# Review of Ansatz Designing Techniques for Variational Quantum Algorithms

Junhan Qin  School of Information Engineering
Minzu University of China
Beijing, China
<EMAIL_ADDRESS>
###### Abstract

For a large number of tasks, quantum computing demonstrates the potential for
exponential acceleration over classical computing. In the NISQ era, variable-
component subcircuits enable applications of quantum computing. To reduce the
inherent noise and qubit size limitations of quantum computers, existing
research has improved the accuracy and efficiency of Variational Quantum
Algorithm (VQA). In this paper, we explore the various ansatz improvement
methods for VQAs at the gate level and pulse level, and classify, evaluate and
summarize them.

###### Index Terms:

Variational Quantum Algorithm, Quantum Machine Learning, Noise on the NISQ
machine

##  I Introduction

Quantum computing (QC) is a new computing paradigm with great potential for
exponential acceleration beyond classical computers to solve classically
intractable problems with greater efficiency and speed. In many fields, such
as pattern recognition [1] and data mining [2], it has advantages over
traditional computers. In the past two decades, quantum hardware has also made
breakthroughs in physical realization technology and made great progress,
which provides the possibility for the application of quantum computing.

Although Quantum computing has made considerable progress, we should be aware
that we are still in the Noisy Intermediate Scale Quantum (NISQ) [3] stage.
Currently, quantum computers usually only have tens to hundreds of qubits.
Limited by the hardware equipment, it is impossible to build a universal
fault-tolerant quantum computer. However, the emergence of variational quantum
algorithms (VQA) [4] makes the current application of quantum computing
possible. We can construct different quantum circuits and loss functions for
different problems. Common VQAs are variational quantum eigensolver (VQE) [5,
6, 7], dynamical quantum simulation [8], and quantum approximation
optimization algorithm (QAOA) [9, 10, 11], quantum machine learning (QML) [12,
13, 14, 15, 16, 17] and so on.

However, VQA still faces many difficulties. Since the current VQA is mostly
based on the quantum environment simulated by the classical simulators, once
applied to the real machine, The huge noise of NISQ phase quantum devices (The
qubits and quantum gates suffer from high error rates of $10^{-3}$ to
$10^{-2}$) will significantly affect the accuracy of the algorithm [13, 14].
Similarly, limited qubits also limit the depth of the algorithm, affecting the
efficiency and accuracy of the algorithm.

This article summarizes existing VQA improvement approaches and outlines the
different directions for improvement at the gate level and pulse level
respectively. We will first look at improved algorithms at the gate level, As
shown in the following table, VQA methods can be divided into two categories:
improving accuracy and improving efficiency. Furthermore, on this basis, the
two directions will adopt different methods to achieve the goal. After a brief
introduction, this paper will discuss whether it has been successfully applied
to real machines, whether it is device dependent, and make a summary of
different methods. For the pulse level, we found that the current review is
not covered much, but it is a promising direction, and we will select
representative methods to brief and evaluate.

The rest of this article is organized as follows. Section II Outlines the
basics of quantum computing. In the same section, the motivation of this paper
will be briefly discussed. Section III will introduce different methods
implemented to improve VQAs. Finally, Section IV will conclude and discuss
some perspective open questions.

##  II BACKGROUND AND MOTIVATION

###  II-A Quantum Basics

Qubit. Unlike conventional bits, which can represent only 0 and 1 states, a
quantum bit (qubit) can represent various linear combinations of the two basic
states, 0 and 1: $|\phi\rangle$ = $\alpha\lvert 0\rangle+\beta\lvert
1\rangle$, for $\alpha,\beta\in\mathbb{C}$, $\lvert a\rvert^{2}+\lvert
b\rvert^{2}$ = 1, this is also been called superposition. Because of this
unique restriction, an N-qubit system can represent $2^{n}$ states, whereas
conventional bits can represent only one state at a time. The qubit of a
quantum computer can generally be simulated in the following ways: 1\. An
electron orbiting a hydrogen atom may be in the ground state($\lvert
0\rangle$) or activated state($\lvert 1\rangle$); 2\. An electron’s spin may
be up ($\lvert 0\rangle$) or down ($\lvert 1\rangle$); 3\. Photon Polarization
direction, may be horizontal ($\lvert 0\rangle$), or along the vertical
($\lvert 1\rangle$);

