QRAM Operators

QRAM (Quantum Random Access Memory) operators implement quantum parallel data access.

Overview

QRAM operators overview

Operator	Operation	Unitarity class
QRAMLoad	Standard QRAM load	SelfAdjoint
QRAMLoadFast	Optimized QRAM load	SelfAdjoint

Quantum Parallel Data Access

QRAM implements quantum parallel memory access:

\[\sum_x \alpha_x |x\rangle |0\rangle \xrightarrow{QRAM} \sum_x \alpha_x |x\rangle |f(x)\rangle\]

This allows quantum algorithms to access multiple data items simultaneously.

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QRAMLoad

Operation: Loads data from the QRAM circuit into a quantum register

Type constraints: - Address register: UnsignedInteger - Data register: UnsignedInteger or General

Bit constraints: - The address size must match the QRAM configuration - The data size must match the QRAM data width

import pysparq as ps

ps.System.clear()

# Create a QRAM circuit (qutrit version)
addr_size = 4  # 4-bit address → 16 memory cells
data_size = 8  # 8-bit data

# Set the memory contents (memory must be passed in at construction)
memory = [i * 10 for i in range(16)]  # 0, 10, 20, ..., 150
qram = ps.QRAMCircuit_qutrit(addr_size, data_size, memory)

# Create registers
ps.System.add_register("addr", ps.UnsignedInteger, addr_size)
ps.System.add_register("data", ps.UnsignedInteger, data_size)

state = ps.SparseState()

# Uniform superposition on the address register
ps.Hadamard_Int_Full("addr")(state)

# QRAM load: access all addresses in parallel
ps.QRAMLoad(qram, "addr", "data")(state)

ps.pprint(state)
# The output contains 16 states:
# |addr=0,data=0⟩, |addr=1,data=10⟩, ...

# QRAMLoad is self-adjoint; applying it again undoes the load
ps.QRAMLoad(qram, "addr", "data")(state)
# The data register is zeroed

QRAMLoadFast

Operation: Optimized QRAM load

Characteristics: Optimized for specific memory patterns, with higher performance.

# Fast load (same interface)
ps.QRAMLoadFast(qram, "addr", "data")(state)

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QRAMCircuit_qutrit

PySparQ provides the QRAMCircuit_qutrit class for configuring a QRAM:

Note

QRAMCircuit_qubit (the qubit-version QRAM in the C++ API) is not available in PySparQ. PySparQ provides only the qutrit version.

Creating and Configuring a QRAM Circuit

import pysparq as ps

# Create a QRAM circuit
addr_bits = 4   # number of address bits
data_bits = 8   # number of data bits

# Set the memory contents (memory must be passed in at construction)
memory_list = [0, 10, 20, 30, 40, 50, 60, 70,
               80, 90, 100, 110, 120, 130, 140, 150]
qram = ps.QRAMCircuit_qutrit(addr_bits, data_bits, memory_list)

# Note: the set_memory() method is not available in PySparQ
# memory must be passed in when constructing QRAMCircuit_qutrit

# Query information
print(f"Address size: {qram.addr_size}")
print(f"Data size: {qram.data_size}")

Conditional Loading

QRAM loading supports conditional execution:

op = ps.QRAMLoad(qram, "addr", "data")

# Load only when control is nonzero
op.conditioned_by_nonzeros("control")(state)

# Load only when bit 0 of flag is 1
op.conditioned_by_bit("flag", 0)(state)

Use Cases

Quantum Database Search

# Database contents
database = [42, 17, 99, 5, ...]

# Create the QRAM (memory is passed in at construction)
qram = ps.QRAMCircuit_qutrit(addr_bits, data_bits, database)

# Address register in superposition
ps.Hadamard_Int_Full("addr")(state)

# Load all data items in parallel
ps.QRAMLoad(qram, "addr", "data")(state)

# Now you can search for a specific value...

Quantum Machine Learning

# Load training data (memory is passed in at construction)
qram = ps.QRAMCircuit_qutrit(addr_bits, data_bits, training_data)
ps.Hadamard_Int_Full("sample_id")(state)
ps.QRAMLoad(qram, "sample_id", "sample_data")(state)

