Stefan Hillmich

Software Competence Center Hagenberg | SCCH

Classical simulation of quantum circuits is an important part of design automation for quantum computing. Moreover, conducting circuit simulation is conceptually simple as it can be done by multiplying matrices representing quantum operations to vectors representing quantum states in a straightforward fashion.

The approaches to quantum circuit simulation proposed in the previous chapters provide efficient routines based on decision diagrams. However, despite the often sub-exponential memory used by decision diagrams, the worst case remains exponential.

The classical simulation of quantum circuits is an important task in design automation for quantum computing as well as for the development and evaluation of quantum algorithms.

In order to keep this book self-contained, this chapter reviews the concepts of quantum computing and particularly quantum circuit simulation.

Despite the initial optimism, the construction of quantum computers and the implementation of quantum algorithms turned out to be exceptionally challenging.

This book is about quantum circuit simulation on classical computers with decision diagrams. As the physical realizations of quantum computers grow more powerful, the corresponding design automation tools have to follow in order to avoid a design gap.

An alternative direction to further improve the implementation of the quantum circuit simulator based on decision diagrams is the utilization of current multi-core CPUs through concurrent simulation.

Quantum computers promise to solve several categories of problems faster than classical computers ever could. Current research mostly focuses on qubits, i.e., systems where the unit of information can assume only two levels. However, the underlying physics of most (if not all) of the technological platforms supports more than two levels, commonly r...

Background Cancer is a leading cause of death worldwide. While routine diagnosis of cancer is performed mainly with biopsy sampling, it is suboptimal to accurately characterize tumor heterogeneity. Positron emission tomography (PET)-driven radiomic research has demonstrated promising results when predicting clinical endpoints. This study aimed to i...

Realizing the promised advantage of quantum computers over classical computers requires both physical devices and corresponding methods for the design, verification and analysis of quantum circuits. In this regard, decision diagrams have proven themselves to be an indispensable tool due to their capability to represent both quantum states and unita...

Quantum computing promises to solve some important problems faster than conventional computations ever could. Currently available NISQ devices on which first practical applications are already executed demonstrate the potential -- with future fault-tolerant quantum hardware for more demanding applications on the horizon. Nonetheless, the advantages...

Most quantum computing architectures to date natively supportmulti-malued logic, albeit being typically operated in a binary fash-ion. Multi-valued, or qudit, quantum processors have access tomuch richer forms of quantum entanglement, which promise tosignificantly boost the performance and usefulness of quantum de-vices. However, much of the theory...

Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude of complex tasks from the classical simulation of quantum circuits, over their compilation to specific devices...

Most quantum computing architectures to date natively support multi-valued logic, albeit being typically operated in a binary fashion. Multi-valued, or qudit, quantum processors have access to much richer forms of quantum entanglement, which promise to significantly boost the performance and usefulness of quantum devices. However, much of the theor...

Quantum computers have the potential to solve some important industrial and scientific problems with greater efficiency than classical computers. While most current realizations focus on two-level qubits, the underlying physics used in most hardware is capable of extending the concepts to a multi-level logic - enabling the use of qudits, which prom...

Quantum computing promises to solve some important problems faster than conventional computations ever could. Currently available NISQ devices on which first practical applications are already executed demonstrate the potential—with future fault-tolerant quantum hardware for more demanding applications on the horizon. Nonetheless, the advantages in...

Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude of complex tasks from the classical simulation of quantum circuits, over their compilation to specific devices...

Quantum computers have the potential to solve some important industrial and scientific problems with greater efficiency than classical computers. While most current realizations focus on two-level qubits, the underlying physics used in most hardware is capable of extending the concepts to a multi-level logic - enabling the use of qudits, which prom...

Decision diagrams have proven to be a useful data structure in both, conventional and quantum computing, to compactly represent exponentially large data in many cases. Several approaches exist to further reduce the size of decision diagrams, i.e., their number of nodes. Reordering is one such approach to shrink decision diagrams by changing the ord...

Quantum computers promise to solve important problems faster than conventional computers ever could. Underneath is a fundamentally different computational primitive that introduces new challenges for the development of software tools that aid designers of corresponding quantum algorithms. The different computational primitives render classical simu...

With quantum computers promising advantages even in the near-term NISQ era, there is a lively community that develops software and toolkits for the design of corresponding quantum circuits. Although the underlying problems are different, expertise from the design automation community, which developed sophisticated design solutions for the conventio...

Quantum machine learning has experienced significant progress in both software and hardware development in the recent years and has emerged as an applicable area of near-term quantum computers. In this work, we investigate the feasibility of utilizing quantum machine learning (QML) on real clinical datasets. We propose two QML algorithms for data c...

