[Paper Review] Circuit implementation of bucket brigade qRAM for quantum state preparation

Pablo A. M. Casares|arXiv (Cornell University)|Jun 21, 2020

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper presents a circuit-level implementation of the bucket brigade qRAM architecture, enabling efficient quantum state preparation using classical data stored in a quantum-accessible data structure. By leveraging O(n) qutrits and controlled rotations via qRAMs, the method prepares arbitrary quantum states in O(poly log n) time, with reusable memory that avoids costly qubit entanglement and allows repeated state preparation after an initial O(2^n) setup cost.

ABSTRACT

In this short review I aim to explain how we can construct a circuit implementation of the bucketbrigade qRAM first proposed in [1]. Used with classical data, this qRAM model can be used incombination with the quantum accessible data structure [2] to prepare arbitrary quantum statesquickly and repeatedly, once the data to be prepared is in memory

Motivation & Objective

• To develop a practical circuit implementation of the bucket brigade qRAM architecture for use in quantum algorithms.
• To enable efficient preparation of arbitrary quantum states using classical data stored in a quantum-accessible data structure.
• To minimize qubit entanglement and gate count during state preparation by exploiting the bucket brigade's low-depth routing mechanism.
• To demonstrate how qRAMs can be used to implement controlled rotations for amplitude encoding with polylogarithmic time complexity.
• To show that the qRAM can be reused for multiple state preparations without reinitialization, reducing overall resource cost.

Proposed method

• The bucket brigade qRAM uses a binary tree of qutrits (|·⟩, |0⟩, |1⟩) to route direction bits through the tree, with nodes storing incoming bits only when in |·⟩ state.
• Direction bits are propagated level-by-level: |0⟩ passes right, |1⟩ passes left, and |·⟩ stores the incoming bit, ensuring only O(n) switches are activated per query.
• Controlled rotations are implemented using qRAMs to retrieve squared amplitudes and signs, enabling amplitude encoding via controlled-U gates.
• The method uses separate qRAMs for amplitude magnitudes (squared) and signs, with data retrieved via controlled routing through the tree structure.
• Ancilla registers (a, b) are prepared using qRAMs to store intermediate amplitude values, then uncomputed using reverse qRAM queries to preserve qRAM state.
• A phase quickback technique applies Z gates to the control qubit after entanglement, efficiently implementing sign flips without additional qRAM access.

Experimental results

Research questions

• RQ1 How can the bucket brigade qRAM architecture be implemented as a physical quantum circuit for state preparation?
• RQ2 What is the resource cost (qubits, gates, depth) of preparing arbitrary quantum states using qRAM-based amplitude encoding?
• RQ3 Can qRAMs be reused for repeated state preparation without significant overhead or state collapse?
• RQ4 How does the bucket brigade architecture reduce entanglement and gate count compared to traditional fanout qRAM designs?
• RQ5 What is the role of quantum-accessible data structures in enabling polylogarithmic-time quantum state preparation?

Key findings

• The bucket brigade qRAM enables quantum state preparation in O(poly log n) time per state, with an initial O(2^n) setup cost for data loading.
• Only O(n) qutrits are entangled during any single query, significantly reducing quantum resource overhead compared to fanout architectures.
• The method allows repeated preparation of the same quantum state using the same qRAM without reinitialization, preserving data integrity.
• Controlled rotations for amplitude encoding are implemented efficiently using qRAMs to retrieve squared amplitudes and signs in parallel.
• The use of ancilla registers and reverse qRAM queries enables uncomputation of intermediate data, maintaining qRAM state for reuse.
• Phase quickback via Z gates allows efficient sign application without additional qRAM access, reducing circuit depth and error probability.