Simulation of the dynamics of quantum materials is emerging as a promising scientific application for noisy intermediate-scale quantum (NISQ) computers. Due to their high gate-error rates and short decoherence times, however, NISQ computers can only produce high-fidelity results for those quantum circuits smaller than some given circuit size. Dynamic simulations, therefore, pose a challenge as current algorithms produce circuits that grow in size with each subsequent time-step of the simulation. This underscores the crucial role of quantum circuit compilers to produce executable quantum circuits of minimal size, thereby maximizing the range of physical phenomena that can be studied within the NISQ fidelity budget. Here, we present two domain-specific quantum circuit compilers for the Rigetti and IBM quantum computers, specifically designed to compile circuits simulating dynamics under a special class of time-dependent Hamiltonians. The compilers outperform state-of-the-art general-purpose compilers in terms of circuit size reduction by around 25-30% as well as wall-clock compilation time by around 40% (dependent on system size and simulation time-step). Drawing on heuristic techniques commonly used in artificial intelligence, both compilers scale well with simulation time-step and system size. Code for both compilers is included to enhance the results of dynamic simulations for future researchers. We anticipate that our domain-specific compilers will enable dynamic simulations of quantum materials on near-future NISQ computers that would not otherwise be possible with general-purpose compilers.
A promising architecture for scaling up quantum computers based on trapped ions are so called Quantum Charged-Coupled Devices (QCCD). These consist of multiple ion traps, each designed for solving specific tasks, that are connected by transport links. In this paper we present the backend compiler phases needed for running quantum circuits on a QCCD architecture, while providing strategies to solve the optimization problems that occur when generating assembly instructions. We implement and test these strategies for the QVLS-Q1 chip architecture.
Compiler Framework for 3D Neutral-Atom Quantum Computers
The Chinese University of Hong Kong（香港中文大学）；Open Quantum Intelligence（开放量子智能）；Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；SIOM, Chinese Academy of Sciences（中国科学院上海光学精密机械研究所）；State Key Laboratory of Quantum Information Technologies and Materials, The Chinese University of Hong Kong（香港中文大学量子信息技术与材料国家重点实验室）
The quantum volume test is a full-system benchmark for quantum computers that is sensitive to qubit number, fidelity, connectivity, and other quantities believed to be important in building useful devices. The test was designed to produce a single-number measure of a quantum computer's general capability, but a complete understanding of its limitations and operational meaning is still missing. We explore the quantum volume test to better understand its design aspects, sensitivity to errors, passing criteria, and what passing implies about a quantum computer. We elucidate some transient behavio…
We present a new algorithm for reducing an arbitrary unitary matrix into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of quantum bits (i.e., a quantum computer). We report on a C++ program called "Qubiter" that implements our algorithm. Qubiter source code is publicly available.
QuYBE is an open-source algebraic compiler for the compression of quantum circuits. It has been applied for the efficient simulation of the Heisenberg Hamiltonian on quantum computers. Currently, it can simulate the time dynamics of one-dimensional chains. It includes modules to generate the quantum circuits for the above as well as produce the compressed circuits, which are independent of the time step. It utilizes the Yang-Baxter equation (YBE) to perform the compression. QuYBE enables users to seamlessly design, execute, and analyze the time dynamics of the Heisenberg Hamiltonian on quantum…
Shuttling Compiler for Trapped-Ion Quantum Computers Based on Fine-Tuned Large Language Models
Institute of Computer Science, Johannes Gutenberg University（计算机科学研究所，约翰内斯·古特堡大学）；Institute of Physics, Johannes Gutenberg University（物理研究所，约翰内斯·古特堡大学）；Department of Computer Science, Saarland University（计算机科学系，萨尔兰大学）
A massive gap exists between current quantum computing (QC) prototypes, and the size and scale required for many proposed QC algorithms. Current QC implementations are prone to noise and variability which affect their reliability, and yet with less than 80 quantum bits (qubits) total, they are too resource-constrained to implement error correction. The term Noisy Intermediate-Scale Quantum (NISQ) refers to these current and near-term systems of 1000 qubits or less. Given NISQ's severe resource constraints, low reliability, and high variability in physical characteristics such as coherence time…
"Qubit routing" refers to the task of modifying quantum circuits so that they satisfy the connectivity constraints of a target quantum computer. This involves inserting SWAP gates into the circuit so that the logical gates only ever occur between adjacent physical qubits. The goal is to minimise the circuit depth added by the SWAP gates. In this paper, we propose a qubit routing procedure that uses a modified version of the deep Q-learning paradigm. The system is able to outperform the qubit routing procedures from two of the most advanced quantum compilers currently available, on both random …
