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Dissipative realization of a quantum distance-based classifier using open quantum walks

Pedro Linck Maciel, Graeme Pleasance, Francesco Petruccione, Nadja K. Bernardes

Abstract

Open quantum walks (OQWs) constitute a class of quantum walks whose dynamics are entirely driven by interactions with the environment. It is well known that OQWs provide a general framework for implementing dissipative quantum computation. In this work, we demonstrate the feasibility of running the previously proposed quantum distance-based classifier within the open quantum walk computation model, and we show that its expected runtime remains finite even in the slower regime.

Dissipative realization of a quantum distance-based classifier using open quantum walks

Abstract

Open quantum walks (OQWs) constitute a class of quantum walks whose dynamics are entirely driven by interactions with the environment. It is well known that OQWs provide a general framework for implementing dissipative quantum computation. In this work, we demonstrate the feasibility of running the previously proposed quantum distance-based classifier within the open quantum walk computation model, and we show that its expected runtime remains finite even in the slower regime.
Paper Structure (12 sections, 52 equations, 6 figures, 1 table)

This paper contains 12 sections, 52 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Open Quantum Walks
  3. Open Quantum Walks
  4. Linear Open Quantum Walks for Quantum Computation
  5. Distance-based classifier algorithms
  6. Classical distance-based classifier
  7. Quantum distance-based quantum classifier
  8. Quantum circuit for distance-based classifier
  9. Distance-based quantum classifier in the OQW model
  10. Implementing the circuit in the framework
  11. Simulation results
  12. Conclusion

Figures (6)

  • Figure 1: An arbitrary open quantum walk can be represented by this visual diagram. If there is an omitted edge in a particular diagram, this means that the corresponding operator $B_i^j$ is zero.
  • Figure 2: An arbitrary two-node open quantum walk.
  • Figure 3: The diagram corresponding to the linear OQW model. Each $U_i$ is a unitary operator, and $\omega, \lambda \geq 0$ are such that $\omega + \lambda = 1$.
  • Figure 4: Open Quantum Walk representing the quantum classifier circuit.
  • Figure 5: Detection probability of finding the walker in node 3 $P_3(n)$ versus the number of iterations $n$ for different values of probability $\omega$.
  • ...and 1 more figures