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Computing n-Time Correlation Functions without Ancilla Qubits.

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We present a novel quantum computing method to measure n-time correlation functions without ancilla qubits. This technique simplifies hardware requirements and enhances practical quantum many-body correlation studies.

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Area of Science:

  • Quantum Information Science
  • Quantum Many-Body Physics
  • Quantum Computing Algorithms

Background:

  • N-time correlation functions are crucial for comparing quantum theory with experiments.
  • Traditional methods like the Hadamard test require ancilla qubits and controlled operations, limiting quantum hardware applications.

Purpose of the Study:

  • To develop a new quantum algorithm for computing n-time correlation functions.
  • To overcome hardware limitations of digital and analog quantum computers.
  • To enable practical measurements of complex quantum correlations.

Main Methods:

  • Introduced a method using only unitary evolutions on the system of interest.
  • Eliminated the need for ancilla qubits and control operations.
  • Implemented an error mitigation technique using signal processing (filtering and correlation analysis).

Main Results:

  • Demonstrated the protocol on IBM quantum hardware (up to 12 qubits).
  • Successfully measured the Schwinger model's single-particle spectrum and the transverse-field Ising model's out-of-time-order correlator.
  • Reproduced noiseless simulation results from noisy hardware using the error mitigation procedure.

Conclusions:

  • The new method relaxes hardware connectivity requirements for digital quantum processors.
  • Enables more feasible n-time correlation function measurements on analog quantum platforms.
  • Provides a practical route for exploring quantum many-body correlations despite hardware noise.