Simulating quantum systems is one of the most important potential applications of quantum computers. The high-level circuit defining the simulation needs to be compiled into one that complies with hardware limitations such as qubit architecture (connectivity) and instruction (gate) set. General-purpose quantum compilers work at the gate level and have little knowledge of the mathematical properties of quantum applications, missing further optimization opportunities. Existing application-specific compilers only apply advanced optimizations in the scheduling procedure and are restricted to the C…
Quilc is an open-source, optimizing compiler for gate-based quantum programs written in Quil or QASM, two popular quantum programming languages. The compiler was designed with attention toward NISQ-era quantum computers, specifically recognizing that each quantum gate has a non-negligible and often irrecoverable cost toward a program's successful execution. Quilc's primary goal is to make authoring quantum software a simpler exercise by making architectural details less burdensome to the author. Using Quilc allows one to write programs faster while usually not compromising---and indeed sometim…
The quantum simulation kernel is an important subroutine appearing as a very long gate sequence in many quantum programs. In this paper, we propose Paulihedral, a block-wise compiler framework that can deeply optimize this subroutine by exploiting high-level program structure and optimization opportunities. Paulihedral first employs a new Pauli intermediate representation that can maintain the high-level semantics and constraints in quantum simulation kernels. This naturally enables new large-scale optimizations that are hard to implement at the low gate-level. In particular, we propose two te…
In this paper, we propose a novel quantum compiler optimization, named relaxed peephole optimization (RPO) for quantum computers. RPO leverages the single-qubit state information that can be determined statically by the compiler. We define that a qubit is in a basis state when, at a given point in time, its state is either in the X-, Y-, or Z-basis. When basis qubits are used as inputs to quantum gates, there exist opportunities for strength reduction, which replaces quantum operations with equivalent but less expensive ones. Compared to the existing peephole optimization for quantum programs,…
A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits. However, the physical limitations of the quantum computing device restrict the set of gates that physicists are able to apply. Thus, they must compose a sequence of gates from the permitted gate set, which approximates the gate they wish to apply - a process called quantum compiling. Austin Fowler proposes a method that finds optimal gate sequences in exponen…
Trapped-ion systems can have a limited number of ions (qubits) in a single trap. Increasing the qubit count to run meaningful quantum algorithms would require multiple traps where ions need to shuttle between traps to communicate. The existing compiler has several limitations which result in a high number of shuttle operations and degraded fidelity. In this paper, we target this gap and propose compiler optimizations to reduce the number of shuttles. Our technique achieves a maximum reduction of $51.17\%$ in shuttles (average $\approx 33\%$) tested over $125$ circuits. Furthermore, the improve…
Quantum computing promises remarkable approaches for processing information, but new tools are needed to compile program representations into the physical instructions required by a quantum computer. Here we present a novel adaptation of the multi-level intermediate representation (MLIR) integrated into a quantum compiler that may be used for checking program execution. We first present how MLIR enables quantum circuit transformations for efficient execution on quantum computing devices and then give an example of compiler transformations based on so-called mirror circuits. We demonstrate that…
The software package \emph{Qcompiler} (CPC, 184 (2013) 853) provides a general quantum compilation framework, which maps any given unitary operation into a quantum circuit consisting of a sequential set of elementary quantum gates. In this paper, we present an extended software \emph{OptQC}, which finds permutation matrices $P$ and $Q$ for a given unitary matrix $U$ such that the number of gates in the quantum circuit of $U = Q^TP^TU'PQ$ is significantly reduced, where $U'$ is equivalent to $U$ up to a permutation and the quantum circuit implementation of each matrix component is considered se…
Before executing a quantum algorithm, one must first decompose the algorithm into machine-level instructions compatible with the architecture of the quantum computer, a process known as quantum compiling. There are many different quantum circuit decompositions for the same algorithm but it is desirable to compile leaner circuits. A fundamentally important cost metric is the $T$ count -- the number of $T$ gates in a circuit. For the single qubit case, optimal compiling is essentially a solved problem. However, multi-qubit compiling is a harder problem with optimal algorithms requiring classical…