Quantum gate and Quantum circuit.. In classical computation, all of the
logical operations can be represented with ”and”, ”or”, and ”not” three
operations. In quantum computing, we also need a similar scheme to complete
the corresponding operation, which is the quantum gate. In the computational
model of quantum computing, especially quantum circuits, a quantum gate is the
basic component of a quantum circuit that operates on the Pauli operations.
The relationship between a quantum gate and a quantum circuit is similar to
the relationship between conventional logic gates and conventional digital
circuits. Quantum gates are often represented by unitary matrices, and a gate
that operates on K qubits can be represented by a 2K x 2k unitary matrix. The
operation of a quantum gate can be represented by multiplying a matrix
representing the gate with a vector representing the state of the qubit.
Common quantum gates are divided into single-qubit gates and multi-qubit
gates. Single qubit gates include Hadamard Gate, Pauli Gate, and so on. Multi-
qubit gates have Controlled - Not gate (CX gate)+, Controlled Phase gate (CZ
gate), and SWAP gate.

To use a quantum computer to perform calculations, we need to build a quantum
circuit to manipulate the state of the qubit. A quantum circuit consists of
multiple quantum gates.

Variational Quantum Algorithm (VQA). The variational quantum algorithms are to
train a quantum circuit with a classical optimizer. The goal of a VQA is to
find a model that can fit the data, that is, to determine an optimal set of
parameters to make the model as close as possible to the given data. The
algorithm of VQA includes three parts: constructing a cost function, building
an ansatz, and adjusting parameters. The common VQA includes variational
quantum eigensolver (VQE), quantum approximation optimization algorithm
(QAOA), quantum machine learning (QML), and so on. VQA is a promising
direction, but it still faces some difficulties. The first is the trainability
of quantum circuits. In some cases, such as barren plateau, the optimizer
cannot effectively train the large circuit due to the limited decoherence
time. The noise of quantum devices can affect the accuracy of VQA in many
ways. Physical noise may slow down the training process, making the noisy
global optimum no longer correspond to the noiseless global optimum, and thus
affecting the final optimal loss value.

Figure 1: Schematic of variational quantum algorithm, the model is designed
based on quantum gates on quantum computer, and the optimization progress is
on classical computer, the classical computer optimizes and updates the
parameters in the trainable layer of the model.

Variational Quantum Eigensolver (VQE). VQE is an algorithm that uses classical
optimizers to train a parametric quantum circuit for solving matrix
eigenvalues and eigenvectors, it is the earliest variational quantum algorithm
and is mainly used to solve the ground state and low excited state of the
quantum system. Due to this property, VQE has been widely used to solve
problems in quantum chemistry. For a quantum system, the dimension of the
Hamiltonian $\mathbb{H}$ grows exponentially with the system size. The other
algorithms often require millions of qubits, far beyond the reach of current
quantum computers. Thus, VQE was proposed to work with NISQ machines.

Quantum Machine Learning. A quantum algorithm can perform quantum supremacy in
solving specific tasks than the algorithms of the fastest known classical
computers. N-dimensional data can theoretically be represented by only log(N)
bits in qubits, unlike classical computer algorithms which require N bits.
Therefore, people can design various algorithms to achieve acceleration by
quantum computers, which is quantum machine learning. Some of the quantum
machine learning inspried by classical machine learning and produced some
useful quantum algorithms, such as qPCA [18, 19], qSVM [20, 21, 22], quantum
deep learning [23, 24] and so on. However, due to the relatively small scale
of the existing quantum computers, and the relatively deep size and depth
required by the existing algorithms, there is still a great gap to truly
surpass classical machine learning. In addition, the noise problem of the
quantum computer, barren plateau phenomenon, etc. in the noise-intermediate-
scale quantum (NISQ) era machines, also restrict the performance of quantum
machine learning.

