is developed with Clifford+T circuits in mind. For benchmarking purposes QUANTIFY includes quantum memory and quantum arithmetic circuits.
  arXiv  Detail & Related papers  (2020-07-21T15:36:25Z)
• Computational advantage from quantum superposition of multiple temporal orders of photonic gates [0.0]
  A control quantum system can coherently determine the order in which a target quantum system undergoes $N$ gate operations. We experimentally demonstrate the quantum $N$-switch with $N=4$ gates acting on a photonic-polarization qubit. This is the first observation of a quantum superposition of more than $N=2$ temporal orders.
  arXiv  Detail & Related papers  (2020-02-18T19:00:01Z)

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.