Compiling a high-level quantum circuit down to a low-level description that can be executed on state-of-the-art quantum computers is a crucial part of the software stack for quantum computing. One step in compiling a quantum circuit to some device is quantum circuit mapping, where the circuit is transformed such that it complies with the architecture's limited qubit connectivity. Because the search space in quantum circuit mapping grows exponentially in the number of qubits, it is desirable to consider as few of the device's physical qubits as possible in the process. Previous work conjectured that it suffices to consider only subarchitectures of a quantum computer composed of as many qubits as used in the circuit. In this work, we refute this conjecture and establish criteria for judging whether considering larger parts of the architecture might yield better solutions to the mapping problem. We show that determining subarchitectures that are of minimal size, i.e., of which no physical qubit can be removed without losing the optimal mapping solution for some quantum circuit, is a very hard problem. Based on a relaxation of the criteria for optimality, we introduce a relaxed consideration that still maintains optimality for practically relevant quantum circuits. Eventually, this results in two methods for computing near-optimal sets of subarchitectures$\unicode{x2014}$providing the basis for efficient quantum circuit mapping solutions. We demonstrate the benefits of this novel method for state-of-the-art quantum computers by IBM, Google and Rigetti.
The mapping of quantum circuits to qubits represented by ion states in a storage ring quantum computer is examined. Serial, parallel and hybrid architectures for mapping such qubits onto a storage ring quantum computer are presented. Parallelism is an important part of the SRQC architecture in terms of multiple ions, windows and lasers. A "predecessor problem" that arises in such architectures is identified and a solution is proposed. Representative numerical sizing and timing calculations are presented. The entire methodology is very general and extends to several implementation options. Open…
The quantum circuit mapping approach is an indispensable part of the software stack for the noisy intermediatescale quantum (NISQ) device. It has a significant impact on the reliability of computational tasks on NISQ devices. To improve the overall fidelity of physical circuits, we propose a quantum circuit mapping method based on multi-agent cooperation. This approach considers the Spatio-temporal variation of quantum operation quality on the NISQ device when inserting ancillary operation. It consists of two core components: the qubit placement algorithm and the qubit routing method. The qubi…
Rapid advancement in the domain of quantum technologies has opened up researchers to the real possibility of experimenting with quantum circuits and simulating small-scale quantum programs. Nevertheless, the quality of currently available qubits and environmental noise poses a challenge in the smooth execution of the quantum circuits. Therefore, efficient design automation flows for mapping a given algorithm to the Noisy Intermediate Scale Quantum (NISQ) computer becomes of utmost importance. State-of-the-art quantum design automation tools are primarily focused on reducing logical depth, gate…
We present a scalable set of universal gates and multiply controlled gates in a qudit basis through a bijective mapping from N qubits to qudits with D = 2^N levels via rotations in U(2). For each of the universal gates (H, CNOT, and T), as well as the NOT gate and multiply-controlled-Z gates, we describe a systematic approach to identifying the set of U(2) rotations required to implement each gate for any qudit of size N and with minimal use of an ancilla level. The qudit gates are analyzed in terms of the total rotation count and gate depth as the system scales with D. We apply the qudit-basi…
Quantum algorithms need to be compiled to respect the constraints imposed by quantum processors, which is known as the mapping problem. The mapping procedure will result in an increase of the number of gates and of the circuit latency, decreasing the algorithm's success rate. It is crucial to minimize mapping overhead, especially for Noisy Intermediate-Scale Quantum (NISQ) processors that have relatively short qubit coherence times and high gate error rates. Most of prior mapping algorithms have only considered constraints such as the primitive gate set and qubit connectivity, but the actual g…
This paper addresses quantum circuit mapping for Noisy Intermediate-Scale Quantum (NISQ) computers. Since NISQ computers constraint two-qubit operations on limited couplings, an input circuit must be transformed into an equivalent output circuit obeying the constraints. The transformation often requires additional gates that can affect the accuracy of running the circuit. Based upon a previous work of quantum circuit mapping that leverages gate commutation rules, this paper shows algorithms that utilize both transformation and commutation rules. Experiments on a standard benchmark dataset conf…
A critical step in quantum compilation is the transformation of a technology-independent quantum circuit into a technology-dependent form for a targeted device. In addition to mapping quantum gates into the supported gate set, it is necessary to map pseudo qubits in the technology-independent circuit into physical qubits of the technology-dependent circuit such that coupling constraints among qubits acting in multiple-qubit gates are satisfied. It is usually not possible to find such a mapping without adding SWAP gates into the circuit. To cope with the technical limitations of NISQ-era quantu…
Mapping logical quantum circuits to Noisy Intermediate-Scale Quantum (NISQ) devices is a challenging problem which has attracted rapidly increasing interests from both quantum and classical computing communities. This paper proposes an efficient method by (i) selecting an initial mapping that takes into consideration the similarity between the architecture graph of the given NISQ device and a graph induced by the input logical circuit; and (ii) searching, in a filtered and depth-limited way, a most useful SWAP combination that makes executable as many as possible two-qubit gates in the logical…
Single flux quantum (SFQ) logic is a promising candidate to replace the CMOS logic for high speed and low power applications due to its superiority in providing high performance and energy efficient circuits. However, developing effective Electronic Design Automation (EDA) tools, which cater to special characteristics and requirements of SFQ circuits such as depth minimization and path balancing, are essential to automate the whole process of designing large SFQ circuits. In this paper, a novel technology mapping tool, called SFQmap, is presented, which provides optimization methods for minimi…
