In quantum control, quantum theory is blended with control theory and advanced technology to take advantage of quantum system properties like superposition and entanglement so that quantum computing, quantum communication, and precision measurements can be executed. Scientists aim to realize the potential of quantum systems by developing state-of-the-art control techniques and experimental protocols, leading to advances in information processing, cryptography, and sensing. With this, it is predicted that quantum technologies will potentially transform a variety of industries and extend the limits of what is possible in the quantum field.

Thank you for reading this post, don’t forget to subscribe!

According to quantum company Q-CTRL, *“Quantum control is a discipline that addresses the following question: How can systems that obey the laws of quantum mechanics be efficiently manipulated to create desired behaviors? Ultimately, quantum control is concerned with how the classical world interacts with quantum devices.”*

## What is Quantum Control & How Does it Work?

In quantum control, quantum systems are engineered and directed to achieve a desired outcome. Quantum systems are steered by external fields or controls to enhance their functionality and improve their behavior for various purposes.

Particles like electrons and photons are capable of being in multiple probabilistic states in quantum mechanics. These act as qubits, unlike classical bits, which can only exist in one state at a time. Quantum control involves manipulating these quantum properties to accomplish specific tasks. Among the many things that can be done is to control the dynamics of a quantum system, repress unwanted effects, augment the properties of the system, or navigate the system towards a specific state or evolution of operability. There are many quantum systems that can be controlled with quantum control techniques, including atoms, ions, molecules, solid-state devices, superconducting qubits, and quantum dots.

Depending on the specific system and the desired manipulation, quantum control takes different forms. Among the techniques frequently used are:

- Through Hamiltonian engineering, one can engineer the system’s Hamiltonian (the underlying mathematical model of its dynamics) to achieve desired operations or states by tailoring its interactions and energy levels with external fields.
- Measuring a quantum system in real-time can provide information about its state, allowing adjustments in real-time to achieve the desired result. To continuously monitor and adjust the system based on the measurement results, feedback control loops can be used.
- Another technique that can be applied is optimal control theory, which uses mathematical optimization techniques to design control fields and sequences to drive quantum systems toward a desired state or to accomplish a specific function.
- For quantum information processing, gates and operations are used to control the evolution of a quantum system. Quantum gates are the building blocks that make up quantum computation.

## Difference between Quantum Control & Classical Control

Classical control and quantum control are two different branches of control theory that deal with systems at different scales and are aligned with different principles. The following are some of the main differences between quantum control and classical control:

- DESCRIPTION OF THE SYSTEM:

Physicists describe classical control systems as following classical laws and based on classical physics. Using differential equations and classical mechanics, it is possible to describe the behaviour of these systems.

Quantum control, on the other hand, relates to quantum mechanical systems. In quantum mechanics, waves and operators are used to describe systems such as quantum particles or quantum systems.

- OPERATING PRINCIPLES:

Depending on the initial conditions and the inputs, classical control works on the principle of determinism, which predicts a system’s state and evolution. As a result, it relies on feedback and feedforward techniques to manipulate the system and achieve the required outcome.

In contrast, quantum control is based on the concept of quantum uncertainty. Quantum systems are inherently probabilistic, and their states cannot be precisely measured or predicted without introducing uncertainty. In quantum control, control fields or operations are applied to manipulate the probabilities of different outcomes.

- STATE REPRESENTATION:

In classical control systems, state variables have definite values. These variables can be measured directly, and their evolution can be described using classical equations of motion.

On the other hand, in quantum control systems wave functions represent the quantum state of the system. It is important to note that these wave functions are probabilistic in nature and carry information about the probabilities of different states. Schrödinger’s equation and unitary transformations describe the evolution of quantum systems.

- METHODS OF CONTROL:

Among the classical control methods are PID (Proportional-Integral-Derivatives), state-space control, and optimal control. Various applications of these methods for controlling classical systems have been established and widely employed.

In contrast to classical control, techniques such as quantum optimal control, quantum feedback control and coherent control are used in quantum control methods. In these methods, control fields or operations are mapped out to optimize specific objectives, like maximizing entanglement or accomplishing the desired quantum states.