# All training samples can now be processed in parallel

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中文版 ===

QRAM 算子

QRAM (Quantum Random Access Memory) 算子实现量子并行数据访问。

概述

QRAM 算子总览

算子	操作	幺正类
QRAMLoad	标准 QRAM 加载	SelfAdjoint
QRAMLoadFast	优化 QRAM 加载	SelfAdjoint

量子并行数据访问

QRAM 实现量子并行存储访问：

\[\sum_x \alpha_x |x\rangle |0\rangle \xrightarrow{QRAM} \sum_x \alpha_x |x\rangle |f(x)\rangle\]

这使得量子算法可以同时访问多个数据项。

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QRAMLoad

操作: 从 QRAM 电路加载数据到量子寄存器

类型约束: - 地址寄存器: UnsignedInteger - 数据寄存器: UnsignedInteger 或 General

位约束: - 地址大小必须匹配 QRAM 配置 - 数据大小必须匹配 QRAM 数据宽度

import pysparq as ps

ps.System.clear()

# 创建 QRAM 电路（qutrit 版本）
addr_size = 4  # 4 位地址 → 16 个存储单元
data_size = 8  # 8 位数据

# 设置存储内容（memory 需在构造时传入）
memory = [i * 10 for i in range(16)]  # 0, 10, 20, ..., 150
qram = ps.QRAMCircuit_qutrit(addr_size, data_size, memory)

# 创建寄存器
ps.System.add_register("addr", ps.UnsignedInteger, addr_size)
ps.System.add_register("data", ps.UnsignedInteger, data_size)

state = ps.SparseState()

# 地址寄存器均匀叠加
ps.Hadamard_Int_Full("addr")(state)

# QRAM 加载：并行访问所有地址
ps.QRAMLoad(qram, "addr", "data")(state)

ps.pprint(state)
# 输出包含 16 个状态：
# |addr=0,data=0⟩, |addr=1,data=10⟩, ...

# QRAMLoad 是自伴的，再次应用撤销
ps.QRAMLoad(qram, "addr", "data")(state)
# 数据寄存器清零

QRAMLoadFast

操作: 优化的 QRAM 加载

特点: 针特定存储模式优化，性能更高。

# 快速加载（相同接口）
ps.QRAMLoadFast(qram, "addr", "data")(state)

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QRAMCircuit_qutrit

PySparQ 提供 QRAMCircuit_qutrit 类用于配置 QRAM：

Note

``QRAMCircuit_qubit``（C++ API 中的 qubit 版本 QRAM）在 PySparQ 中**不可用**。PySparQ 仅提供 qutrit 版本。

创建和配置 QRAM 电路

import pysparq as ps

# 创建 QRAM 电路
addr_bits = 4   # 地址位数
data_bits = 8   # 数据位数

# 设置存储内容（memory 需在构造时传入）
memory_list = [0, 10, 20, 30, 40, 50, 60, 70,
               80, 90, 100, 110, 120, 130, 140, 150]
qram = ps.QRAMCircuit_qutrit(addr_bits, data_bits, memory_list)

# 注意：set_memory() 方法在 PySparQ 中不可用
# memory 必须在构造 QRAMCircuit_qutrit 时传入

# 查询信息
print(f"地址大小: {qram.addr_size}")
print(f"数据大小: {qram.data_size}")

条件加载

QRAM 加载支持条件执行：

op = ps.QRAMLoad(qram, "addr", "data")

# 仅当 control 非零时加载
op.conditioned_by_nonzeros("control")(state)

# 仅当 flag 的第 0 位为 1 时加载
op.conditioned_by_bit("flag", 0)(state)

使用场景

量子数据库搜索

# 数据库内容
database = [42, 17, 99, 5, ...]

# 创建 QRAM（memory 在构造时传入）
qram = ps.QRAMCircuit_qutrit(addr_bits, data_bits, database)

# 地址叠加态
ps.Hadamard_Int_Full("addr")(state)

# 并行加载所有数据项
ps.QRAMLoad(qram, "addr", "data")(state)

# 现在可以搜索特定值...

量子机器学习

# 加载训练数据（memory 在构造时传入）
qram = ps.QRAMCircuit_qutrit(addr_bits, data_bits, training_data)
ps.Hadamard_Int_Full("sample_id")(state)
ps.QRAMLoad(qram, "sample_id", "sample_data")(state)

# 现在可以并行处理所有训练样本