Time-dependent Hamiltonian simulation (TDHS) is a critical task in quantum computing. Existing algorithms are generally biased with a small algorithmic error $\varepsilon$, and the gate complexity scales as $O(\text{poly}(1/\varepsilon))$ for product formula-based methods and could be improved to be polylogarithmic with complicated circuit constructions. Here, we develop an unbiased random compiler for TDHS by combining Dyson expansion, an unbiased continuous sampling method for quantum evolution, and leading order rotations, and it is free from algorithmic errors. Our method has the single- and two-qubit gate complexity $O(Λ^2)$ with a constant sampling overhead, where $Λ$ is the time integration of the Hamiltonian strength. We perform numerical simulations for a spin model under the interaction picture and the adiabatic ground state preparation for molecular systems. In both examples, we observe notable improvements of our method over existing ones. Our work paves the way to efficient realizations of TDHS.
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…
"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 …
Multilevel Circuit Optimization in Quantum Compilers: A Case Study
IBM Quantum Japan（IBM量子日本）；Quantum Computing Center, Keio University（庆应义塾大学量子计算中心）；Toyota Central R&D Labs., Inc.（丰田中央研发研究所）；Department of Applied Physics and Physico-Informatics, Keio University（庆应义塾大学应用物理与物理信息学系）
Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not 'optimal' either in terms of the circuit depth (and therefore the error burden) or the specifics of the target platform, i.e. the native gates and topology of a system. This work introduces a variational compiler for efficiently finding the encoding circuit of general quantum error correcting codes with given quantum hardware. Focusing on the noi…
Over the last decade, Quantum Computing hardware has rapidly developed and become a very intriguing, promising, and active research field among scientists worldwide. To achieve the desired quantum functionalities, quantum algorithms require translation from a high-level description to a machine-specific physical operation sequence. In contrast to classical compilers, state-of-the-art quantum compilers are in their infancy. We believe there is a research need for a quantum compiler that can deal with generic unitary operators and generate basic unitary operations according to quantum machines' …
When working with algorithms on quantum devices, quantum memory becomes a crucial bottleneck due to low qubit count in NISQ-era devices. In this context, the concept of `divide and compute', wherein a quantum circuit is broken into several subcircuits and executed separately, while stitching the results of the circuits via classical post-processing, becomes a viable option, especially in NISQ-era devices. This paper introduces \textbf{Qurzon}, a proposed novel quantum compiler that incorporates the marriage of techniques of divide and compute with the state-of-the-art algorithms of optimal qub…
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…
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 circui…
QTUNER: A Feature-Guided Adaptive Framework for Quantum-Compiler Optimization Pass Tuning
The Chinese University of Hong Kong（香港中文大学）；Nebius；State Key Laboratory of Quantum Information Technologies and Materials (CUHK)（量子信息科技与材料国家重点实验室（香港中文大学））
This paper presents Giallar, a fully-automated verification toolkit for quantum compilers. Giallar requires no manual specifications, invariants, or proofs, and can automatically verify that a compiler pass preserves the semantics of quantum circuits. To deal with unbounded loops in quantum compilers, Giallar abstracts three loop templates, whose loop invariants can be automatically inferred. To efficiently check the equivalence of arbitrary input and output circuits that have complicated matrix semantics representation, Giallar introduces a symbolic representation for quantum circuits and a s…
A Neutral-Atom Quantum Compiler with Application-Specific Layout and Hub-Assisted Shuttling
Faculty of Science and Technology, Keio University（庆应义塾大学理工学部）；Department of Physics, Graduate School of Science, Tokyo University of Science（东京理科大学理学研究部物理学专攻）
The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work out a simple and efficient method based on cyclic generation of mutually unbiased bases. The basic generator requires only Hadamard and controlled-phase gates, which are available in most practical realizations of these systems. We show how complete sets of mutually unbiased bases with different entanglement structures can be realized for three and four qubits…
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…
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…
It is imperative to compile quantum circuits for Noisy Intermediate-Scale Quantum (NISQ) devices because of the limited connectivity of physical qubits and the high error rates of gate operations. One of the most critical steps in quantum circuit compilation is qubit routing, an NP-Hard problem that involves placing and moving logical qubits to minimize compilation overhead. In this study, we propose ISing mAchine Assisted Quantum compiler (ISAAQ) to perform qubit routing with Ising machines, which can efficiently solve Quadratic Unconstrained Binary Optimization (QUBO) problems. ISAAQ accurat…