Noise on the NISQ machine. First, the noise in quantum computing, due to the
imperfect control signal crosstalk between qubits, real quantum computer
interaction, and interference from the external environment, inevitably there
will be noise, this greatly affected the accuracy of quantum machine learning,
so you need to frequent the quantum machine were characterized and
calibration, to reduce the influence of noise. At the same time, NISQ devices
incur decoherence errors over time, which limited the depth and width of the
circuit, making it impractical to implement complex quantum circuits.

Ansatz. ansatz is the basic architecture of a circuit, a set of gates that act
on a specific subsystem [25]. ansatz is essentially a few prior assumptions,
which are guesses about the appropriate training circuit. On the one hand, the
problem ansatz usually depends on the specific problem, it can combine the
property of the problem and then solve the problem. On the other hand, some
ansatz architectures are generic and problem-neutral, meaning that they can be
used generally for kinds of problems on quantum hardware, we call this type of
ansatz as hardware ansatz.

###  II-B Motivation

In recent years, the research community on quantum computing has gradually
grown. More and more studies show that compared with classical computers, VQAs
have excellent acceleration potential in a large number of tasks. Studies have
shown that a two-dimensional programmable superconducting quantum processor,
Zuchongzhi, which is composed of 66 functional qubits, can do a random quantum
circuit sampling task in 1.2 hours, which would take eight years for today’s
most powerful supercomputers [26]. The advantage of quantum computing is that
an n-dimensional piece of data (a vector) can theoretically be represented by
only log(N) bits, rather than the classical N bits. One qubit can be in a
superposition of 0 and 1 states and be coherent with each other, and multiple
qubits can be entangled to represent more complex states or perform more
complex operations.

However, the current VQAs still face great challenges. Most of the advantages
of existing VQAs are demonstrated in the quantum environment simulated by the
classical simulators, and their efficiency and accuracy will decrease
significantly in the real quantum environment in NISQ machines. This is due to
the high noise characteristics of NISQ machines and the small scale of qubits
of existing quantum computers. In the case that the scale and technology of
quantum computers still have a gap with quantum supremacy, what we can do in
the gate level optimization is to further optimize the quantum circuit to
improve the efficiency and accuracy to reduce the gap. Furthermore, some
researchers state the gate level is not a good abstraction layer, and several
works have been proposed to gain the benefits from pulse level control.

To better understand the function of state of art circuit optimization methods
as well as make it easier for choosing the matched framework for users’
quantum program. We proposed a review of existing circuit optimization methods
for VQAs in Section III. We can find a variety of optimization methods and
whether it is useful. In terms of methods, some studies focus on reducing the
impact of noise, some use pruning to reduce overhead, and some take a holistic
view and use some algorithms of traditional machine learning for circuit
optimization. At the same time, there will be a discussion on whether it has
been successfully applied to real machines and whether it is device dependent.

TABLE I: Proposed category of the summarized existing techniques. Three major categories and five sub-categories were defined and the models involved in this review stated, besides the application-specific or not for each model discussed. Method | Specific Method | Model | Application Specific or general
---|---|---|---
Improving Accuracy | Noise Suppression |  QuantumNAT [27] | General
QF-RobustNN [28] | Specific
Better Circuit |  QAS [29] | General
QuantumNAS [6] | General
QMLP [30] | Specific
DRL-QAS [31] | General
Approaches for particular problems |  QUILT [32] | Specific
Improving Efficiency | Pruning |  On-chip QNN [33] | Specific
CompVQC [34] | General
Optimization mapping method |  ML-QCP [35] | General
HA [36] | General
Pulse Level Control |  PAN [37] | General

##  III Different kinds of Variational Quantum Algorithm

To make better use of the quantum acceleration characteristics of quantum
machines and solve various problems faced by current VQA, we need to summarize
and classify the existing VQA methods. As shown in the following table, gate-
level VQA methods can be divided into two categories: improving accuracy and
improving efficiency. Furthermore, on this basis, the two directions will
adopt different methods to achieve the goal. After that, pulse level control
will also be discussed.