Prevailing proposals for the first generation of quantum computers make use of 2-level systems, or qubits, as the fundamental unit of quantum information. However, recent innovations in quantum error correction and magic state distillation protocols demonstrate that there are advantages of using d-level quantum systems, known as \emph{qudits}, over the qubit analogues. When designing a quantum architecture, it is crucial to consider protocols for compilation, the optimal conversion of high-level instructions used by programmers into low-level instructions interpreted by the machine. In this wo…
We present a new algorithm for reducing an arbitrary unitary matrix U into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of quantum bits (i.e., a quantum computer). Our algorithm applies recursively a mathematical technique called the CS Decomposition to build a binary tree of matrices whose product, in some order, equals the original matrix U. We show that the Fast Fourier Transform (FFT) algorithm is a special case of our algorithm. We report on a C++ program called "Qubiter" that…
The dynamics of a quantum system can be simulated using a quantum computer by breaking down the unitary into a quantum circuit of one and two qubit gates. The most established methods are the Trotter-Suzuki decompositions, for which rigorous bounds on the circuit size depend on the number of terms $L$ in the system Hamiltonian and the size of the largest term in the Hamiltonian $Λ$. Consequently, Trotter-Suzuki is only practical for sparse Hamiltonians. Trotter-Suzuki is a deterministic compiler but it was recently shown that randomised compiling offers lower overheads. Here we present and ana…
Recently author suggested [quant-ph/0010071] an application of Clifford algebras for construction of a "compiler" for universal binary quantum computer together with later development [quant-ph/0012009] of the similar idea for a non-binary base. The non-binary case is related with application of some extension of idea of Clifford algebras. It is noncommutative torus defined by polynomial algebraic relations of order l. For l=2 it coincides with definition of Clifford algebra. Here is presented the joint consideration and comparison of both cases together with some discussion on possible physic…
Compiler Optimization for Quantum Computing Using Reinforcement Learning
Technical University of Munich（慕尼黑工业大学）；Johannes Kepler University Linz（约翰内斯·开普勒大学林茨分校）；Software Competence Center Hagenberg GmbH (SCCH)（哈根伯格软件能力中心有限公司）
Quantum volume is a single-number metric which, loosely speaking, reports the number of usable qubits on a quantum computer. While improvements to the underlying hardware are a direct means of increasing quantum volume, the metric is "full-stack" and has also been increased by improvements to software, notably compilers. We extend this latter direction by demonstrating that error mitigation, a type of indirect compilation, increases the effective quantum volume of several quantum computers. Importantly, this increase occurs while taking the same number of overall samples. We encourage the adop…
ArQTiC is an open-source, full-stack software package built for the simulations of materials on quantum computers. It currently can simulate materials that can be modeled by any Hamiltonian derived from a generic, one-dimensional, time-dependent Heisenberg Hamiltonain. ArQTiC includes modules for generating quantum programs for real- and imaginary-time evolution, quantum circuit optimization, connection to various quantum backends via the cloud, and post-processing of quantum results. By enabling users to seamlessly perform and analyze materials simulations on quantum computers by simply provi…
Wuhan University（武汉大学）；JD Explore Academy（京东探索研究院）；University of Maryland（马里兰大学）
Efficient quantum compiling tactics greatly enhance the capability of quantum computers to execute complicated quantum algorithms. Due to its fundamental importance, a plethora of quantum compilers has been designed in past years. However, there are several caveats to current protocols, which are low optimality, high inference time, limited scalability, and lack of universality. To compensate for these defects, here we devise an efficient and practical quantum compiler assisted by advanced deep reinforcement learning (RL) techniques, i.e., data generation, deep Q-learning, and AQ* search. In t…
This paper presents the definition and implementation of a quantum computer architecture to enable creating a new computational device - a quantum computer as an accelerator. In this paper, we present explicitly the idea of a quantum accelerator which contains the full stack of the layers of an accelerator. Such a stack starts at the highest level describing the target application of the accelerator. The next layer abstracts the quantum logic outlining the algorithm that is to be executed on the quantum accelerator. In our case, the logic is expressed in the universal quantum-classical hybrid …
Quantum Compiler Design for Fault-Tolerant Quantum Computing
