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

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.