The circuit-to-Hamiltonian construction has found widespread use within the field of Hamiltonian complexity, particularly for proving QMA-hardness results. In this work we examine the ground state energies of the Hamiltonian for standard clock constructions and those which require dynamic initialisation. We put exponentially tight bounds on these ground state energies and also determine improved scaling bounds in the case where there is a constant probability of the computation being rejected. Furthermore, we prove a collection of results concerning the low-energy subspace of quantum walks on …
Quantum error correction (QEC) and fault-tolerant (FT) mechanisms are essential for reliable quantum computing. However, QEC considerably increases the computation size up to four orders of magnitude. Moreover, FT implementation has specific requirements on qubit layouts, causing both resource and time overhead. Reducing spatial-temporal costs becomes critical since it is beneficial to decrease the failure rate of quantum computation. To this purpose, scalable qubit plane architectures and efficient mapping passes including placement and routing of qubits as well as scheduling of operations ar…
The recent progress in the physical realization of quantum computers (the first publicly available ones--IBM's QX architectures--have been launched in 2017) has motivated research on automatic methods that aid users in running quantum circuits on them. Here, certain physical constraints given by the architectures which restrict the allowed interactions of the involved qubits have to be satisfied. Thus far, this has been addressed by inserting SWAP and H operations. However, it remains unknown whether existing methods add a minimum number of SWAP and H operations or, if not, how far they are aw…
We construct a constant depth quantum circuit that maps between Morita equivalent string-net models. Due to its constant depth and unitarity, the circuit cannot alter the topological order, which demonstrates that Morita equivalent string-nets are in the same phase. The circuit is constructed from an invertible bimodule category connecting the two input fusion categories of the relevant string-net models, acting as a generalized Fourier transform for fusion categories. The circuit does not only act on the ground state subspace, but acts unitarily on the full Hilbert space when supplemented wit…
In the past years, quantum computers more and more have evolved from an academic idea to an upcoming reality. IBM's project IBM Q can be seen as evidence of this progress. Launched in March 2017 with the goal to provide access to quantum computers for a broad audience, this allowed users to conduct quantum experiments on a 5-qubit and, since June 2017, also on a 16-qubit quantum computer (called IBM QX2 and IBM QX3, respectively). Revised versions of these 5-qubit and 16-qubit quantum computers (named IBM QX4 and IBM QX5, respectively) are available since September 2017. In order to use these,…
A quantum circuit must be preprocessed before implementing on NISQ devices due to the connectivity constraint. Quantum circuit mapping (QCM) transforms the circuit into an equivalent one that is compliant with the NISQ device's architecture constraint by adding SWAP gates. The QCM problem asks the minimal number of auxiliary SWAP gates, and is NP-complete. The complexity of QCM with fixed parameters is studied in the paper. We give an exact algorithm for QCM, and show that the algorithm runs in polynomial time if the NISQ device's architecture is fixed. If the number of qubits of the quantum c…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical qubits, an important step in the compilation process is to map the circuit in such a way that all its gates are executable on the hardware. Existing solutions delivering optimal solutions to this task are severely challenged by the exponential complexity of the problem. In this paper, we show that the search space of the mapping problem can be limited drast…
Quantum computing is an emerging technology that has the potential to revolutionize fields such as cryptography, machine learning, optimization, and quantum simulation. However, a major challenge in the realization of quantum algorithms on actual machines is ensuring that the gates in a quantum circuit (i.e., corresponding operations) match the topology of a targeted architecture so that the circuit can be executed while, at the same time, the resulting costs (e.g., in terms of the number of additionally introduced gates, fidelity, etc.) are kept low. This is known as the quantum circuit mappi…
Unitary synthesis is an optimization technique that can achieve optimal multi-qubit gate counts while mapping quantum circuits to restrictive qubit topologies. Because synthesis algorithms are limited in scalability by their exponentially growing run time and memory requirements, application to circuits wider than 5 qubits requires divide-and-conquer partitioning of circuits into smaller components. In this work, we will explore methods to reduce the depth (program run time) and multi-qubit gate instruction count of wide (16-100 qubit) mapped quantum circuits optimized with synthesis. Reducing…
Quantum computers have recently made great strides and are on a long-term path towards useful fault-tolerant computation. A dominant overhead in fault-tolerant quantum computation is the production of high-fidelity encoded qubits, called magic states, which enable reliable error-corrected computation. We present the first detailed designs of hardware functional units that implement space-time optimized magic-state factories for surface code error-corrected machines. Interactions among distant qubits require surface code braids (physical pathways on chip) which must be routed. Magic-state facto…
Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the locality of the operators comes at the expense of increasing the Hilbert space with auxiliary degrees of freedom. In order to retrieve the lower-dimensional physical Hilbert space that represents fermionic degrees of freedom, one must satisfy a set of constraints. In this work, we introduce quantum circuits that exactly satisfy these stringent constraints. We demonstrate how maintaining locality allows one to carry out a Trotterized time-evolution with constant circuit depth per ti…
Quantum algorithms promise quadratic or exponential speedups for applications in cryptography, chemistry and material sciences. The topologies of today's quantum computers offer limited connectivity, leading to significant overheads for implementing such quantum algorithms. One-dimensional topology displacements that remedy these limits have been recently demonstrated for architectures based on Rydberg atoms, and they are possible in principle in photonic and ion trap architectures. We present the first optimal quantum circuit-to-architecture mapping algorithm that exploits such one-dimensiona…
One of the key compilation steps in Quantum Computing (QC) is to determine an initial logical to physical mapping of the qubits used in a quantum circuit. The impact of the starting qubit layout can vastly affect later scheduling and placement decisions of QASM operations, yielding higher values on critical performance metrics (gate count and circuit depth) as a result of quantum compilers introducing SWAP operations to meet the underlying physical neighboring and connectivity constraints of the quantum device. In this paper we introduce a novel qubit mapping approach, string-based qubit mappi…