###  III-A Improving Accuracy

The first direction we will discuss is to improve the accuracy and at the same
time ensure that the efficiency of VQA is not greatly affected or even
improved. To improve the accuracy, there are generally two method/s: Noise
Suppression and Supercircuit. These two methods try to improve the accuracy of
VQA from different angles. At the same time, they do not conflict with each
other and can be used in combination.

####  III-A1 Noise Suppression

Currently, we are in the NISQ phase, where quantum operations suffer from a
high error rate of $10^{-2}$ to $10^{-3}$, much higher than the CPU/GPU’s
$10^{-6}$, so effective Noise Suppression can significantly improve VQA
accuracy.

QuantumNAT In this method, a noise suppression framework dedicated to PQC
problems is proposed, which optimizes the robustness of PQC in both the
training and reasoning phases.

In this method, the authors propose to collect the measured results of Noise-
free Simulation and Real Device on a batch of input samples respectively for
each qubit and calculate its mean value and standard deviation. The effect of
quantum noise on PQC measurements can be observed as a linear mapping of
noise-free measurements with scaling and shift factors. Therefore, the
difference in feature distribution between noiseless and noisy scenes can be
reduced by normalization. On the other hand, according to the actual noise
model of quantum hardware, the author inserts quantum error gates into the
PQC, to inject noise into the training process. Finally, post-measurement
quantization is introduced to quantize the measurement results into discrete
values to achieve the denoising effect.

It can be seen from the results that QuantumNAT experiments with four
different QNN architectures on eight tasks running on five quantum devices.
QuantumNAT always achieves the highest accuracy in 26 benchmark tests. On
average, normalization, noise injection, and quantization improve the accuracy
by 10%, 9%, and 3% respectively. However, this method is only effective for
PQC tasks and is hardware-dependent.

QF-RobustNN It is a method to learn qubit errors in quantum networks through
training. It proposes a general training framework for error perception
learning, to reduce the impact of noise on neural networks.

As a result, the performance of QF-RobustNN was evaluated on IBM Qiskit-based
simulators and IBM quantum processors. The accuracy of QF-RobustNN is much
better than that of the general model under the condition of high error rate.
On the other hand, QF-RobustNN has fewer additional SWAP gates and is more
efficient than other methods due to the selection of appropriate mapping
methods.

QF-RobustNN implements the learning of noise so that errors can be predicted,
effectively reducing the impact of noise on QNN and improving the accuracy of
the model. At the same time, due to the use of a more suitable mapping mode of
quantum circuits, the number of additional gates can be effectively reduced,
thus reducing consumption and ensuring efficiency. This method is an effective
method for QNN, which is verified by simulators and tested by IBM Quantum
Processor (i.e., the ibmq-montreal backend with 27 qubits). Due to the small
number of machines used, can’t determine whether the method is hardware-
dependent.

Summarize of Noise Suppression: From the above two noise-aware methods, we can
find that this method has an obvious effect in improving the accuracy of the
model, but it doesn’t significantly reduce the efficiency of the model, which
is a fruitful attempt. However, most noise-aware methods need to learn the
noise to achieve the effect of suppression, and the noise of different quantum
devices or the same device at different times is always different, so such
methods are generally hardware-dependent.

Figure 2: Workflow of commonly used noise-aware techniques implementation on
quantum computing. The difference and correlation between works have been
marked.

