Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit depth, as well as the ability to perform inverse quantum Fourier transform, making it expensive to implement on an early fault-tolerant quantum computer. We propose an alternative method to estimate the ground state energy of a Hamiltonian with Heisenberg-limited precision scaling, which employs a simple quantum circuit with one ancilla qubit, and a classical post-processing procedure. Besides the ground state energy, our algorithm also produces an approximate cumulative distribution function of the spectral measure, which can be used to compute other spectral properties of the Hamiltonian.
We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on concatenated codes. To realize fault-tolerant quantum computing, the fault-tolerant quantum protocols should be transformed into executable quantum circuits based on the nearest-neighbor interaction. Unlike topological codes that are defined based on local operations fundamentally, for the concatenated codes, it is possible to obtain the circuits composed of the local operations by applying the quantum circuit synthesis. However, by the existing quantum circuit synthesis develo…
I will give an overview of what I see as some of the most important future directions in the theory of fault-tolerant quantum computation. In particular, I will give a brief summary of the major problems that need to be solved in fault tolerance based on low-density parity check codes and in hardware-specific fault tolerance. I will then conclude with a discussion of a possible new paradigm for designing fault-tolerant protocols based on a space-time picture of quantum circuits.
A Flexible GKP-State-Embedded Fault-Tolerant Quantum Computation Configuration Based on a Three-Dimensional Cluster State
Shanxi University（山西大学）；State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（量子光学技术和器件国家重点实验室，山西大学）；College of Physics and Electronic Engineering, Shanxi University（山西大学物理电子工程学院）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
Comment on "Resilient Quantum Computation in Correlated Environments: A Quantum Phase Transition Perspective" and "Fault-tolerant Quantum Computation with Longe-range Correlated Noise"
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while operating the logical qubit, and are essential for realizing error suppression in practice. While fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. In this work, we experimenta…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable correct output of logical qubits under the presence of errors. However, strict requirements to encode qubits and operators render the implementation of a full fault-tolerant computation challenging even for the achievable noisy intermediate-scale quantum technology. Here, we experimentally demonstrate the existence of the threshold in a special fault-toleran…
Constant-space-overhead fault-tolerant quantum input/output and communication
Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo（滑铁卢大学量子计算研究所与组合优化系）；Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo（东京大学信息理工学研究科计算机科学系）
A Three-Layer Architecture for Fault-Tolerant Quantum Computing
Center on Frontiers of Computing Studies, Peking University（前沿计算研究中心，北京大学）；School of Computer Science, Peking University（计算机学院，北京大学）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
The quantum logic gates used in the design of a quantum computer should be both universal, meaning arbitrary quantum computations can be performed, and fault-tolerant, meaning the gates keep errors from cascading out of control. A number of no-go theorems constrain the ways in which a set of fault-tolerant logic gates can be universal. These theorems are very restrictive, and conventional wisdom holds that a universal fault-tolerant logic gate set cannot be implemented natively, requiring us to use costly distillation procedures for quantum computation. Here, we present a general framework for…