- APPLICATIONS:

There are many applications of classical control, including engineering, robotics, automation, and aerospace. Classical systems are regulated and stabilized, performance is improved, and goals are achieved with its help.

Among the many applications of quantum control are quantum technology, quantum information processing, quantum computing, and quantum communication. Its goals include preparing quantum states, operating quantum gates, and correcting quantum errors through manipulation and harnessing quantum phenomena.

As a general rule, quantum control differs from classical control primarily in terms of the underlying principles, the description of the system, and the methods used to control and manipulate the system. The classical controlled system is governed by the laws of determinism, whereas quantum-controlled systems are governed by the laws of probabilities.

## Benefits of Using Quantum Control

Several fields can benefit from quantum control techniques. We will now go through them and mention their key advantages:

### 1. ENHANCED PRECISION AND SENSITIVITY:

It is possible to manipulate and control quantum systems precisely through quantum control. Compared to classical methods, quantum mechanics makes measurements and manipulations more precise and sensitive and there are numerous applications for this improved precision, including atomic clocks, sensor technologies and spectroscopy.

### 2. QUANTUM INFORMATION PROCESSING:

Another area where quantum control plays an important role is in quantum information processing, where it enables the manipulation of quantum bits or qubits, the fundamental units of information in quantum computers. In certain computational tasks, quantum algorithms can be executed by carefully controlling and manipulating the quantum states of qubits.

### 3. QUANTUM SIMULATION:

Quantum simulation involves simulating and studying complex quantum systems that are difficult to simulate on classical computers, requiring quantum control techniques. It is possible to simulate the behavior of molecules, materials and other quantum systems by accurately controlling the interactions between quantum particles. As a consequence, new drugs can be designed, chemical reactions can be optimized, and fundamental quantum phenomena can be understood more effectively.

### 4. QUANTUM METROLOGY & SENSING:

It is possible to develop highly sensitive measurement devices and sensors through quantum control. A quantum sensor capable of detecting extremely weak magnetic fields or electric fields can be created using quantum control techniques. Sensors like these are used in medical imaging, geophysical exploration and at airports for security screening.

### 5. QUANTUM COMMUNICATION & CRYPTOGRAPHY:

Quantum communication and cryptography rely heavily on quantum control. Communication channels can be established that ensure unconditional security of information transmission by controlling the quantum states of particles like photons. Additionally, quantum control allows the implementation of quantum key distribution protocols, which enable secure encryption and decryption, ensuring quantum security.

### 6. QUANTUM ERROR CORRECTION:

Noise in the environment and hardware imperfections can lead to errors in quantum systems. It is vital for error correction codes to be implemented using quantum control techniques so that quantum information is protected from error. Errors can be detected and corrected using precise control operations, enhancing the reliability and robustness of quantum systems.

### 7. FUNDAMENTAL RESEARCH & DISCOVERY:

Finally, important research and discovery in quantum mechanics can be greatly enhanced by quantum control. By manipulating and controlling quantum systems, researchers can gain insights into quantum phenomena, test theoretical predictions and uncover new physics, opening up possibilities for potential new discoveries.

## Challenges & Limitations:

In spite of considerable progress in quantum control, several challenges and limitations remain. We will now briefly go through the biggest hurdles:

### 1. DECOHERENCE

In quantum systems, decoherence occurs when coherence is lost and a quantum state turns into a classical state because of interactions with the surroundings. Quantum state fidelity and duration of quantum control operations are limited by decoherence.

### 2. NOISE & ERRORS:

Thermal fluctuations, control imperfections, and coupling to uncontrolled environmental degrees of freedom can cause noise and errors in quantum systems. Quantum devices can be adversely affected by these errors by introducing inaccuracies in quantum control operations.

### 3. LIMITED CONTROLLABILITY:

Quantum systems are often restricted in their ability to be controlled by technological constraints. As a system’s qubit count increases, for example, it becomes more challenging to precisely manipulate quantum states and perform operations on individual qubits.

### 4. COMPLEXITY & OPTIMIZATION:

Optimal control strategies for achieving desired quantum states or dynamics are often involved in quantum control problems. Identifying global solutions can be difficult due to highly nonlinear optimization landscapes with many local optima.

