TensorFlowQuantum：融合深度学习与量子计算的框架

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"TensorFlowQuantum (TFQ) 是一个软件框架，旨在促进量子机器学习的发展，将量子计算与深度学习相结合。由Google Research等多机构的研究人员开发，它为研究者提供了一种工具，能够在经典计算机上模拟和设计量子算法，并与TensorFlow现有的深度学习能力集成。" TensorFlowQuantum (TFQ) 是一个创新性的框架，它的出现是为了解决量子计算与深度学习这两个领域的融合问题。TFQ允许研究人员在TensorFlow环境中构建、训练和评估量子神经网络（QNNs），这是一种结合了量子比特操作和经典机器学习模型的新型结构。通过这种方式，TFQ为探索量子优势和解决量子计算中的复杂问题开辟了新的途径。在TFQ中，量子电路可以被看作是神经网络的层，而量子态则作为这些层的输入和输出。用户可以利用Python API来构建和操作量子电路，这些电路可以与经典的TensorFlow图无缝集成。这使得研究人员能够利用TensorFlow的优化工具，如梯度下降法，来调整量子门参数，以最小化特定的成本函数或最大化期望值。 TFQ支持多种量子门集和量子比特操作，包括单量子比特旋转、CNOT门和其他多量子比特门。此外，它还内置了对量子仿真器的支持，可以在没有实际量子硬件的情况下进行实验和验证。这种仿真能力对于测试和优化量子算法至关重要，因为它允许在实际硬件可用之前进行大量的迭代和调试。量子机器学习的一个关键应用是在处理量子数据时，如量子纠缠和量子纠缠检测。TFQ可以用来构建针对这类问题的模型，通过学习量子系统的特性来提高我们理解和预测量子系统行为的能力。另一个潜在的应用是量子增强学习，其中量子计算机可以作为智能体的一部分，帮助探索复杂的决策空间。 TFQ的出现对量子计算和深度学习领域具有重要意义，因为它降低了量子计算的入门门槛，使得更多的机器学习专家能够参与到量子计算的研究中来。同时，这也推动了跨学科的合作，有助于加速量子计算和人工智能的前沿研究。总而言之，TensorFlowQuantum是一个强大的工具，它将量子计算的潜力与深度学习的灵活性结合在一起，为未来的量子信息科学和人工智能提供了新的可能性。随着量子硬件的发展和TFQ框架的不断优化，我们有望看到更多突破性的成果在量子计算和机器学习的交叉领域诞生。

Figure 3. The TensorFlow graph generated to calculate the

expectation value of a parameterized circuit. The symbol

values can come from other TensorFlow ops, such as from

the outputs of a classical neural network. The output can be

passed on to other ops in the graph; here, for illustration, the

output is passed to the absolute value op.

to re-learn how to interface with quantum comput-

ers or re-learn how to solve problems using machine

learning.

First, we provide a bottom-up overview of TFQ to

provide intuition on how the framework functions at a

fundamental level. In TFQ, circuits and other quantum

computing constructs are tensors, and converting these

tensors into classical information via simulation or exe-

cution on a quantum device is done by ops. These ten-

sors are created by converting Cirq objects to TensorFlow

string tensors, using the tfq.convert_to_tensor function.

This takes in a cirq.Circuit or cirq.PauliSum object and

creates a string tensor representation. The cirq.Circuit

objects may be parameterized by SymPy symbols.

