We propose a method to assist fault mitigation in quantum computation through the use of sensors co-located near physical qubits. Specifically, we consider using transition edge sensors co-located on silicon substrates hosting superconducting qubits to monitor for energy injection from ionizing radiation, which has been demonstrated to increase decoherence in transmon qubits. We generalize from these two physical device concepts and explore the potential advantages of co-located sensors to assist fault mitigation in quantum computation. In the simplest scheme, co-located sensors beneficially assist rejection of calculations potentially affected by environmental disturbances. Investigating the potential computational advantage further required development of an extension to the standard formulation of quantum error correction. In a specific case of the standard three-qubit, bit-flip quantum error correction code, we show that given a 20% overall error probability per qubit, approximately 90% of repeated calculation attempts are correctable. However, when sensor-detectable errors account for 45% of overall error probability, the use of co-located sensors uniquely associated with independent qubits boosts the fraction of correct final-state calculations to 96%, at the cost of rejecting 7% of repeated calculation attempts.
A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general framework to discuss the value of the available, non-ideal magic resources, relative to those ideally required. We single out a quantity, the Quantum-assisted Robustness of Magic (QRoM), which measures the overhead of simulating the ideal resource with the non-ideal ones through quasiprobability-based methods. This extends error mitigation techniques, originally…
In the era of quantum computing without full fault-tolerance, it is essential to suppress noise effects via the quantum error mitigation techniques to enhance the computational power of the quantum devices. One of the most effective noise-agnostic error mitigation schemes is the generalized quantum subspace expansion (GSE) method, which unifies various mitigation algorithms under the framework of the quantum subspace expansion. Specifically, the fault-subspace method, a subclass of GSE method, constructs an error-mitigated quantum state with copies of quantum states with different noise levels…
The schemes for fault-tolerant postselected quantum computation given in [Knill, Fault-Tolerant Postselected Quantum Computation: Schemes, http://arxiv.org/abs/quant-ph/0402171] are analyzed to determine their error-tolerance. The analysis is based on computer-assisted heuristics. It indicates that if classical and quantum communication delays are negligible, then scalable qubit-based quantum computation is possible with errors above 1% per elementary quantum gate.
Quantum computing (QC) and deep learning techniques have attracted widespread attention in the recent years. This paper proposes QC-based deep learning methods for fault diagnosis that exploit their unique capabilities to overcome the computational challenges faced by conventional data-driven approaches performed on classical computers. Deep belief networks are integrated into the proposed fault diagnosis model and are used to extract features at different levels for normal and faulty process operations. The QC-based fault diagnosis model uses a quantum computing assisted generative training p…
Medium-scale quantum devices that integrate about hundreds of physical qubits are likely to be developed in the near future. However, such devices will lack the resources for realizing quantum fault tolerance. Therefore, the main challenge of exploring the advantage of quantum computation is to minimize the impact of device and control imperfections without encoding. Quantum error mitigation is a solution satisfying the requirement. Here, we demonstrate an error mitigation protocol based on gate set tomography and quasiprobability decomposition. One- and two-qubit circuits are tested on a supe…
It is hard to achieve a theoretical quantum advantage on NISQ devices. Besides the attempts to reduce error using error mitigation and dynamical decoupling, small quantum error correction and fault-tolerant schemes that reduce the high overhead of traditional schemes have also been proposed. According to the recent advancements in fault tolerance, it is possible to minimize the number of ancillary qubits using flags. While implementing those schemes is still impossible, it is worthwhile to bridge the gap between the NISQ era and the FTQC era. Here, we introduce a benchmarking method to test fa…
The efficient decomposition of multi-controlled gates is a significant factor in quantum compiling, both in circuit depth and T-gate count. Recent work has demonstrated that qudits have the potential to reduce resource requirements from linear to logarithmic depth and to avoid fractional phase rotations. Here we argue, based on the scaling of decoherence in high-index states, that circuit depth is not the primary factor, and that both the choice of entangling gate and interaction network topology act together to determine the spread of errors and ultimate failure rate in a circuit. We further …
Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers. In this paper we show that codes for these systems can be derived from already known codes, and in particular this procedure removes the need for shared entanglement in entanglement-assisted quantum error-correcting codes, which is a result which could prove to be useful for fault-tolerant qudit, and even qubit, quantum computers.
We show a significant reduction of errors for an architecture of quantum annealers (QA) where bosonic modes mediate the interaction between qubits. These systems have a large redundancy in the subspace of solutions, supported by arbitrarily large bosonic occupations. We explain how this redundancy leads to a mitigation of errors when the bosonic modes operate in the ultrastrong coupling regime. Numerical simulations also predict a large increase of qubit coherence for a specific annealing problem with mediated interactions. We provide evidences that noise reduction occurs in more general types…
High-fidelity two-qubit entangling gates are essential building blocks for fault-tolerant quantum computers. Over the past decade, tremendous efforts have been made to develop scalable high-fidelity two-qubit gates with superconducting quantum circuits. Recently, an easy-to-scale controlled-phase gate scheme that utilizes the tunable-coupling architecture with fixed-frequency qubits [Phys. Rev. Lett. 125, 240502; Phys. Rev. Lett. 125, 240503] has been demonstrated with high fidelity and attracted broad interest. However, in-depth understanding of the underlying mechanism is still missing, prev…
It is vital to minimise the impact of errors for near-future quantum devices that will lack the resources for full fault tolerance. Two quantum error mitigation (QEM) techniques have been introduced recently, namely error extrapolation [Li2017,Temme2017] and quasi-probability decomposition [Temme2017]. To enable practical implementation of these ideas, here we account for the inevitable imperfections in the experimentalist's knowledge of the error model itself. We describe a protocol for systematically measuring the effect of errors so as to design efficient QEM circuits. We find that the effe…
In the early years of fault-tolerant quantum computing (FTQC), it is expected that the available code distance and the number of magic states will be restricted due to the limited scalability of quantum devices and the insufficient computational power of classical decoding units. Here, we integrate quantum error correction and quantum error mitigation into an efficient FTQC architecture that effectively increases the code distance and $T$-gate count at the cost of constant sampling overheads in a wide range of quantum computing regimes. For example, while we need $10^4$ to $10^{10}$ logical op…
Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, may have a wider range of uses, including information transmission, quantum simulation/computation, and fault-tolerance. These invite us to rethink QEC, in particular, about the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially near-term hybrid quantum-classical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (…
In this paper we introduce a universal operator theoretic framework for quantum fault tolerance. This incorporates a top-down approach that implements a system-level criterion based on specification of the full system dynamics, applied at every level of error correction concatenation. This leads to more accurate determinations of error thresholds than could previously be obtained. This is demonstrated both formally and with an explicit numerical example. The basis for our approach is the Quantum Computer Condition (QCC), an inequality governing the evolution of a quantum computer. We show that…
Error-Mitigated Hamiltonian Simulation: Complexity Analysis and Optimization for Near-Term and Early-Fault-Tolerant Quantum Computers
The University of Tokyo（东京大学）；Institute for Physics of Intelligence, The University of Tokyo（东京大学物理智能研究所）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；NTT Computer and Data Science Laboratories, NTT Inc.（日本电信电话公司计算机与数据科学实验室）；NTT Research Center for Theoretical Quantum Information, NTT Inc.（日本电信电话公司理论量子信息研究中心）
