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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
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Solving the Sampling Problem of the Sycamore Quantum Circuits.

Feng Pan1,2, Keyang Chen1,3, Pan Zhang1,4,5

  • 1CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.

Physical Review Letters
|September 9, 2022
PubMed
Summary
This summary is machine-generated.

We developed a classical method to generate samples from Google's Sycamore quantum circuits, achieving quantum supremacy. This tensor network contraction approach is significantly more efficient for producing quantum circuit samples.

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Area of Science:

  • Quantum Computing
  • Computational Physics
  • Classical Simulation

Background:

  • Google's Sycamore processor demonstrated quantum supremacy using complex quantum circuits.
  • Generating independent samples from these circuits is computationally challenging for classical supercomputers.

Purpose of the Study:

  • To propose an efficient classical method for generating samples from Sycamore quantum circuits.
  • To achieve a target fidelity in the generated samples, simulating the quantum output distribution.

Main Methods:

  • Tensor network contraction of the quantum circuit.
  • Single contraction to generate a large number of uncorrelated samples.
  • Utilized a computational cluster with 512 GPUs.

Main Results:

  • Generated 1x10^6 uncorrelated bitstrings from the Sycamore circuit (53 qubits, 20 cycles) with fidelity F≈0.0037.
  • The computation took approximately 15 hours.
  • The simulation cost is estimated to be significantly faster on future ExaFLOPS supercomputers.

Conclusions:

  • The proposed tensor network method offers a massively more efficient classical approach to sample quantum circuits.
  • This method can potentially simulate quantum supremacy experiments faster than quantum hardware with future computational resources.