Connecting multiple processors via quantum interconnect technologies could help to overcome issues of scalability in single-processor quantum computers. Transmission via these interconnects can be performed more efficiently using quantum multiplexing, where information is encoded in high-dimensional photonic degrees of freedom. We explore the effects of multiplexing on logical error rates in surface codes and hypergraph product codes. We show that, although multiplexing makes loss errors more damaging, assigning qubits to photons in an intelligent manner can minimize these effects, and the ability to encode higher-distance codes in a smaller number of photons can result in overall lower logical error rates. This multiplexing technique can also be adapted to quantum communication and multimode quantum memory with high-dimensional qudit systems.

Boson sampling is a paradigmatic example of a task that can be performed by a quantum photonic computer yet is hard for digital classical computers. In a typical boson sampling experiment, the scattering amplitude is determined by the permanent of a submatrix of a unitary drawn from an ensemble of random matrices. Random matrix theory plays a very important role in quite diverse fields while at the same time being intimately related to quantum signatures of chaos. Within this framework, a chaotic quantum system exhibits level statistics characteristic of ensembles of random matrices. Such quantum signatures are encoded in the unitary evolution and so in this work we combine the dynamics of chaotic systems with boson sampling. One of the key results of our work is that we demonstrate the intimate relation between out-of-time-order correlators and boson sampling. We show that the unitary dynamics of a Floquet system may be exploited to perform sampling tasks with identical particles using single-mode phase shifters and multiport beamsplitters. At the end of our paper propose a photonic implementation of the multiparticle kicked rotor, which provides a concrete example of our general approach.

Large-scale quantum information processing requires the use of quantum error correcting codes to mitigate the effects of noise in quantum devices. Topological error-correcting codes, such as surface codes, are promising candidates as they can be implemented using only local interactions in a two-dimensional array of physical qubits. Procedures such as defect braiding and lattice surgery can then be used to realize a fault-tolerant universal set of gates on the logical space of such topological codes. However, error correction also introduces a significant overhead in computation time, the number of physical qubits, and the number of physical gates. While optimizing fault-tolerant circuits to minimize this overhead is critical, the computational complexity of such optimization problems remains unknown. This ambiguity leaves room for doubt surrounding the most effective methods for compiling fault-tolerant circuits for a large-scale quantum computer. In this paper, we show that the optimization of a special subset of braided quantum circuits is NP-hard by a polynomial-time reduction of the optimization problem into a specific problem called Planar Rectilinear 3SAT.

Various physical constraints limit the number of qubits that can be implemented in a single quantum processor, and thus it is necessary to connect multiple quantum processors via quantum interconnects. While several compiler implementations for interconnected quantum computers have been proposed, there is no suitable representation as their compilation target. The lack of such representation impairs the reusability of compiled programs and makes it difficult to reason formally about the complicated behavior of distributed quantum programs. We propose InQuIR, an intermediate representation that can express communication and computation on distributed quantum systems. InQuIR has formal semantics that allows us to describe precisely the behaviors of distributed quantum programs. We give examples written in InQuIR to illustrate the problems arising in distributed programs, such as deadlock. We present a roadmap for static verification using type systems to deal with such a problem. We also provide software tools for InQuIR and evaluate the computational costs of quantum circuits under various conditions. Our tools are available at this URL.

The quantum extreme reservoir computation (QERC) is a versatile quantum neural network model that combines the concepts of extreme machine learning with quantum reservoir computation. Key to QERC is the generation of a complex quantum reservoir (feature space) that does not need to be optimized for different problem instances. Originally, a periodically driven system Hamiltonian dynamics was employed as the quantum feature map. In this work we capture how the quantum feature map is generated as the number of time-steps of the dynamics increases by a method to characterize unitary matrices in the form of weighted networks. Furthermore, to identify the key properties of the feature map that has sufficiently grown, we evaluate it with various weighted network models that could be used for the quantum reservoir in image classification situations. At last, we show how a simple Hamiltonian model based on a disordered discrete time crystal with its simple implementation route provides nearly optimal performance while removing the necessity of programming of the quantum processor gate by gate.

Quantum communication technologies will play an important role in quantum information processing in the near future as we network devices together. However, their implementation is still a challenging task due to both loss and gate errors. Quantum error correction codes are one important technique to address this issue. In particular, the Quantum Reed-Solomon codes are known to be quite efficient for quantum communication tasks. The high degree of physical resources required, however, makes such a code difficult to use in practice. A recent technique called quantum multiplexing has been shown to reduce resources by using multiple degrees of freedom of a photon. In this work, we propose a method to decompose multi-controlled gates using fewer CX gates via this quantum multiplexing technique. We show that our method can significantly reduce the required number of CX gates needed in the encoding circuits for the quantum Reed-Solomon code. Our approach is also applicable to many other quantum error correction codes and quantum algorithms, including Grovers and quantum walks.

