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Universal Measurement-Based Quantum Computation in a One-Dimensional Architecture Enabled by Dual-Unitary Circuits.

David T Stephen1,2, Wen Wei Ho3,4, Tzu-Chieh Wei5,6

  • 1Department of Physics and Center for Theory of Quantum Matter, <a href="https://ror.org/02ttsq026">University of Colorado Boulder</a>, Boulder, Colorado 80309 USA.

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This summary is machine-generated.

Dual-unitary circuits offer a new framework for measurement-based quantum computation (MBQC). This method effectively performs quantum computation spatially, generating resource states for universal MBQC and new topological phases.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Quantum Computation

Background:

  • Dual-unitary circuits are a powerful tool in many-body quantum dynamics.
  • These circuits exhibit unitarity even when measured spatially.
  • Measurement-based quantum computation (MBQC) is a leading paradigm for quantum computing.

Purpose of the Study:

  • To establish dual-unitary circuits as an ideal framework for understanding and expanding MBQC.
  • To demonstrate how dual-unitary dynamics can implement spatial quantum computation.
  • To explore the connection between dual-unitary circuits, MBQC resource states, and topological phases.

Main Methods:

  • Applying dual-unitary circuits to many-body states followed by measurements.
  • Utilizing the dynamics of the one-dimensional kicked Ising chain with specific parameters.
  • Analyzing the resulting states as resources for universal deterministic MBQC.

Main Results:

  • Dual-unitary circuits effectively implement quantum computation in the spatial direction.
  • The kicked Ising chain dynamics generate resource states for universal MBQC.
  • A depth-k quantum circuit is achieved with approximately 3k/4 encoded qubits after k time steps.
  • The protocol allows for space-time rotation of quantum circuits, enabling resource trade-offs.

Conclusions:

  • Dual-unitary circuits provide a novel and powerful approach to MBQC.
  • The protocol generates a vast generalization of cluster states, leading to new symmetry-protected topological phases.
  • This work offers new ways to manage resources like qubit number and coherence time in quantum computers.
  • The developed protocol is robust to symmetry-respecting deformations.