In current quantum devices, physical qubits are not fully connected so that two-qubit interaction can only be performed between specific pairs of physical qubits. To execute a quantum circuit, it is necessary to transform it into a functionally equivalent one that respects the constraints imposed by the target architecture. Quantum circuit transformation inevitably introduces additional gates which reduces the fidelity of the circuit. Therefore, it is important that the transformation method completes the transformation with minimal overheads. Quantum circuit transformation consists of two steps, initial mapping and qubit routing, and here we propose a DEAR (Dynamically-Extract-and-Route) framework to solve the qubit routing problem. A key insight of DEAR is that by maintaining a sufficient lookahead ability all the time, we can make much better routing decisions while effectively controlling the runtime. In our DEAR framework, we periodically extract a subcircuit by identifying a set of remaining gates that should be executed earlier than the others, and then applies A* search to determine how to insert a sequence of additional SWAP and BRIDGE operations into the subcircuit to obtain a high quality routing solution with minimum number of additional gates. In this work, we consider the insertion of both SWAP and BRIDGE operations while most previous works deal with SWAP insertion only. We evaluate our approach with four benchmark sets with different characterization on IBM Tokyo. The experimental results show that our approach outperforms the state-of-the-art work utilizing SWAP and BRIDGE insertion with 19.1% and 77.5% average reduction in the number of additional gates and runtime, respectively, starting from the same initial mapping. We also performed experiments on larger quantum devices such as Google Sycamore and IBM Rochester both with 53 physical qubits that have largely different architectures from one another and from IBM Tokyo. Again, DEAR was much faster and required significantly less amount of additional gates.
In current quantum devices, physical qubits are not fully connected so that two-qubit interaction can only be performed between specific pairs of physical qubits. To execute a quantum circuit, it is necessary to transform it into a functionally equivalent one that respects the constraints imposed by the target architecture. Quantum circuit transformation inevitably introduces additional gates which reduces the fidelity of the circuit. Therefore, it is important that the transformation method completes the transformation with minimal overheads. Quantum circuit transformation consists of two steps, initial mapping and qubit routing, and here we propose a DEAR (Dynamically-Extract-and-Route) framework to solve the qubit routing problem. A key insight of DEAR is that by maintaining a sufficient lookahead ability all the time, we can make much better routing decisions while effectively controlling the runtime. In our DEAR framework, we periodically extract a subcircuit by identifying a set of remaining gates that should be executed earlier than the others, and then applies A* search to determine how to insert a sequence of additional SWAP and BRIDGE operations into the subcircuit to obtain a high quality routing solution with minimum number of additional gates. In this work, we consider the insertion of both SWAP and BRIDGE operations while most previous works deal with SWAP insertion only. We evaluate our approach with four benchmark sets with different characterization on IBM Tokyo. The experimental results show that our approach outperforms the state-of-the-art work utilizing SWAP and BRIDGE insertion with 19.1% and 77.5% average reduction in the number of additional gates and runtime, respectively, starting from the same initial mapping. We also performed experiments on larger quantum devices such as Google Sycamore and IBM Rochester both with 53 physical qubits that have largely different architectures from one another and from IBM Tokyo. Again, DEAR was much faster and required significantly less amount of additional gates.
Quantum computing is gaining more and more attention due to its huge potential and the constant progress in quantum computer development. IBM and Google have released quantum architectures with more than 50 qubits. However, in these machines, the physical qubits are not fully connected so that two-qubit interaction can only be performed between specific pairs of the physical qubits. To execute a quantum circuit, it is necessary to transform it into a functionally equivalent one that respects the constraints imposed by the target architecture. Quantum circuit transformation inevitably introduces additional gates which reduces the fidelity of the circuit. Therefore, it is important that the transformation method completes the transformation with minimal overheads. It consists of two steps, initial mapping and qubit routing. Here we propose a reinforcement learning-based model to solve the initial mapping problem. Initial mapping is formulated as sequence-to-sequence learning and self-attention network is used to extract features from a circuit. For qubit routing, a DEAR (Dynamically-Extract-and-Route) framework is proposed. The framework iteratively extracts a subcircuit and uses A* search to determine when and where to insert additional gates. It helps to preserve the lookahead ability dynamically and to provide more accurate cost estimation efficiently during A* search. The experimental results show that our RL-model generates better initial mappings than the best known algorithms with 12% fewer additional gates in the qubit routing stage. Furthermore, our DEAR-framework outperforms the state-of-the-art qubit routing approach with 8.4% and 36.3% average reduction in the number of additional gates and execution time starting from the same initial mapping.
Despite rapid advances in quantum computing technologies, the qubit connectivity limitation remains to be a critical challenge. Both near-term NISQ quantum computers and relatively long-term scalable quantum architectures do not offer full connectivity. As a result, quantum circuits may not be directly executed on quantum hardware, and a quantum compiler needs to perform qubit routing to make the circuit compatible with the device layout. During the qubit routing step, the compiler inserts SWAP gates and performs circuit transformations. Given the connectivity topology of the target hardware, there are typically multiple qubit routing candidates. The state-of-the-art compilers use a cost function to evaluate the number of SWAP gates for different routes and then select the one with the minimum number of SWAP gates. After qubit routing, the quantum compiler performs gate optimizations upon the circuit with the newly inserted SWAP gates.In this paper, we observe that the aforementioned qubit routing is not optimal, and qubit routing should not be independent on subsequent gate optimizations. We find that with the consideration of gate optimizations, not all of the SWAP gates have the same basis-gate cost. These insights lead to the development of our qubit routing algorithm, NASSC (Not All Swaps have the Same Cost). NASSC is the first algorithm that considers the subsequent optimizations during the routing step. Our optimization-aware qubit routing leads to better routing decisions and benefits subsequent optimizations. We also propose a new optimization-aware decomposition for the inserted SWAP gates. Our experiments show that the routing overhead compiled with our routing algorithm is reduced by up to 69.30% (21.30% on average) in the number of CNOT gates and up to 43.50% (7.61% on average) in the circuit depth compared with the state-of-the-art scheme, SABRE.