These tensors are then converted to classical informa-

tion via state simulation, expectation value calculation,

or sampling. TFQ provides ops for each of these compu-

tations. The following code snippet shows how a simple

parameterized circuit may be created using Cirq, and

its

Z expectation evaluated at diﬀerent parameter values

using the tfq expectation value calculation op. We feed

the output into the tf.math.abs op to show that tfq ops

integrate naively with tf ops.

qubit = cirq . Gri dQub it (0 , 0)

theta = sympy . Symb ol (’ theta ’)

c = cirq . C irc uit ( cirq .X( qub it ) ** the ta )

c_tens or = tfq . convert _ t o_tens o r ([ c] * 3)

the t a_va l ues = tf . c onst ant ([ [0] ,[1] ,[2]])

m = cirq .Z ( qubit )

pa uli s = tfq . conve r t _to_t e n sor ([ m] * 3)

exp e c tatio n _op = tfq . get_exp e c tation _ o p ()

ou tpu t = e xpect a t ion_o p (

c_tensor , [ ’ the ta ’] , t het a_v alu es , paulis )

abs _out p ut = tf . math . abs ( output )

We supply the expectation op with a tensor of parame-

terized circuits, a list of symbols contained in the circuits,

a tensor of values to use for those symbols, and tensor

operators to measure with respect to. Given this, it out-

puts a tensor of expectation values. The graph this code

generates is given by Fig. 3.

The expectation op is capable of running circuits on

a simulated backend, which can be a Cirq simulator or

our native TFQ simulator qsim (described in detail in

TF Keras Models

TF Layers

TF Execution Engine

TPU

Cirq

TFQ Ops

TFQ Layers

TFQ

Differentiators

TFQ

TensorFlow

Classical

hardware

Quantum

hardware

TFQ qsim

GPU

CPU

QPU

TF Ops

Classical Data:

integers/ﬂoats/strings

Quantum Data:

Circuits/Operators

Figure 4. The software stack of TFQ, showing its interactions

with TensorFlow, Cirq, and computational hardware. At the

top of the stack is the data to be processed. Classical data

is natively processed by TensorFlow; TFQ adds the ability to

process quantum data, consisting of both quantum circuits

and quantum operators. The next level down the stack is the

Keras API in TensorFlow. Since a core principle of TFQ is

native integration with core TensorFlow, in particular with

Keras models and optimizers, this level spans the full width

of the stack. Underneath the Keras model abstractions are

our quantum layers and diﬀerentiators, which enable hybrid

quantum-classical automatic diﬀerentiation when connected

with classical TensorFlow layers. Underneath the layers and

diﬀerentiators, we have TensorFlow ops, which instantiate the

dataﬂow graph. Our custom ops control quantum circuit ex-

ecution. The circuits can be run in simulation mode, by in-

voking qsim or Cirq, or eventually will be executed on QPU

hardware.

section II F), or on a real device. This is conﬁgured on

instantiation.

The expectation op is fully diﬀerentiable. Given

that there are many ways to calculate the gradient of

a quantum circuit with respect to its input parame-

ters, TFQ allows expectation ops to be conﬁgured with

one of many built-in diﬀerentiation methods using the

tfq.Differentiator interface, such as ﬁnite diﬀerencing,

parameter shift rules, and various stochastic methods.

The tfq.Differentiator interface also allows users to de-

ﬁne their own gradient calculation methods for their spe-

ciﬁc problem if they desire.

The tensor representation of circuits and Paulis along

with the execution ops are all that are required to solve

any problem in QML. However, as a convenience, TFQ

provides an additional op for in-graph circuit construc-

tion. This was found to be convenient when solving prob-

lems where most of the circuit being run is static and

only a small part of it is being changed during train-

ing or inference. This functionality is provided by the

tfq.tfq_append_circuit op. It is expected that all but

the most dedicated users will never touch these low-

level ops, and instead will interface with TFQ using our

tf.keras.layers that provide a simpliﬁed interface.

The tools provided by TFQ can interact with both

core TensorFlow and, via Cirq, real quantum hardware.

Prepare

Quantum Dataset

Evaluate

Quantum

Model

Sample

Average

Evaluate

Classical

Model

Evaluate

Cost

Function

𝛉

Evaluate Gradients &

Update Parameters

Figure 5. Abstract pipeline for inference and training of

a hybrid discriminative model in TFQ. Here, Φ represents

the quantum model parameters and θ represents the classical

model parameters.