####  III-A2 Better Circuit

Another way to improve accuracy is to find a circuit that is good enough to
provide a relatively better circuit-qubit mapping for a given task on the
target machine, an idea made possible by the adjustability of VQA parameters.
In general, we can choose to build a super-circuit large enough to ensure that
it contains the optimal solution we need, construct enough circuits and find
the optimal one. Or, on the other hand, We can also choose to use some special
architecture, or apply some methods from classical computers to this problem.

QAS The current VQA is faced with two problems: 1. When the qubit number and
circuit depth increase, the performance of vqa will decrease significantly due
to the balance between expressiveness and trainability; 2. A deep circuit
depth means that the gradient information received by the classical optimizer
is full of noise, and the effective information disappears exponentially,
which may lead to divergent optimization or barren plateaus. QAS solves the
problem by unifying noise suppression and trainability enhancement into a
learning problem.

QAS outperformed traditional VQAs in both machine learning and VQE tasks. In
the task of data classification for quantum devices with noise, the
classification accuracy of traditional quantum classifiers is only 50%, while
the quantum neural network and corresponding parameters output by QAS can
reach 100% accuracy.

QuantumNAS proposes noise-adaptive quantum circuits to provide a relatively
better circuit-qubit mapping for a given task on a target machine. For
parameterized quantum circuits, there can be many circuits with different
architectures to achieve the same goal, and quantum gates with different
numbers and positions are used. QuantumNAS can find the most suitable quantum
circuit architecture for the target machine and the corresponding Qubit
mapping.

This research draws on the idea of neural network search (NAS) in classical
deep learning. First, construct a Supercircuit that is large enough. The
Supercircuit contains multiple blocks, each with multiple layers of
parameterized gates, whose parameters are accomplished by iteratively sampling
and updating subcircuits. subcircuit is its subset. Due to the high training
cost, only the gradient calculation of the subcircuit is carried out in the
training of the supercircuit and the parameter subset of the supercircuit is
updated. After building the right supercircuit, QuantumNAS uses genetic
algorithms to find the right Subcircuit. Finally, redundant quantum gates are
further removed to reduce the noise of the selected Subcircuit, and the
iterative pruning method is used for pruning.

However, this method is hardware-dependent, because according to its
experimental results, the accuracy of the experiment after three days’
intervals is significantly reduced, which may be caused by IBM’s correction
machine.

QMLP In this paper, we propose a quantum multilayer perceptron (QMLP)
architecture, which enhances the fault tolerance of QNN circuits, provides
abundant nonlinearity and proposes the use of a circuit with parameterized
two-qubit entangled gates. The characteristics of this method are shown in
that the fault-tolerant coding method provided by this method can generate
more accurate low-level features, improve the original RUU layer design,
provide adjustable nonlinearity, facilitate the construction of deep QNN, and
ansatz constructed using parameterized double qubit gates.

The accuracy of QMLP in the ten-classification task on the MNIST dataset was
75%, higher than that of QuantumFlow and QuantumNAS (69% and 67%). In the
aspect of QNN design overhead, the number of QMLP gates and parameters are
reduced by 2 times and 3 times respectively. However, as the circuit becomes
more complex, the performance improvement will be offset by the side effects
of gate errors when noise is involved, which shows certain limitations of this
method. The tradeoff between model depth and noise tolerance should be
considered when designing a QMLP model in practice.

DRL-QAS This paper proposes a quantum architecture search framework with deep
reinforcement learning (DRL) capability. In this framework, DRL agents have
access to the expected value of PAUL-X, Y, Z and a predefined set of quantum
operations for learning target quantum states, optimized by the dominant
actor-Critical (A2C) and Proximal Strategy Optimization (PPO) algorithms. The
advantage of this approach is that no quantum physics knowledge is encoded in
the agent, and it can be used with other DRL architectures or optimization
methods.

The authors demonstrate the successful generation of a multi-qubit GHZ state
quantum gate sequence, proving that the method is indeed feasible, but the
method requires a lot of resources, for the current NISQ phase, and still
cannot be applied to the real machine.

