論文

Equilibration plays a fundamental role in our understanding of statistical mechanics and the long-time dynamics of many-body systems. In quantum systems, the route to equilibration is intimately related to level repulsion and quantum signatures of chaos that are encoded in their unitary evolution. Chaotic quantum systems exhibit level statistics characteristic of ensembles of random matrices. In this work, we demonstrate that single-particle chaos leads to equilibration of many noninteracting photons. We show that the underlying mechanisms for equilibration are operator spreading and quantum interference. More specifically, we demonstrate that the unitary dynamics of a general Floquet system implemented using single-mode phase shifters and multiport beamsplitters leads to equilibration of photons. We propose a realistic photonic implementation of the multiparticle kicked rotor, which is a Floquet system that we use as 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 2-D 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 article, 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 PlanarRectilinear3SAT.

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.

Connecting multiple processors via quantum interconnect technologies could help overcome scalability issues 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.

Fault-tolerant quantum computers are expected to be offered as cloud services due to their significant resource and infrastructure requirements. Quantum multiprogramming, which runs multiple quantum jobs in parallel, is a promising approach to maximize the utilization of such systems. A key challenge in this setting is the need for an online scheduler capable of handling jobs submitted dynamically while other programs are already running. In this study, we formulate the online job scheduling problem for fault-tolerant quantum computing systems based on lattice surgery and propose an efficient scheduler to address it. To meet the responsiveness required in an online environment, our scheduler approximates lattice surgery programs, originally represented as polycubes, by using simpler cuboid representations. This approximation enables efficient scheduling while improving overall throughput. In addition, we incorporate a defragmentation mechanism into the scheduling process, demonstrating that it can further enhance the utilization of quantum processing unit.

Quantum error correction is an indispensable tool for quantum technologies. However, its implementation requires significant physical resources. Here, we reduce the number of two-qubit gates required to implement an error correction code using quantum multiplexing.

Quantum error correction is an indispensable tool for quantum technologies. However, its implementation requires significant physical resources. Here, we reduce the number of two-qubit gates required to implement an error correction code using quantum multiplexing.

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-correcting codes are one important technique to address this issue. In particular, the quantum Reed-Solomon codes well suited to communication tasks as photons can naturally carry more than one qubit of information. 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 multicontrolled gates using fewer controlled-x (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-correcting codes and quantum algorithms, including Grovers and quantum walks.