We present an approach for a deep-learning compiler of quantum circuits, designed to reduce the output noise of circuits run on a specific device. We train a convolutional neural network on experimental data from a quantum device to learn a hardware-specific noise model. A compiler then uses the trained network as a noise predictor and inserts sequences of gates in circuits so as to minimize expected noise. We tested this approach on the IBM 5-qubit devices and observed a reduction in output noise of 12.3% (95% CI [11.5%, 13.0%]) compared to the circuits obtained by the Qiskit compiler. Moreov…
Efficient compilation of quantum algorithms is vital in the era of Noisy Intermediate-Scale Quantum (NISQ) devices. While multiple open-source quantum compilation and circuit optimization frameworks are available, e.g. IBM Qiskit, CQC Tket, Google Cirq, Rigetti Quilc, PyZX, their relative performance is not always clear to a quantum programmer. The growth of complexity and diversity of quantum circuit compilation algorithms creates a demand for a dedicated tool for cross-benchmarking and profiling of inner workflow of the quantum compilation stack. We present an open-source software package, A…
We present t$|$ket$\rangle$, a quantum software development platform produced by Cambridge Quantum Computing Ltd. The heart of t$|$ket$\rangle$ is a language-agnostic optimising compiler designed to generate code for a variety of NISQ devices, which has several features designed to minimise the influence of device error. The compiler has been extensively benchmarked and outperforms most competitors in terms of circuit optimisation and qubit routing.
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…
Parameterized circuit instantiation is a common technique encountered in the generation of circuits for a large class of hybrid quantum-classical algorithms. Despite being supported by popular quantum compilation infrastructures such as IBM Qiskit and Google Cirq, instantiation has not been extensively considered in the context of circuit compilation and optimization pipelines. In this work, we describe algorithms to apply instantiation during two common compilation steps: circuit optimization and gate-set transpilation. When placed in a compilation workflow, our circuit optimization algorithm…
Modeling and simulation is essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. We present a method of simulating noisy Clifford circuits that is both accurate and practical in experimentally relevant regimes. In particular, the cost is weakly exponential in the size and the degree of non-Cliffordness of the circuit. Our approach is based on the construction of exact representations of quantum channels as quasiprobability distributions over…
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,…
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…
Existing quantum compilers focus on mapping a logical quantum circuit to a quantum device and its native quantum gates. Only simple circuit identities are used to optimize the quantum circuit during the compilation process. This approach misses more complex circuit identities, which could be used to optimize the quantum circuit further. We propose Quanto, the first quantum optimizer that automatically generates circuit identities. Quanto takes as input a gate set and generates provably correct circuit identities for the gate set. Quanto's automatic generation of circuit identities includes sin…
We present CertiQ, a verification framework for writing and verifying compiler passes of Qiskit, the most widely-used quantum compiler. To our knowledge, CertiQ is the first effort enabling the verification of real-world quantum compiler passes in a mostly-automated manner. Compiler passes written in the CertiQ interface with annotations can be used to generate verification conditions, as well as the executable code that can be integrated into Qiskit. CertiQ introduces the quantum circuit calculus to enable the efficient checking of equivalence of quantum circuits by encoding such a checking p…
When scheduling quantum operations, a shorter overall execution time of the resulting schedule yields a better throughput and higher fidelity output. In this paper, we demonstrate that quantum operation scheduling can be interpreted as a special type of job-shop problem. On this basis, we provide its formulation as Constraint Programming while taking into account commutation between quantum operations. We show that this formulation improves the overall execution time of the resulting schedules in practice through experiments with a real quantum compiler and quantum circuits from two common ben…
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.
The Noisy Intermediate-Scale Quantum (NISQ) technology is currently investigated by major players in the field to build the first practically useful quantum computer. IBM QX architectures are the first ones which are already publicly available today. However, in order to use them, the respective quantum circuits have to be compiled for the respectively used target architecture. While first approaches have been proposed for this purpose, they are infeasible for a certain set of SU(4) quantum circuits which have recently been introduced to benchmark corresponding compilers. In this work, we anal…