Summarize of Better Circuit: The above methods are classified as a better
circuit, which can also be divided into two different directions. Taking QAS
and QuantumNAS as examples, the method constructs a supercircuit and selects a
good enough subcircuit from it through their different methods. This method
does play a role in improving accuracy. At the same time, this method is
usually application general. However, due to the great workload of
constructing the supercircuit, this part of the work still needs to be handed
over to the classical computer in the NISQ environment. However, QMLP and DRL-
QAS represent an attempt in another direction, which applies some methods on
classical computers to the generation of an auxiliary circuit, to make the
model stronger. The problem with this method is also reflected in the
excessive workload of circuit construction, which can only be applied to the
environment of the simulator at present.

####  III-A3 Approachs for particular problems

In addition to more general methods, we can also find some specific methods
for some special problems. Such attempts tend to be poor in scalability and
elongation but can be very effective in improving the accuracy of individual
problems.

QUILT This method is aimed at quantum classifiers with multiple classification
tasks, which often have poor accuracy. By establishing the integration of
quantum classifiers QUILT makes up the deficiency of this field to some
extent. A key idea behind the Quilt is the integration of smaller classifier
models as opposed to using a single large classifier model. Such decisions
ensure that the effects of quantum errors are minimized. This method divides
classifiers into core classifiers that can classify all categories and
OneVsALL classifiers that can improve the accuracy of each class. The problem
is solved through the integration of one core classifier and multiple OneVsAll
classifiers.

The performance of QUILT is equal to that of existing classifiers in binary
tasks, but with the increase of categories, QUILT provides a 22% and 46%
improvement in quad and octant tasks, respectively.

###  III-B Improving Efficiency

The other direction we will discuss is to improve the efficiency of VQA while
ensuring that its accuracy is not compromised. The reason for studying this
direction is that quantum machines currently have fewer resources, and in the
case of NISQ, it would be valuable to perform the same or more tasks with
fewer resources.

####  III-B1 Pruning

In the context of NISQ, the limited quantum resources limit the depth of the
VQA. With appropriate pruning methods, removing circuits with little impact on
the model can effectively compress the required resources at the expense of
very little accuracy, thus making it possible to further increase the depth of
the model.

On-chip QNN In this context, the authors observed that in the vast majority of
cases, small gradients tend to have large relative variations or even wrong
directions under quantum noises, So such small gradient calculation is often
unnecessary. By calculating only the gradients with high reliability and
cutting out the small gradients, the resources required by the model can be
compressed and the accuracy can be maintained or even increased.

The computational training engine of the In-situ gradient consists of three
parts: 1. Jacobian calculation via parameter shift 2. Down-stream gradient
backpropagation. 3. Gradient calculation. Finally, we can get the gradient of
each parameter.

The author has conducted extensive experiments on 5 classification tasks with
5 real quantum machines, and the results are slightly stronger than that of
fixed pruning. It can be seen that pruning does not affect the accuracy of the
model, and the accuracy of the classification tasks of 2 and 4 kinds of images
is more than 90% and 60%, respectively. Probabilistic gradient pruning is 7%
more accurate than unpruned QNN. Is the percent of the time and save
$r*\frac{wp}{wa+wp}*100\%$, increased the efficiency. This method can only be
applied to QNN, which has some limitations and can be implemented on real
machines.

CompVQC Due to the high noise and limited resources of NISQ devices, CompVQC
proposed a quantum neural network pruning compression method based on ADMM.

The method consists of three phases. the first stage is preparation, starting
with QNN pruning, which provides the basis of what pruning is in a quantum
scenario; The authors propose that: A quantum gate can be pruned not only when
its parameter/weight is 0. Then there is QNN Quantization, some special values
should be substituted to make its parameter/weight become 0, to reduce the
depth. Finally, we need to build a Compression-Level look-up table (LUT) for
each door. The second stage is Compression, which turns the non-abrupt problem
with constraints into an unconstrained convex problem. Using ADMM to construct
Compression Level LUT Reconstruction, to achieve QNN Compression. Finally, the
author develops a logical quantum circuit that converts the above-compressed
VQC input to the compiler for mapping into a fixed quantum device.