QudeLeap Research；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；Shanghai Jiao Tong University（上海交通大学）；Hangzhou MatriQ Computing Co., Ltd（杭州矩阵量子计算有限公司）；Atomqubic Quantum Technology Co., Ltd（上海原子立方量子科技有限公司）；State Key Laboratory of Quantum Optics Technologies and Devices, and Institute of Opto-Electronics, Shanxi University（山西大学光电研究所及量子光学技术与器件国家重点实验室）；CAS Cold Atom Technology (Wuhan) Co., Ltd.（中科院冷原子技术（武汉）有限公司）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
In the era of noisy-intermediate-scale quantum computers, we expect to see quantum devices with increasing numbers of qubits emerge in the foreseeable future. To practically run quantum programs, logical qubits have to be mapped to the physical qubits by a qubit allocation algorithm. However, on present day devices, qubits differ by their error rate and connectivity. Here, we establish and demonstrate on current experimental devices a new allocation algorithm that combines the simulated annealing method with local search of the solution space using Dijkstra's algorithm. Our algorithm takes int…
Reconfigurable Quantum Instruction Set Computers for High Performance Attainable on Hardware
The Hong Kong University of Science and Technology（香港科技大学）；Fudan University（复旦大学）；Shanghai Institute for Mathematics and Interdisciplinary Sciences（上海数学与交叉学科研究院）；Tsinghua University（清华大学）；DAMO Academy, Alibaba Group（阿里巴巴集团达摩院）
In recent years, Quantum Computing (QC) has progressed to the point where small working prototypes are available for use. Termed Noisy Intermediate-Scale Quantum (NISQ) computers, these prototypes are too small for large benchmarks or even for Quantum Error Correction, but they do have sufficient resources to run small benchmarks, particularly if compiled with optimizations to make use of scarce qubits and limited operation counts and coherence times. QC has not yet, however, settled on a particular preferred device implementation technology, and indeed different NISQ prototypes implement qubi…
Quantum computers promise to solve certain problems that are intractable for classical computers, such as factoring large numbers and simulating quantum systems. To date, research in quantum computer engineering has focused primarily at opposite ends of the required system stack: devising high-level programming languages and compilers to describe and optimize quantum algorithms, and building reliable low-level quantum hardware. Relatively little attention has been given to using the compiler output to fully control the operations on experimental quantum processors. Bridging this gap, we propos…
Multigrid has become a popular method for solving some of the most challenging real-world computational problems, such as computational fluid dynamics (CFD). The reason for this is the very good scaling properties of multigrid, which is often linear, or close to linear, with respect to problem size. In this paper a method is presented, which can be used to implement a quantum version of the multigrid algorithm. The method relies upon a quantum state that is maintained in a equal superposition throughout the calculation, and where information is encoded digitally in the qubits in a way more sim…
Recent developments in engineering and algorithms have made real-world applications in quantum computing possible in the near future. Existing quantum programming languages and compilers use a quantum assembly language composed of 1- and 2-qubit (quantum bit) gates. Quantum compiler frameworks translate this quantum assembly to electric signals (called control pulses) that implement the specified computation on specific physical devices. However, there is a mismatch between the operations defined by the 1- and 2-qubit logical ISA and their underlying physical implementation, so the current pra…
Many proposals to scale quantum technology rely on modular or distributed designs where individual quantum processors, called nodes, are linked together to form one large multinode quantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, a limiting factor of these machines will be internode gates, which may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require a range of techniques, including improvements in entanglement gene…
Thermal properties of nanomaterials are crucial to not only improving our fundamental understanding of condensed matter systems, but also to developing novel materials for applications spanning research and industry. Since quantum effects arise at the nano-scale, these systems are difficult to simulate on classical computers. Quantum computers can efficiently simulate quantum many-body systems, yet current quantum algorithms for calculating thermal properties of these systems incur significant computational costs in that they either prepare the full thermal state on the quantum computer, or th…
Quantum computing (QC) is at the cusp of a revolution. Machines with 100 quantum bits (qubits) are anticipated to be operational by 2020 [googlemachine,gambetta2015building], and several-hundred-qubit machines are around the corner. Machines of this scale have the capacity to demonstrate quantum supremacy, the tipping point where QC is faster than the fastest classical alternative for a particular problem. Because error correction techniques will be central to QC and will be the most expensive component of quantum computation, choosing the lowest-overhead error correction scheme is critical to…