The functionality of all three software products and the

interfaces between them can be visualized with the help

of a “software-stack” diagram, shown in Fig. 4.

In the next section, we describe an example of an

abstract quantum machine learning pipeline for hybrid

discriminator model that TFQ was designed to support.

Then we illustrate the TFQ pipeline via a Hello Many-

Worlds example, which involves building the simplest

possible hybrid quantum-classical model for a binary

classiﬁcation task on a single qubit. More detailed in-

formation on the building blocks of TFQ features will be

given in section II E.

2. The Abstract TFQ Pipeline for a speciﬁc hybrid

discriminator model

Here, we provide a high-level abstract overview of the

computational steps involved in the end-to-end pipeline

for inference and training of a hybrid quantum-classical

discriminative model for quantum data in TFQ.

(1) Prepare Quantum Dataset: In general, this

might come from a given black-box source. However,

as current quantum computers cannot import quantum

data from external sources, the user has to specify quan-

tum circuits which generate the data. Quantum datasets

are prepared using unparameterized cirq.Circuit ob-

jects and are injected into the computational graph using

tfq.convert_to_tensor .

(2) Evaluate Quantum Model: Parameterized

quantum models can be selected from several categories

based on knowledge of the quantum data’s structure.

The goal of the model is to perform a quantum compu-

tation in order to extract information hidden in a quan-

tum subspace or subsystem. In the case of discrimina-

tive learning, this information is the hidden label pa-

rameters. To extract a quantum non-local subsystem,

the quantum model disentangles the input data, leaving

the hidden information encoded in classical correlations,

thus making it accessible to local measurements and clas-

sical post-processing. Quantum models are constructed

using cirq.Circuit objects containing SymPy symbols,

and can be attached to quantum data sources using the

tfq.AddCircuit layer.

(3) Sample or Average: Measurement of quantum

states extracts classical information, in the form of sam-

ples from a classical random variable. The distribution

of values from this random variable generally depends

on both the quantum state itself and the measured ob-

servable. As many variational algorithms depend on

mean values of measurements, TFQ provides methods

for averaging over several runs involving steps (1) and

(2). Sampling or averaging are performed by feeding

quantum data and quantum models to the

tfq.Sample

or tfq.Expectation layers.

(4) Evaluate Classical Model: Once classical

information has been extracted, it is in a format

amenable to further classical post-processing. As the

extracted information may still be encoded in classi-

cal correlations between measured expectations, clas-

sical deep neural networks can be applied to distill

such correlations. Since TFQ is fully compatible with

core TensorFlow, quantum models can be attached di-

rectly to classical tf.keras.layers.Layer objects such as

tf.keras.layers.Dense .

(5) Evaluate Cost Function: Given the results of

classical post-processing, a cost function is calculated.

This may be based on the accuracy of classiﬁcation if the

quantum data was labeled, or other criteria if the task

is unsupervised. Wrapping the model built in stages (1)

through (4) inside a tf.keras.Model gives the user access

to all the losses in the tf.keras.losses module.

(6) Evaluate Gradients & Update Parameters:

After evaluating the cost function, the free parame-

ters in the pipeline is updated in a direction expected

to decrease the cost. This is most commonly per-

formed via gradient descent. To support gradient de-

scent, TFQ exposes derivatives of quantum operations

to the TensorFlow backpropagation machinery via the

tfq.differentiators.Differentiator interface. This allows

both the quantum and classical models’ parameters to

be optimized against quantum data via hybrid quantum-

classical backpropagation. See section III for details on

the theory.

In the next section, we illustrate this abstract pipeline

by applying it to a speciﬁc example. While simple, the

example is the minimum instance of a hybrid quantum-

classical model operating on quantum data.

3. Hello Many-Worlds: Binary Classiﬁer for Quantum

Data

Binary classiﬁcation is a basic task in machine learn-

ing that can be applied to quantum data as well. As a

minimal example of a hybrid quantum-classical model,

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