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Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers.

Luca Razzoli1,2, Gabriele Cenedese1,2, Maria Bondani3

  • 1Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy.

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We developed an efficient quantum circuit for discrete-time quantum walks (DTQW), reducing gate count for scalable quantum computation. This breakthrough enables more complex quantum algorithms on current hardware.

Keywords:
quantum algorithmsquantum circuitsquantum computingquantum walks

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Area of Science:

  • Quantum Computing
  • Quantum Information Science

Background:

  • Quantum walks are universal for quantum computation, offering speed-ups.
  • Discrete-time quantum walks (DTQW) are suitable for circuit implementation.
  • Existing DTQW circuits are large and deep, limiting scalability and time steps.

Purpose of the Study:

  • To propose an efficient and scalable quantum circuit for DTQW on a 2n-cycle.
  • To reduce the number of two-qubit gates required for DTQW implementation.

Main Methods:

  • The proposed circuit utilizes the diagonalization of the conditional shift operator.
  • It achieves a gate complexity of O(n2+nt) for t time steps.
  • Experimental validation was performed on an IBM quantum device.

Main Results:

  • The new circuit requires significantly fewer gates than previous methods (O(n2t)).
  • Experimental results on 4-cycle and 8-cycle demonstrated periodic dynamics and entanglement generation.
  • The approach is effective beyond a few time steps.

Conclusions:

  • The proposed circuit offers an efficient and scalable method for implementing DTQW.
  • This work facilitates the reliable use of DTQW on current quantum computers.
  • It paves the way for more advanced quantum algorithms and applications.