From the experimental results, CompVQC reduced circuit depth (almost more than
2.5%), achieved a speedup of about 2.5 times, and reduced accuracy (¡1%) is
negligible. This method is limited to VQC tasks and has poor scalability.
However, the results of this method are similar on different quantum machines,
which proves that it is not hardware-dependent.

Summarize of Pruning: Pruning is a very effective method to save resources and
improve efficiency in the NISQ environment. The model efficiency of both On-
chip QNN and CompVQC has been greatly improved. In addition, the accuracy of
the model can be further improved by the correct pruning method to remove some
counterproductive parts in the model. However, in terms of universality, this
approach is often Device dependent, because different parts of the model may
have different functions under different quantum devices.

Figure 3: Overview of supercircuit. 1) Build and train the supercircuit
according to the different algorithms. 2) Search for suitable subcircuits. 3)
Sort the obtained subcircuits and select the best circuit. 4) Iterative
trimming and fine-tuning to remove the excess gate. 5) Compile and deploy on
the actual device.

####  III-B2 Optimization mapping method

Due to the need to map logical qubits to physical qubits, this operation is
not a one-to-one correspondence and often needs to convert complex gates in
logical qubits into multiple basic gates [38, 39, 40, 41]. Therefore, qubit
mapping requires certain strategies to reduce the error rate and speed up the
running of quantum programs.

ML-QCP This paper describes QCP as a two-layer optimization problem and
proposes a new framework based on machine learning (ML). This method uses a
strategy-based deep reinforcement learning (DRL) algorithm for low-level
combinatorial optimization problems. This method overcomes the disadvantages
of the traditional heuristic method and the precise method, and at the same
time can ensure the optimality-runtime trade-off. In this method, the low
level is a combination problem, which is solved by deep reinforcement learning
(DRL), while the high-level discrete search problem is solved by an
evolutionary algorithm. According to different tasks, the number of SWAP gates
required by this method is reduced compared with other existing methods, and
the maximum is more than 90%. Optimize the circuits mapped to the machine by
reducing the number of base gates to reduce consumption and improve
performance, reducing the uptime by 40%. However, this method may not be
suitable for large-scale circuits and has some limitations.

Figure 4: Two different ways for pruning: 1) Pruning according to the
different gradients. 2) Establishing a Compression-Level LUT as the basis and
pruning based on the ADMM.

HA In this paper, a mapping conversion algorithm considering hardware topology
and calibration data is proposed to improve the overall output state fidelity
and reduce the total execution time. This method is based on the SABRE
algorithm. By defining the appropriate heuristic function, the iterative
method is used to ensure that all circuits get the appropriate mapping. In
particular, in addition to choosing to insert SWAP gates, this method inserts
Bridge gates if the topology allows.

The author used ibmq_almaden and ibmq_tokyo to compare the algorithm with the
most advanced algorithms in terms of the number of additional gates. The
optimal output was obtained when the HA algorithm was combined with the SABRE
algorithm. Compared with the original circuit, the number of gates was reduced
by 30% on average, and the effect was better than using the SABRE algorithm
alone. The authors claim that this method can be used on machines outside IBM,
so it is not hardware dependent. The HA algorithm only takes into account
calibration data, including gate errors and execution time. However, other
physical constraints, such as crosstalk errors, may be included to account for
crosstalk coupling between interconnects.

