Research Areas

Pioneering advances in quantum computing through focused research in error correction, circuit notation, and academic collaboration.

Quantum Error Correction

Building the foundation for fault-tolerant quantum computing

The Challenge

Current quantum computers have error rates around 1 in 100 operations before failure. For practical quantum computing applications, we need error rates as low as 1 in a trillion - representing a million-fold improvement in performance.

Our Approach

We focus on breakthrough solutions for this fundamental challenge by:

  • Scalable Control Systems: Developing control architectures that can manage thousands of qubits efficiently.
  • Fast Decoders: Creating algorithms that can detect and correct errors in real-time.
  • Optimal Algorithms: Designing quantum algorithms specifically optimized for error-corrected quantum computers.

Research Impact

  • Cryptography applications
  • Drug discovery simulations
  • Financial modeling
  • Climate change research

Algebraic Quantum Circuits

A new language for quantum circuit representation and optimization.

The Problem

Traditional quantum circuit representation relies primarily on graphical notation, which is intuitive but limited for:

  • Text-based circuit descriptions
  • Quantum state calculations
  • Circuit optimization algorithms
  • Automated circuit generation

Our Solution

We propose an algebraic notation system for quantum circuits, similar to Boolean expressions in classical computing. This enables:

  • Consistent Parameterization: Systematic description of quantum algorithms
  • Algebraic Manipulation: Mathematical operations on circuit representations
  • Optimization: Powerful reductions in gate counts
  • Automation: Programmatic circuit generation and analysis

Mathematical Foundation

For any qubit |a⟩, we use the notation:

$$a_0 = \langle a|0\rangle \text{ and } a_1 = \langle a|1\rangle$$

$$|a\rangle = a_0|0\rangle + a_1|1\rangle$$

Multi-Qubit Systems:

For $n$ qubits $|a_1\rangle\dots|a_n\rangle$, the composite state $|a\rangle = |a_1\cdots a_n\rangle$ can be written as:

$$|a\rangle = a_{k0}|a_1\cdots a_{k-1}0a_{k+1}\cdots a_n\rangle + a_{k1}|a_1\cdots a_{k-1}1a_{k+1}\cdots a_n\rangle$$

Simplified Notation:

Using our notation $|a\rangle^k_\gamma = |a_1\cdots a_{k-1}\gamma a_{k+1}\cdots a_n\rangle$:

$$|a\rangle = a_{k0}|a\rangle^k_0 + a_{k1}|a\rangle^k_1$$

Applications

  • Circuit optimization
  • Quantum compiler design
  • Algorithm verification
  • Hardware mapping

Benefits

  • Reduced gate counts
  • Automated optimization
  • Clearer algorithm design
  • Enhanced debugging

Interested in Our Research?

Learn more about our founder, explore collaboration opportunities, or get in touch to discuss potential partnerships.

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