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Fast stabilizer state preparation via AI-optimized graph decimation

Michael Doherty, Matteo Puviani, Jasmine Brewer, Gabriel Matos, David Amaro, Ben Criger, David T. Stephen

Abstract

We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces the number of edges in the graph using two-qubit Clifford gates to produce a unitary preparation circuit. We explore various heuristic search and AI-based approaches to optimally choose Clifford gates at each step, the most sophisticated of which is a combination of reinforcement learning and Monte Carlo tree search that we call QuSynth. We apply our method to synthesize code states of various quantum error correcting codes including the 23-qubit Golay code and the 144-qubit gross code, the latter of which is significantly beyond the qubit number that is accessible to prior optimal circuit synthesis methods. We demonstrate that our techniques are capable of reducing the required two-qubit gates by up to a factor of 2.5 compared to previous approaches while retaining low circuit depth.

Fast stabilizer state preparation via AI-optimized graph decimation

Abstract

We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces the number of edges in the graph using two-qubit Clifford gates to produce a unitary preparation circuit. We explore various heuristic search and AI-based approaches to optimally choose Clifford gates at each step, the most sophisticated of which is a combination of reinforcement learning and Monte Carlo tree search that we call QuSynth. We apply our method to synthesize code states of various quantum error correcting codes including the 23-qubit Golay code and the 144-qubit gross code, the latter of which is significantly beyond the qubit number that is accessible to prior optimal circuit synthesis methods. We demonstrate that our techniques are capable of reducing the required two-qubit gates by up to a factor of 2.5 compared to previous approaches while retaining low circuit depth.
Paper Structure (34 sections, 14 equations, 22 figures, 2 tables)

This paper contains 34 sections, 14 equations, 22 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Graph States
  3. Graph state preparation circuits
  4. Graph decimation
  5. Heuristic search methods
  6. Best-first search (BeFS)
  7. Beam search
  8. Search-informed reinforcement learning with QuSynth
  9. Monte Carlo tree search
  10. Reinforcement Learning framework
  11. Model-free reinforcement learning
  12. QuSynth: MCTS-guided reinforcement learning
  13. Results
  14. Discussion
  15. Further applications of graph decimation
  16. ...and 19 more sections

Figures (22)

  • Figure 1: Transformations of graph states. Each circle represents a qubit initialized in $|+\rangle$, and solid edges denote ${\sf{CZ}}\xspace$ gates. Left: Illustration of the local complementation operation, where the highlighted region denotes $n(i)$. Middle: Illustration of \ref{['eq:cx_derivation']} where the arrow point from control qubit to target qubit and the highlighted region denotes $n(j)$. Right: Same as previous panel for \ref{['eq:rule_y']} where the highlighted region now denotes $n(j)\cup \{j\}$.
  • Figure 2: Left: Example of a pair of graphs that define a complete orbit under local complementation (LC), up to node relabeling. The minimal edge count in the LC orbit is thus equal to 9 (bottom graph). Middle: Circuit derived using our technique which uses a ${\sf{CX}}\xspace$ gate to prepare the bottom-left graph state using 8 two-qubit gates. Right: Circuit that uses ${\sf{CY}}\xspace$ gates to prepare the same graph state using 7 two-qubit gates.
  • Figure 3: Left: The star and fully connected graphs define an LC-orbit representing the GHZ state. Middle: A circuit to prepare the star graph using ${\sf{CX}}\xspace$ gates that simplifies connectivity to nearest-neighbor. Right: A circuit that reduces depth from linear to logarithmic in system size.
  • Figure 4: Schematic of the graph decimation task. The initial state is the graph of the quantum state we seek to implement. The terminal state is the fully disconnected graph with no edges.
  • Figure 5: Schematics of the heuristic search methods developed in this work. Left: best-first search (BeFS); Right: Beam search algorithm.
  • ...and 17 more figures