Current fault-tolerant quantum computer (FTQC) architectures utilize several encoding techniques to enable reliable logical operations with restricted qubit connectivity. However, such logical operations demand additional memory overhead to ensure fault tolerance. Since the main obstacle to practical quantum computing is the limited qubit count, our primary mission is to design floorplans that can reduce memory overhead without compromising computational capability. Despite extensive efforts to explore FTQC architectures, even the current state-of-the-art floorplan strategy devotes 50% of memory space to this overhead, not to data storage, to guarantee unit-time random access to all logical qubits. In this paper, we propose an FTQC architecture based on a novel floorplan strategy, Load/Store Quantum Computer Architecture (LSQCA), which can achieve almost 100% memory density. The idea behind our architecture is to separate the whole memory regions into small computational space called Computational Registers (CR) and space-efficient memory space called Scan-Access Memory (SAM). We define an instruction set for these abstract structures and provide concrete designs named point-SAM and line-SAM architectures. With this design, we can improve the memory density by allowing variable-latency memory access while concealing the latency with other bottlenecks. We also propose optimization techniques to exploit properties of quantum programs observed in our static analysis, such as access locality in memory reference timestamps. Our numerical results indicate that LSQCA successfully leverages this idea. In a resource-restricted situation, a specific benchmark shows that we can achieve approximately 90% memory density with 5% increase in the execution time compared to a conventional floorplan, which achieves at most 50% memory density for unit-time random access. Our design is defined as an abstract form, making this principle ubiquitous and applicable to a wide range of quantum devices, qubit-connectivity configurations, and error-correcting codes.

Abstract Fault-tolerant quantum computation using lattice surgery can be abstracted as operations on graphs, wherein each logical qubit corresponds to a vertex of the graph, and multi-qubit measurements are accomplished by connecting the vertices with paths between them. Operations attempting to connect vertices without a valid path will result in abnormal termination. As the permissible paths may evolve during execution, it is necessary to statically verify that the execution of a quantum program can be completed. This paper introduces a type-based method to statically verify that well-typed programs can be executed without encountering halts induced by surgery operations. Alongside, we present $$\mathcal {Q}_{LS}$$ Q LS , a first-order quantum programming language to formalize the execution model of surgery operations. Furthermore, we provide a type checking algorithm by reducing the type checking problem to the offline dynamic connectivity problem.

Large error rates of quantum bits (qubits) are one of the main difficulties in the development of quantum computing. Performing quantum error correction (QEC) with surface codes is considered the most promising approach to reduce the error rates of qubits effectively. To perform error correction, we need an error-decoding unit, which estimates errors in the noisy physical qubits repetitively, to create a robust logical qubit. While complicated graph-matching problems must be solved within a strict time restriction for the error decoding, several hardware implementations that satisfy the restriction at a large code distance have been proposed.

Due to the high error rate of a qubit, detecting and correcting errors on it is essential for fault-tolerant quantum computing (FTQC). Surface code (SC) associated with its decoding algorithm is one of the most promising quantum error correction (QEC) methods because it has high fidelity and requires only nearest neighbor qubits connectivity. To realize FTQC, we need a decoder circuit capable of not only QEC in a 3-D lattice to deal with errors in measurement on ancillary qubits but also quantum operations on logically constructed qubits. Whereas several methods to perform logical operations on SC, such as lattice surgery (LS), are known, no practical decoders supporting them have been proposed yet.One of the most promising QC implementations today is made up of superconducting qubits that are located in a cryogenic environment. To reduce the hardware complexity of QC and latency of QEC, we are supposed to perform QEC in a cryogenic environment. Hence a power-efficient decoder is required due to the limited power budget inside a dilution refrigerator.In this paper, we propose an online-QEC algorithm that supports LS with a practical decoder circuit, as well as a new FTQC architecture. We design a key building block of the proposed architecture with a hybrid of SFQ- and Cryo-CMOS-based digital circuits and evaluate it with a SPICE-level simulation. Each logic element includes about 2400 Josephson junctions, and power consumption is estimated to be 2.07 μW when operating with a 2 GHz clock frequency. We evaluate the decoder performance by a quantum error simulator for an essential operation of LS with code distances up to 11, and it achieves a 0.6% accuracy threshold. In an LS-based architecture further supporting a magic-state distillation protocol, which is expected to run for near-term universal quantum computing, we evaluate the QEC performance and power consumption of the architecture and show that it is practical to be operated in 4-K temperature region of a dilution refrigerator.

Demonstrating small error rates by integrating quantum error correction (QEC) into an architecture of quantum computing is the next milestone towards scalable fault-tolerant quantum computing (FTQC). Encoding logical qubits with superconducting qubits and surface codes is considered a promising candidate for FTQC architectures. In this paper, we propose an FTQC architecture, which we call Q3DE, that enhances the tolerance to multi-bit burst errors (MBBEs) by cosmic rays with moderate changes and overhead. There are three core components in Q3DE: in-situ anomaly DEtection, dynamic code DEformation, and optimized error DEcoding. In this architecture, MBBEs are detected only from syndrome values for error correction. The effect of MBBEs is immediately mitigated by dynamically increasing the encoding level of logical qubits and re-estimating probable recovery operation with the rollback of the decoding process. We investigate the performance and overhead of the Q3DE architecture with quantum-error simulators and demonstrate that Q3DE effectively reduces the period of MBBEs by 1000 times and halves the size of their region. Therefore, Q3DE significantly relaxes the requirement of qubit density and qubit chip size to realize FTQC. Our scheme is versatile for mitigating MBBEs, i.e., temporal variations of error properties, on a wide range of physical devices and FTQC architectures since it relies only on the standard features of topological stabilizer codes.

Due to the low error tolerance of a qubit, detecting and correcting errors on it is essential for fault-tolerant quantum computing. Surface code (SC) associated with its decoding algorithm is one of the most promising quantum error correction (QEC) methods. % One of the challenges of QEC is its high complexity and computational demand. QEC needs to be very power-efficient since the power budget is limited inside of a dilution refrigerator for superconducting qubits by which one of the most successful quantum computers (QCs) is built. In this paper, we propose an online-QEC algorithm and its hardware implementation with SFQ-based superconducting digital circuits. We design a key building block of the proposed hardware with an SFQ cell library and evaluate it by the SPICE-level simulation. Each logic element is composed of about 3000 Josephson junctions and power consumption is about 2.78 uW when operating with 2 GHz clock frequency which meets the required decoding speed. Our decoder is simulated on a quantum error simulator for code distances 5 to 13 and achieves a 1.0% accuracy threshold.