We consider the problem of estimating quantum ob-servables on a collection of qubits, given as a linear combinationof Pauli operators, with shallow quantum circuits consisting ofsingle-qubit rotations. We introduce estimators based on ran-domised measurements, which use decision diagrams to samplefrom probability distributions on measurement bases....

Quantum machine learning has experienced a significant progress in both software and hardware development in the recent years and has emerged as an applicable area of near-term quantum computers. In this work, we investigate the feasibility of utilizing quantum machine learning (QML) on real clinical datasets. We propose two QML algorithms for data...

With quantum computers promising advantages even in the near-term NISQ era, there is a lively community that develops software and toolkits for the design of corresponding quantum circuits. Although the underlying problems are different, expertise from the design automation community, which developed sophisticated design solutions for the conventio...

We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on randomised measurements, which use decision diagrams to sample from probability distributions on measurement bases...

Quantum computers promise to solve important problems faster than conventional computers. However, unleashing this power has been challenging. In particular, design automation runs into (1) the probabilistic nature of quantum computation and (2) exponential requirements for computational resources on non-quantum hardware. In quantum circuit simulat...

Quantum computers are constantly growing in their number ofqubits, but continue to suffer from restrictions such as the limitedpairs of qubits that may interact with each other. Thus far, this prob-lem is addressed by mapping and moving qubits to suitable positionsfor the interaction (known asquantum circuit mapping). However,this movement requires...

Quantum computers promise to solve important problems faster than conventional computers. However, unleashing this power has been challenging. In particular, design automation runs into (1) the probabilistic nature of quantum computation and (2) exponential requirements for computational resources on non-quantum hardware. In quantum circuit simulat...

Quantum computers are constantly growing in their number of qubits, but continue to suffer from restrictions such as the limited pairs of qubits that may interact with each other. Thus far, this problem is addressed by mapping and moving qubits to suitable positions for the interaction (known as quantum circuit mapping). However, this movement requ...

With quantum computers on the brink of practical applicability, there is a lively community that develops toolkits for the designof corresponding quantum circuits. Many of the problems to betackled here are similar to design problems from the classical realm for which sophisticated design automation tools have been developed in the previous decades...

Despite the recent progress in the physical implementation of quantum computers, a significant amount of research still depends on the use of quantum circuit simulators running on classical hardware. While there are several techniques for quantum circuit simulation, many state-of-the-art simulators rely on an array-based simulation approach. Howeve...

High-level descriptions of quantum algorithms do not take the restrictions of physical hardware into account. Therefore actually executing an algorithm in the form of a quantum circuit on a quantum computer requires compiling it for the desired target architecture first. The compilation of quantum circuits depends on efficient methods to be feasibl...

Quantum computers promise significant speedups in solving problems intractable for conventional computers but, despite recent progress, remain limited in scaling and availability. Therefore, quantum software and hardware development heavily rely on simulation that runs on conventional computers. Most such approaches perform strong simulation in tha...

Quantum computers promise significant speedups in solving problems intractable for conventional computers but, despite recent progress, remain limited in scaling and availability. Therefore, quantum software and hardware development heavily rely on simulation that runs on conventional computers. Most such approaches perform strong simulation in tha...

The computational power of quantum computers poses major challenges to new design tools since representing pure quantum states typically requires exponentially large memory. As shown previously, decision diagrams can reduce these memory requirements by exploiting redundancies. In this work, we demonstrate further reductions by allowing for small in...

The computational power of quantum computers poses major challenges to new design tools since representing pure quantum states typically requires exponentially large memory. As shown previously, decision diagrams can reduce these memory requirements by exploiting redundancies. In this work, we demonstrate further reductions by allowing for small in...

Despite recent progress in physical implementations of quantum computers, a significant amount of research still depends on simulating quantum computations on classical computers. Here, most state-of-the-art simulators rely on array-based approaches which are perfectly suited for acceleration through concurrency using multi- or many-core processors...

Quantum computers are becoming a reality today due to the rapid progress made by researchers in the last years. In the process of building quantum computers, IBM has developed several versions—starting from 5-qubit architectures like IBM QX2 and IBM QX4 to larger 16-or 20-qubit architectures. These architectures support arbitrary rotations of a sin...

Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum functionality. In the classical domain, decision diagrams have been successfully employed as a powerful alternative to s...

Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum functionality. In the classical domain, decision diagrams have been successfully employed as a powerful alternative to...

Optical circuits are considered a promising emerging technology for applications in ultra-high-speed networks or interconnects. However, the development of (automatic) synthesis approaches for such circuits is still in its infancy. Although first generic and automatic synthesis approaches have been proposed, no clear understanding exists yet on how...

On-chip coding provides a huge potential to improve the energy efficiency of on-chip interconnects. However, the logic design of the encoder/decoder faces a main challenge: the area and power overhead should be minimal while, at the same time, decodability has to be guaranteed. To address these problems, we propose the concept of approximate coding...