[Paper Review] Loading Classical Data into a Quantum Computer

John A. Cortese, Timothy M. Braje|arXiv (Cornell University)|Mar 5, 2018

Quantum Computing Algorithms and Architecture50 citations

TL;DR

The paper presents three circuit families for loading classical binary data into quantum states, enabling logarithmic qubit usage and exploring compression techniques to optimize data transfer into quantum memory.

ABSTRACT

This document describes a family of quantum circuits which load classical data into a quantum state. When loading $N$ classical bits, the result quantum state is of order $\log_2(N)$ qubits. Furthermore the gate depth of the data loading circuit is of order $\log_2(N)$. Limitations to the efficiency of the data loading process such as the Holevo bound are discussed. Methods to improve the efficiency of the data loading procedure such as combining classical compression techniques with quantum decompression circuitry, are also discussed. Simulations using the Quipper language were conducted to verify the circuits behavior.

Motivation & Objective

• Motivate and formalize the problem of efficiently transferring classical data into quantum format for quantum computation.
• Develop and compare circuit families that load N classical bits into quantum states with varying qubit counts and gate depths.
• Introduce compression and disentangling techniques to reduce resource requirements and enable qubit reuse.
• Analyze gate depth, qubit count, and gate counts for the proposed circuit families to assess scalability.

Proposed method

• Define quantum state formats for representing classical data (e.g., |00b00⟩+|01b01⟩+...).
• Present Circuit Family #1 that loads N bits into N qubits with gate depth 1.
• Introduce Circuit Family #2 achieving logarithmic qubit count via recursive data loading and swapping gates.
• Describe quantum gates used (Swap, CSWAP, Toffoli, CNOT) and their decompositions.
• Explain data flow optimization through classical compression/decompression guided by Shannon’s channel capacity theorems.
• Discuss disentangling techniques to reuse discarded qubits while preserving superposition states.

Experimental results

Research questions

• RQ1 How can classical binary data be efficiently encoded into quantum states with minimal qubits and gate depth?
• RQ2 What is the impact of data compression on the circuit depth and resource requirements for loading data into quantum memory?
• RQ3 How can discarded qubits be safely reused without disturbing ongoing quantum computations?
• RQ4 How do different data loading circuit families scale in qubit count, gate depth, and total gates for large data sets?

Key findings

• Circuit Family #1 loads N bits into N qubits with gate depth 1 and uses N qubits.
• Circuit Family #2 compresses data into log2(N) qubits enabling potential exponential speedups, at the cost of additional circuit structure (Swaps and CSWAPs).
• Compression/decompression can reduce the number of loading stages from N to M, where M ≤ N, yielding qubit savings of N−M under certain data statistics.
• Disentangling techniques allow reusing discarded qubits by removing entanglement and maintaining the integrity of the remaining quantum state.
• The work provides asymptotic analyses and resource tabulations for Circuit Family #2 and discusses gate depth, qubit counts, and key gate counts (Hadamard, CSWAP, CNOT, CCNot) across circuit families.