# Quantum Control

# Quantum controls execute a quantum algorithm by means of analog electromagnetic waves that couple to a quantum gate’s physical substrate, e.g., a collection of trapped ions. The outcomes are read out by analog (amplitude and/or phase) measurements made on electromagnetic waves emitted from the underlying physical substrate. Unavoidable analog imperfections — like temperature fluctuations, electronic noise, extraneous electromagnetic fields, environmental coupling, etc. — can then accumulate and disturb or destroy the coherent superpositions on which qubit-based computation relies. Unlike classical computation, however, quantum computation cannot defeat analog error accumulation by simply restoring binary logic levels to standard values. Two major issues for building large-scale quantum computers thus arise: (1) how to be resilient against a quantum architecture’s predominant errors; and (2) how to make error recovery that works for one and two qubits scale up to work for thousands. Feedback, the use of information about a system’s present state to correct its future behavior, will be an essential ingredient in this regard.

Quantum controls execute a quantum algorithm by means of analog electromagnetic waves that couple to a quantum gate’s physical substrate, e.g., a collection of trapped ions. The outcomes are read out by analog (amplitude and/or phase) measurements made on electromagnetic waves emitted from the underlying physical substrate. Unavoidable analog imperfections — like temperature fluctuations, electronic noise, extraneous electromagnetic fields, environmental coupling, etc. — can then accumulate and disturb or destroy the coherent superpositions on which qubit-based computation relies. Unlike classical computation, however, quantum computation cannot defeat analog error accumulation by simply restoring binary logic levels to standard values. Two major issues for building large-scale quantum computers thus arise: (1) how to be resilient against a quantum architecture’s predominant errors; and (2) how to make error recovery that works for one and two qubits scale up to work for thousands. Feedback, the use of information about a system’s present state to correct its future behavior, will be an essential ingredient in this regard.

## Main directions in Quantum Control Optimization:

Main directions in Quantum Control Optimization:

- Analog control pulse shape optimization.
- Quantum gate control design.
- Quantum circuit optimization.
- Real-time Feedback Control.

## Analog Control Pulse Optimization -- with deep reinforcement Learning

Analog Control Pulse Optimization -- with deep reinforcement Learning

# Stochastic control errors in analog control pulse shape can severely perturb the actual quantum control outcomes if they are not well accounted for during control optimizations.

Stochastic control errors in analog control pulse shape can severely perturb the actual quantum control outcomes if they are not well accounted for during control optimizations.

# Traditional methods for improving the control robustness against control errors have centered around closed-loop feedback optimizations, which necessitates frequent measurements of the quantum system. Since existing experimental measurements are relatively slow and can degrade subsequent gate fidelities, such closed-loop optimization has yet to become practical for near-term devices. The majority of openloop control optimizations address robustness through analysis of the control-noise spectrum and control curvature given by the control Hessian, which quickly becomes computationally exorbitant as system size increases.

Traditional methods for improving the control robustness against control errors have centered around closed-loop feedback optimizations, which necessitates frequent measurements of the quantum system. Since existing experimental measurements are relatively slow and can degrade subsequent gate fidelities, such closed-loop optimization has yet to become practical for near-term devices. The majority of openloop control optimizations address robustness through analysis of the control-noise spectrum and control curvature given by the control Hessian, which quickly becomes computationally exorbitant as system size increases.

# In Universal Quantum Control through Deep Reinforcement Learning, we propose a control framework, called Universal control cost Function Optimization (UFO), towards overcoming these fundamental challenges in quantum control by connecting deeper physical knowledge of the underlying quantum dynamics with state-of-the-art RL techniques.

In Universal Quantum Control through Deep Reinforcement Learning, we propose a control framework, called Universal control cost Function Optimization (UFO), towards overcoming these fundamental challenges in quantum control by connecting deeper physical knowledge of the underlying quantum dynamics with state-of-the-art RL techniques.

Overview of the RL implementation.

## Quantum Gate Control Design

Quantum Gate Control Design

# Another key component that determines the practical applications of near-term quantum devices is the universality of the quantum gates realizable by analog controls. For pre-fault-tolerant quantum computers, quantum operations are not limited to a finite gate set otherwise necessary for achieving fault tolerance. Consequently, implementing a high-fidelity and fast quantum gate with one control-pulse sequence instead of a deep circuit through optimal gate synthesis can greatly reduce the resource overhead and expand the feasible computational tasks.

Another key component that determines the practical applications of near-term quantum devices is the universality of the quantum gates realizable by analog controls. For pre-fault-tolerant quantum computers, quantum operations are not limited to a finite gate set otherwise necessary for achieving fault tolerance. Consequently, implementing a high-fidelity and fast quantum gate with one control-pulse sequence instead of a deep circuit through optimal gate synthesis can greatly reduce the resource overhead and expand the feasible computational tasks.

# In Demonstrating a Continuous Set of Two-Qubit Gates for Near-Term Quantum Algorithms, we propose and implemented a paradigm of directly realizing a continuously parameterized two-qubit gate through analog control. It takes advantage of the adjustable coupling of gmon qubits to provide a threefold reduction in circuit depth as compared to a standard decomposition into standard universal quantum gate set.