NISQ (Noisy, Intermediate-Scale Quantum) computing requires error mitigation to achieve meaningful computation. Our compilation tool development focuses on the fact that the error rates of individual qubits are not equal, with a goal of maximizing the success probability of real-world subroutines such as an adder circuit. We begin by establishing a metric for choosing among possible paths and circuit alternatives for executing gates between variables placed far apart within the processor and test our approach on two IBM 20-qubit systems named Tokyo and Poughkeepsie. We find that a single-number metric describing the fidelity of individual gates is a useful but imperfect guide. Our compiler uses this subsystem and maps complete circuits onto the machine using a beam search-based heuristic that will scale as processor and program sizes grow. To evaluate the whole compilation process, we compiled and executed adder circuits, then calculated the Kullback–Leibler divergence (KL-divergence, a measure of the distance between two probability distributions). For a circuit within the capabilities of the hardware, our compilation increases estimated success probability and reduce KL-divergence relative to an error-oblivious placement.

As the execution speed of the atomic operations of quantum computation in many physical systems is slower than that in classical computation, large-scale quantum computation is required to achieve a computational advantage. Fault-tolerant quantum computation, one of the frameworks for realizing large-scale quantum computation, introduces spatial overhead, including a large number of physical qubits, and temporal overhead, including logical gates and magic state distillation. In addition to these, costs related to classical computational resources for a system software are non-negligible. In this talk, we will give an overview of the system software configuration required for large-scale quantum computers. Then, we will discuss the results and prospects of resource optimization in distributed quantum computing systems with quantum interconnects, a promising approach for scaling up quantum computers. As a further developmental topic, we deal with formal language for distributed quantum computing; we show a method for detecting deadlocks in quantum programs with a type system.

In recent years, the development of quantum computers has accelerated, and the number of qubits implemented on a quantum processor is rapidly increasing. In order to handle such processors, there is a growing trend to implement system software and language processing systems for quantum computers. This has revealed the practical resources required to implement quantum algorithms and quantum communication protocols that have been proposed theoretically, as well as efficient ways to handle quantum circuits. Furthermore, quantum programming contests are now being held using quantum programming SDKs such as Qiskit, enabling a deeper understanding of quantum computation through small-scale implementations of algorithms. In addition, by describing various quantum applications as concrete code, it has become clear what functions a language processor for quantum computers should have and even what kind of computational difficulties it may face. In this presentation, in addition to results and issues related to language processing systems for quantum computers, I will introduce InQuIR, an intermediate representation for distributed quantum computation[1].
[1] Shin Nishio and Ryo Wakizaka. (2022). InQuIR: Intermediate Representation for Interconnected Quantum Computers. In The 4th International Workshop on Quantum Resource Estimation (QRE2022).

Various physical constraints limit the number of qubits that can be implemented in a single quantum processor, and thus it is necessary to connect multiple quantum processors via quantum interconnects. While several compiler implementations for interconnected quantum computers have been proposed, there is no suitable programming language as their compilation target. We propose InQuIR, an intermediate language that can express communication and computation on distributed systems. InQuIR allows various compilation strategies to be evaluated under the same configuration and enhances the reusability of programs. Furthermore, InQuIR facilitates the introduction of static program analysis, such as type systems, to verify that a given program does not have specific program errors and bugs. We also discuss the challenges inherent in quantum programs running on distributed systems, such as failure of communication because of qubit memory exhaustion.
Index Terms: Quantum Interconnect, Quantum Computer Cluster, Distributed Quantum Computation, Quantum Programming Language

Large-scale quantum information processing requires using error-correcting codes to achieve fault-tolerant quantum computation (FTQC). However, FTQC has significant resource requirements. Optimization of FTQC circuits is therefore an important problem, but its computational complexity in common FTQC models, specifically for braided surface code quantum computation, remains unknown. This ambiguity leaves room for doubt surrounding the most efficient circuits and compilation methods. In this paper, we show that the optimization of a special subset of braided quantum circuits is NP-hard and that as a result so too is the problem of braided circuit optimization more generally.
Keywords: Fault-tolerant quantum computation, Quantum circuit optimization, Surface code, Braiding Circuits, Computational Complexity, NP-complete, Planar rectilinear 3SAT