In the era of noisy intermediate-scale quantum (NISQ) computing, the limited connectivity between qubits is one of the common physical limitations faced by current quantum computing devices. Quantum circuit mapping methods transform quantum circuits into equivalent circuits that satisfy physical connectivity constraints by remapping logical qubits, making them executable. The optimization problem of quantum circuit mapping has NP-hard computational complexity, and existing heuristic mapping algorithms still have significant potential for optimization in terms of the number of quantum gates generated. To reduce the number of SWAP gates inserted during mapping, the solution space of the mapping problem is represented as a tree structure, and the mapping process is equivalent to traversing this tree structure. To effectively and efficiently complete the search process, a beam search framework (BSF) is proposed for solving quantum circuit mapping. By iteratively selecting, expanding, and making decisions, high-quality target circuits are generated. Experimental results show that this method can significantly reduce the number of inserted SWAP gates on medium to large circuits, achieving an average reduction of 44% compared to baseline methods, and is applicable to circuits of various sizes and complexities.
To execute a quantum program, it has to be compiled for execution on the target quantum processor. The program is first converted into a logical circuit composed of elementary gates supported by the target processor. Most often the logical circuit cannot be executed directly on the quantum processor due to the limited connectivity between the physical qubits of the processor. So, a quantum compiler needs to perform qubit routing by inserting auxiliary gates to execute operations like SWAP, MOVE, and BRIDGE in order to satisfy the connectivity constraint. Qubit routing yields a physical circuit that can be executed on the target processor. Finally, the physical circuit still has to be scheduled considering the gate delays and the control constraints imposed by the shared classical control electronics of the quantum processor. For noisy intermediate-scale quantum processors, it is important to minimize the latency of the final scheduled physical circuit. However, solving qubit routing without considering gate delays and control constraints will inevitably lead to suboptimal final results. Here we propose a control and timing-aware qubit routing algorithm, CTQr, considering gate delays and control constraints. Moreover, CTQr performs gate merging on the fly in order to minimize the final circuit latency. The experimental results show that CTQr outperforms the state-of-art approach with 11.2%, 8.8%, and 54.6% average reduction in the circuit latency, number of additional gates, and execution time, respectively.
Quantum circuits are typically represented by a (ordered) sequence of gates over a set of virtual qubits. During compilation, the virtual qubits of the gates are assigned to the physical qubits of the underlying quantum hardware, a step often referred to as the qubit assignment problem. To ensure that the resulting circuit respects hardware connectivity constraints, additional SWAP gates are inserted as needed, which is known as the qubit routing problem. Together, they are called the Qubit Mapping Problem (QMP), which is known to be NP-hard. A very common way to deal with the complexity of the QMP is to partition the sequence of gates into a sequence of gate groups (or layers). However, this imposes a couple of important restrictions: (1) SWAP gates can only be added between pairs of consecutive groups, and (2) all the gates belonging to a certain group have to be executed (in parallel) in the same time slot. The first one prevents gates to be re-arranged optimally, while the second one imposes a time discretization that practically ignores gate execution time. While this clearly reduces the size of the feasible space, little is still known about how much is actually lost by imposing a fixed layering when looking at the minimization of either the number of SWAPs or the makespan of the compiled circuit. In this paper, we present a flexible branch and bound algorithm for a generalized version of the QMP that either considers or ignores the gate layering and the gate execution time. The algorithm can find find proven optimal solutions for all variations of the QMP, but also offers a great platform for different heuristic algorithms. We present results on several benchmark sets of small quantum circuits, and we show how ignoring the layering can significantly improve some key performance indicators of the compiled circuit.
Quantum computing has already demonstrated great computational potential across multiple domains and has received more and more attention. However, due to the connectivity limitations of Noisy Intermediate-Scale Quantum (NISQ) devices, most of the quantum algorithms cannot be directly executed without the help of inserting SWAP gates. Nevertheless, more SWAP gates lead to a longer execution time and, inevitably, lower fidelity of the algorithm. To this end, this paper proposes an optimized qubit mapping algorithm based on a dynamic look-ahead strategy to minimize the number of SWAP gates inserted. Firstly, a heuristic algorithm is proposed based on maximizing physical qubit connectivity to generate the optimal initial qubit mapping, which reduces the need for logical qubit shifts during subsequent SWAP gate insertion. Secondly, in the form of directed acyclic graphs, we identify quantum gates that violate the constraints of physical coupling and insert SWAP gates to remap qubits, thereby overcoming the limitations of qubit interactions. Finally, the optimal SWAP gate insertion strategy is built by comparing the cost of different SWAP gate insertion strategies through a multi-window look-ahead strategy to reduce the number of SWAP gates inserted. The experimental results show that the strategy in this paper decreases the number of SWAP gate insertions and significantly reduces the depth of quantum circuits when performing qubit mapping compared with state-of-the-art methods.