### 5. SCALABILITY:

With the increase in the size of quantum systems, it becomes more challenging to control and manipulate an increasing number of qubits.

### 6. SENSITIVITY TO INITIAL CONDITIONS:

Depending on the initial conditions, quantum systems can be highly sensitive to even the smallest of disturbances. Hence, it can be difficult to maintain robust and reliable control over a long period of time due to this sensitivity.

### 7. LACK OF COMPLETE KNOWLEDGE:

In quantum control, it is often necessary to know the Hamiltonian, which describes the quantum system’s dynamics. Although complete knowledge of the system is not always available in practice, uncertainties may impact the effectiveness of control strategies.

### 8. QUANTUM CONTROL COMPLEXITY:

Performing quantum control operations requires advanced control techniques as well as specialized hardware, which can be challenging and time-consuming. This results in several challenges when it comes to designing and implementing practical quantum control systems.

It is imperative to address these challenges and limitations in order to advance quantum control techniques and make quantum technologies as effective as possible. Decoherence and noise mitigation techniques, robust control strategies, and error-correction methods are among the current research efforts currently ongoing in this area.

## 5 Key Commercial Players in Quantum Control:

Having looked at what quantum control is, how it works, the differences between quantum control and classical control, its theory and concepts, and the benefits, challenges, and applications of it, we will now move on to some of the companies contributing to quantum control.

Although big corporations like IBM, Google and Microsoft have their own dedicated research teams focused on quantum control, we will skip over these and just highlight some of the startups and private companies, with some of these companies managing their control stacks in-house:

### 1. Q-CTRL

An Australian startup led by University of Sydney professor Michael Biercuk, Q-CTRL is a company that is developing a firmware framework for quantum computers to address error control concerns. Q-CTRL’s first software product is called Black Opal, a hardware-agnostic control software program that reduces decoherence and errors at the physical layer.

### 2. QBLOX

A spinoff of quantum institute QuTech, Qblox designs low-latency qubit control equipment that is scalable and designed to support scientists all over the world. The company’s products are quantum control stacks for quantum computers that can be integrated with customers’ systems and there is no levelling of noise in the stacks, and arbitrary control flows can be performed in a low latency manner using arbitrary control flows.

### 3. QRUISE

With the aid of algorithms such as optimizers, simulators, machine learning tools, and other software components, Qruise provides algorithms designed to accelerate the development of quantum technology and enhance its application. By using ML and Quantum Optimal Control, Qruise’s first product addresses the obstacle of controlling current generation noisy quantum computers (NISQ devices).

### 4. QUANTUM MACHINES

With technology based on the integration of a wide range of fields, including digital signal processing, algorithms, FPGA, chip design, RF/microwave engineering, programming, optimization, machine learning and quantum physics, Quantum Machines focuses on creating hardware and software that will enable the realization of quantum computing’s potential.

### 5. ZURICH INSTRUMENTS

A subsidiary of Rohde & Schwarz, Zurich Instruments AG develops and sells advanced test and measurement instruments with dynamic signal analysis software. Founded in 2008, the company has offices in Zurich, Switzerland, Shanghai, and Boston. Zurich Instruments introduced its first commercial Quantum Computing Control System (QCCS) in 2018, designed to control more than 100 superconducting and spin qubits.

## Conclusion

For decades now, a significant portion of quantum error correction research has been devoted to mathematical strategies for encoding qubits and detecting errors in encoded sets efficiently. Yet, it has only been recently that investigators have begun to examine how a fully automated quantum error correction feedback loop can be implemented in real hardware. The community is becoming increasingly aware that by combining quantum error correction and control theory, new, revolutionary approaches may just be around the corner, ushering in a new epoch for quantum computation.

To end, though, we shall leave the last word to Michael Biercuk, founder of Q-CTRL and an expert on quantum control in an interview with The University of Sydney:

*“The ability to identify and suppress sources of performance degradation in quantum hardware is critical to both basic research and industrial efforts building quantum sensors and quantum computers.*

take from: https://thequantuminsider.com/

## Leave a Reply