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Polylogarithmic-depth controlled-NOT gates without ancilla qubits.

Baptiste Claudon1,2, Julien Zylberman3, César Feniou4,5

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This summary is machine-generated.

This study presents new quantum circuits for decomposing controlled-NOT gates (Cn(X)). These methods offer improved performance for quantum algorithms, advancing fault-tolerant quantum computing and its applications.

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Area of Science:

  • Quantum Computing
  • Quantum Information Science
  • Algorithm Optimization

Background:

  • Controlled operations, specifically n-control-NOT gates (Cn(X)), are essential components in quantum algorithms.
  • Efficiently decomposing Cn(X) gates into fundamental single-qubit and CNOT gates is a significant challenge in quantum circuit design.

Purpose of the Study:

  • To introduce novel Cn(X) gate decomposition circuits that outperform existing methods.
  • To provide efficient circuit decompositions applicable in both asymptotic and non-asymptotic quantum computing regimes.

Main Methods:

  • Developed three distinct decomposition strategies for Cn(X) gates.
  • One exact decomposition utilizes a single ancilla qubit, achieving a circuit depth of .
  • An approximate decomposition requires no ancilla qubits, with a circuit depth of .
  • An adjustable-depth exact decomposition is presented, where depth decreases with available ancilla qubits (m≤n) as .

Main Results:

  • The proposed Cn(X) circuits demonstrate superior performance compared to previous decomposition techniques.
  • Achieved exponential speedups in circuit complexity for controlled operations.
  • The decompositions are effective in both asymptotic and non-asymptotic scenarios.

Conclusions:

  • The developed Cn(X) decomposition methods offer significant improvements for quantum circuit construction.
  • These advancements are expected to enhance the efficiency of numerous quantum algorithms across diverse fields.
  • Potential impact on fault-tolerant quantum computing, quantum chemistry, physics, finance, and quantum machine learning.