In Demonstrating a Continuous Set of Two-Qubit Gates for Near-Term Quantum Algorithms, we propose and implemented a paradigm of directly realizing a continuously parameterized two-qubit gate through analog control. It takes advantage of the adjustable coupling of gmon qubits to provide a threefold reduction in circuit depth as compared to a standard decomposition into standard universal quantum gate set.

## Quantum circuit optimization

Quantum circuit optimization

# A central aspect for operating future quantum computers is quantum circuit optimization, i.e., the search for efficient realizations of quantum algorithms given the device capabilities. In recent years, powerful approaches have been developed which focus on optimizing the high-level circuit structure. However, these approaches do not consider and thus cannot optimize for the hardware details of the quantum architecture, which is especially important for near-term devices.

A central aspect for operating future quantum computers is quantum circuit optimization, i.e., the search for efficient realizations of quantum algorithms given the device capabilities. In recent years, powerful approaches have been developed which focus on optimizing the high-level circuit structure. However, these approaches do not consider and thus cannot optimize for the hardware details of the quantum architecture, which is especially important for near-term devices.

# In Quantum circuit optimization with deep reinforcement learning, we present an approach to quantum circuit optimization based on reinforcement learning. We demonstrate how an agent, realized by a deep convolutional neural network, can autonomously learn generic strategies to optimize arbitrary circuits on a specific architecture, where the optimization target can be chosen freely by the user. We demonstrate the feasibility of this approach by training agents on 12-qubit random circuits, where we find on average a depth reduction by 27% and a gate count reduction by 15%. We examine the extrapolation to larger circuits than used for training, and envision how this approach can be utilized for near-term quantum devices.

In Quantum circuit optimization with deep reinforcement learning, we present an approach to quantum circuit optimization based on reinforcement learning. We demonstrate how an agent, realized by a deep convolutional neural network, can autonomously learn generic strategies to optimize arbitrary circuits on a specific architecture, where the optimization target can be chosen freely by the user. We demonstrate the feasibility of this approach by training agents on 12-qubit random circuits, where we find on average a depth reduction by 27% and a gate count reduction by 15%. We examine the extrapolation to larger circuits than used for training, and envision how this approach can be utilized for near-term quantum devices.

## Real-time Feedback Control

Real-time Feedback Control

# Feedback for quantum systems need not solely rely on projective measurements and digital gates. Analog signals obtained from weak quantum measurements on a quantum system can be used to apply analog controls to that system. Weak quantum measurements are well suited to this purpose: their operation is intrinsically analog and continuous in time, and they minimally impact the measured systems. Analog control of quantum dynamics has been demonstrated in recent experiments, and feedback using weak measurements and analog control has succeeded in generating highly entangled quantum state. Better feedback control laws are necessary to fully exploit continuous-time quantum measurements and controls. I have discovered that neural networks provide powerful representations for highly nonlinear feedback control laws in my research. Neural networks can further be enhanced with memory (e.g., recurrent neural networks or long short-term memory nets) to perform non-local feedbacks, which is expected to significantly extend the capability of quantum computing systems. Another exciting aspect is that neural networks can be trained on simulated or real data, using techniques from reinforcement learning (RL), to identify more effective and previously undiscovered feedback laws. This idea has already revolutionized other fields as illustrated by AlphaGo’s use of nonlocal feedback control rules encoded in a neural network to defeat the world-champion Go player. My research in optimizing universal quantum controls for a two-qubit system using RL-based on deep recurrent neural networks has opened the door to similar achievements in quantum computation. I am thrilled to continue this endeavor of developing new kinds of feedback algorithms inspired by advanced machine learning for quantum computing systems of many more qubits.

Feedback for quantum systems need not solely rely on projective measurements and digital gates. Analog signals obtained from weak quantum measurements on a quantum system can be used to apply analog controls to that system. Weak quantum measurements are well suited to this purpose: their operation is intrinsically analog and continuous in time, and they minimally impact the measured systems. Analog control of quantum dynamics has been demonstrated in recent experiments, and feedback using weak measurements and analog control has succeeded in generating highly entangled quantum state. Better feedback control laws are necessary to fully exploit continuous-time quantum measurements and controls. I have discovered that neural networks provide powerful representations for highly nonlinear feedback control laws in my research. Neural networks can further be enhanced with memory (e.g., recurrent neural networks or long short-term memory nets) to perform non-local feedbacks, which is expected to significantly extend the capability of quantum computing systems. Another exciting aspect is that neural networks can be trained on simulated or real data, using techniques from reinforcement learning (RL), to identify more effective and previously undiscovered feedback laws. This idea has already revolutionized other fields as illustrated by AlphaGo’s use of nonlocal feedback control rules encoded in a neural network to defeat the world-champion Go player. My research in optimizing universal quantum controls for a two-qubit system using RL-based on deep recurrent neural networks has opened the door to similar achievements in quantum computation. I am thrilled to continue this endeavor of developing new kinds of feedback algorithms inspired by advanced machine learning for quantum computing systems of many more qubits.