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A quantum random access memory (QRAM) using a polynomial encoding of binary strings.

Priyanka Mukhopadhyay1

  • 1Department of Computer Science, University of Toronto, Toronto, ON, Canada. mukhopadhyay.priyanka@gmail.com.

Scientific Reports
|March 31, 2025
PubMed
Summary
This summary is machine-generated.

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We introduce a new polynomial encoding for quantum random access memory (QRAM) circuits. This design offers exponential improvements in T-depth and reduced T-count for quantum oracles, enhancing quantum algorithm efficiency.

Area of Science:

  • Quantum computing
  • Quantum algorithms
  • Quantum information science

Background:

  • Quantum algorithms offer significant speedups but rely on efficient quantum oracle implementation.
  • Quantum Random Access Memory (QRAM) is a key architecture for realizing these oracles.
  • Optimizing non-Clifford gates (like T gates) is crucial for fault-tolerant quantum computing.

Purpose of the Study:

  • To develop a novel, efficient QRAM design using polynomial encoding.
  • To optimize the T-count and T-depth of QRAM and quantum look-up tables (qLUTs).
  • To improve the performance of quantum oracles for practical quantum algorithms.

Main Methods:

  • Developed a new QRAM design, termed [Formula: see text], utilizing polynomial encoding of bit strings.

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  • Implemented the QRAM design using Clifford+T circuits, focusing on T-depth and T-count optimization.
  • Constructed a quantum look-up table ([Formula: see text]) by combining two [Formula: see text] modules.

    • Main Results:

    • The [Formula: see text] QRAM design achieves exponential improvement in T-depth over bucket brigade architectures, with reduced T-count and same qubit count.
    • The combined [Formula: see text] qLUT achieves a double exponential improvement in T-depth compared to CSWAP architectures, with similar T-count and qubit count.
    • A method to optimize Toffoli counts in circuits, particularly those with multi-controlled-NOT gates, was developed using polynomial encoding.

    Conclusions:

    • The novel polynomial encoding approach significantly enhances the efficiency of QRAM and qLUT implementations.
    • This work provides a pathway to more practical and resource-efficient quantum oracles for various quantum algorithms.
    • The developed techniques contribute to reducing the overhead of fault-tolerant quantum computation.