Summarize of Optimization Mapping Method: From the two examples of ML-QCP and
HA, there is no doubt that a more effective mapping method will greatly reduce
the consumption of resources and improve the efficiency of the model. At the
same time, fewer basic gates also mean less noise, which can also provide an
improvement in accuracy. Because of the transformation from logical to
physical circuits during model deployment, the improved mapping method is
probably the closest approach to the basics at the gate level, This approach
is application-general and often hardware independent. (As shown in Fig. 4)

###  III-C Pulse Level Control

The existing quantum algorithms basically take gate as the basic element, but
the circuit construction in this way is not compatible with the underlying
topology of quantum devices. Because in this case we need a compiler to
compile it into a control signal on a physical qubit as shown in Fig. 5. So
there is a lot more room for improvement in the decomposition and tuning of
the circuit at the pulse level [15, 42, 7, 43, 44, 45, 46, 47].

Figure 5: Compilation workflow of quantum computing.

PAN It was the first to demonstrate the feasibility of native-pulse ansatz on
a NISQ machine. This avoids the redundancy that gate compilers can create,
bypasses the severe limitations that exist with existing pulse generator
optimizations such as QOC, and provides greater freedom. PAN will first
extract the configuration of the NISQ computer, including information about
the quantum bit frequency and the mapping between the native gate and the
native pulse. Next, build the native pulse ansatz from this information.
Ansatz has two different types of layers, one consisting of single qubit
primary pulses on all qubits, while the other consists of double qubit primary
pulses on all connections, and both types of layers are inserted in turn
during training. When building ansatz, you need to consider setting up
entangled qubits with the topology of the corresponding NISQ machine to save
on the consumption of qubit mapping. In particular, PAN proposes an
incremental approach to extend the pulse circuit to limit the number of
parameters held by the optimizer to ensure the optimizer’s efficiency. After
Ansatz is built, further pruning is needed to remove redundant parameters. The
results show that the effect of PAN is comparable to that of full
configuration interaction, and the comparison with true amplitude Ansatz
proves that PAN can reduce the duration by 73.6% while maintaining the
performance of Ansatz. From the above performance, pulse level operation is
indeed superior to the general gate level operation in many aspects, because
the pause level is more suitable for the characteristics of quantum devices
and can provide greater training freedom. Compared with the gate level, there
are fewer studies in this direction, so there are fewer references available
in the construction of the model, which may be the difficulty of the attempt.

##  IV Related Work

In the quantum computing field, there has been a lot of existing work
summarizing methods for better designing ansatz of VQAs.

[48] talked about the error problem of QML and emphatically discussed how to
deal with the Noise-aware problem of QML. However, the QML improvement Method
discussed in [48] is relatively simple compared with ours. Besides Noise
Suppression, our paper also adds a summary and discussion of VQA improvement
methods in other directions such as Pruning, Mapping methods, and Better
Circuits. Non-general methods for special problems are also studied. Beyond
the gate level, the pulse level is also an important research direction.

The main research object of [49] and [50] is QML, and they respectively
summarized different algorithms in QML and their applications. Their content
is limited to QML but with more details. While our paper discusses VQAs that
include QML with details techniques of how to better design a good ansatz for
VQAs.

##  V Conclusion

Variational Quantum Algorithms are an important method of applying Quantum
Computing in the NISQ environment. However, VQA is still facing many
difficulties and further improvement is needed. This paper summarizes the
existing VQA improvement approaches and outlines the different directions for
improvement at the gate level and pulse level respectively. At the gate level,
this paper first divides the methods into two categories for accuracy
improvement and efficiency improvement further subdivides them and summarizes
and evaluates different subdivision methods. This paper also discusses beyond
circuit level work, which is on the pulse level. pulse level is a relatively
new direction, but because of its characteristics, there is a lot more place
for improvement in the decomposition and tuning of the circuit at the pulse
level. Among the methods described here, some are computationally expensive,
while others are exponentially dependent on quanta, and although they perform
well in their environments, they are not suitable for large-scale quantum
applications. Even though there are a lot of technologies out there, I think
it’s still an open question how to develop a method that is computationally
cheap and can be implemented with large-scale quantum algorithms on real
machines.

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