1 Approximate Quantum Random Access Memory Architectures

2025-04-30 0 0 941.52KB 5 页 10玖币

Approximate Quantum Random Access Memory

Architectures

Koustubh Phalak, Student Member, IEEE, Junde Li, Student Member, IEEE, Swaroop Ghosh, Senior Member, IEEE

Abstract—Quantum supremacy in many applications using well-known quantum algorithms rely on availability of data in quantum

format. Quantum Random Access Memory (QRAM), an equivalent of classical Random Access Memory (RAM), fulﬁlls this

requirement. However, the existing QRAM proposals either require qutrit technology and/or incur access challenges. We propose an

approximate Parametric Quantum Circuit (PQC) based QRAM which takes address lines as input and gives out the corresponding data

in these address lines as the output. We present two applications of the proposed PQC-based QRAM namely, storage of binary data

and storage of machine learning (ML) dataset for classiﬁcation. For the machine learning task, we perform binary classiﬁcation using

three different setups, (a) QNN with QRAM (QRAM + QNN), (b) QNN with normal data embedding and (c) Fully Connected Neural

Network (FCNN). We show that QRAM + QNN converges (with 100% classiﬁcation accuracy) faster i.e., by 6th epoch, compared to

the other two setups which converge at around 10th and 15th epochs. The loss for QRAM + QNN (0.53) is less than FCNN setup

(0.89) and comparable to QNN with normal embedding (0.48). For the storage of binary data, we evaluate Hamming Distance (HD)

and percentage correct prediction metrics to quantify the performance. We observe an increase in HD from 0 to 3.97 and decrease in

percentage of correct predictions from 100%to 0.58%as we increase the number of address and data lines from 2 to 9. We propose

agglomerative clustering of data as a pre-processing step before training the QRAM to improve the HD i.e., from 3.97 to 2.17 and

increase the percentage correct predictions to 10.1% from 0.58% till 9 address lines.

Index Terms—Quantum Random Access Memory, classiﬁcation, binary data, storage.

1 INTRODUCTION

RECENT advances of quantum computing in various ﬁelds

such as, machine learning (ML) have shown great po-

tential. Machine learning methods augmented with quantum

computing like quantum clustering, quantum decision trees,

quantum support vector machines, and quantum neural net-

works (QNNs) [1] are able to provide quantum speedup using

quantum algorithms compared to their classical counterparts

[2]. An important aspect for such augmented quantum algo-

rithms is the conversion of classical data into quantum domain.

Encoding methods like basis embedding, amplitude embed-

ding, angle embedding [3] (Chapters 5 and 6) use various

mathematical formulae to embed classical data onto qubits.

Basis embedding encodes binary data of nbits onto nqubits.

Amplitude embedding normalizes 2ndata and embeds them

onto nqubits. Angle embedding performs rotation operation

on qubits, either using RX, RY or RZ gates and embeds n

classical datapoints onto nqubits. While these methods are

useful for small and simple datasets, they are not efﬁcient

for more complex datasets. Quantum Random Access Memory

(QRAM) to store and load quantum data could be much more

effective for quantum machine learning problems. The user

should be able to store new classical data or update it onto

the QRAM and load the stored quantum data as needed.

In this paper, we propose a Parametric Quantum Circuit

(PQC)-based trainable approximate QRAM which takes ad-

dress as input and gives output as the data for that address.

We say that the QRAM is approximate because the predicted

output of QRAM will not be exactly same as the input. This

happens because data loading methods for NISQ era quantum

computers are not perfect and there are different errors in exe-

cution of quantum circuits. We introduce relevant background

on quantum computing and quantum machine learning and

previously published related works on QRAM in Section 2 and

the architectures for the proposed QRAM in Section 3. We then

show two applications for the proposed QRAM architecture:

one for storage of digit images for performing binary classiﬁ-

cation and other for storage of binary data, in Sections 4 and 5

respectively. We give concluding remarks in Section 6. To the

best of knowledge, this is the ﬁrst approximate QRAM architecture

which can be used to load arbitrary data in quantum form to any

quantum circuit.

2 BACKGROUND AND RELATED WORKS

2.1 Background

Qubits: Qubits are the fundamental units of a quantum com-

puter (analogous to classical bits for a classical computer).

Unlike classical bits, qubits store information in the form of

states represented using ket notation |ψi=a

bwhere a2

denotes the probability of the qubit being measured to 0 and

b2denotes the probability of the qubit being measured to 1.

Each qubit has two basis states, one with a= 1, b = 0 (deﬁned

as |0i) and one with a= 0, b = 1 (deﬁned as |1i). There are

different types of qubits like superconducting qubits, ion trap

qubits, photonic qubits, neutral atom qubits, etc.

Quantum Gates: A quantum gate is a unitary operation per-

formed on a qubit that changes the state of the said qubit. Every

quantum gate can be represented as a unitary matrix, and can

work on either a single qubit or more than one qubits. The

most common ones are single qubit gates like hadamard gate

(H), bit-ﬂip gate (X), Pauli Y and Z gates, and two qubit gates

like CNOT gate, SWAP gate, and controlled Pauli gates. There

are also special gates like reset gate and measurement gate.

Quantum Circuit: A quantum circuit is a program that contains

an ordered sequence of various quantum gates that act on spec-

iﬁed number of qubits and may contain intermediate reset and

measurement operations. A user typically builds a quantum

circuit, and obtains classical measurement output back. Based

on the gates used and their placement, various quantum circuits

can be used for targeted applications.

Parametric Quantum Circuit: A Parametric Quantum Circuit

(PQC) is a special type of quantum circuit where user can feed

arXiv:2210.14804v2 [quant-ph] 27 Oct 2022

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1ApproximateQuantumRandomAccessMemoryArchitecturesKoustubhPhalak,StudentMember,IEEE,JundeLi,StudentMember,IEEE,SwaroopGhosh,SeniorMember,IEEEAbstractQuantumsupremacyinmanyapplicationsusingwell-knownquantumalgorithmsrelyonavailabilityofdatainquantumformat.QuantumRandomAccessMemory(QRAM),anequivalent...

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