Recent Research Highlight
1.Topological quantum devices and Majorana zero modes
How to verify and confirm Majorana zero modes?
The potential system for realizing Majorana zero modes and topological quantum computing has garnered widespread attention. After a decade of continuous research, the current focus of scientific debate is how to experimentally distinguish between Majorana zero modes and Andreev bound states, both of which can manifest as zero-bias conductance peaks during transport. We have developed a new method for distinguishing Andreev bound states, which aids in the future experimental verification of Majorana zero modes.
By introducing a dissipative resistor next to traditional nanowire devices, tunneling electrons within the device will excite plasmons in the dissipative resistor, thereby inducing an "environmental Coulomb blockade". This many-body interaction causes renormalization of the electron's tunneling within the device. In our previous study in 2013, we demonstrated that the presence of a dissipative resistor induces the splitting of zero-bias conductance peaks attributed to Andreev bound states at low temperatures, while the existence of Majorana zero bias conductance peaks remains unaffected quantitively. The latest work in 2022 further quantifies the scaling behaviors under different conditions. The fundamental principle entails harnessing the renormalization effects arising from the interactions between tunneling electrons and environmental bosons, leading to distinct scaling behaviors and temperature-voltage dependencies observed in Majorana transport signals compared to transport signals originating from other topologically trivial states.
How to verify the non-local nature of topological devices?
Topological states offer a non-local framework for quantum information storage through their degenerate topological ground states. This non-locality constitutes a key aspect for the topological protection of quantum information. Through the fusion and braiding of non-Abelian anyons present in topological states, researchers can verify their non-local properties. However, the state-of-the-art techniques for fusion and braiding experiments exceed the technological capabilities. Therefore, there is a pressing need for simpler experimental techniques, such as quantum transport detection, to verify those non-local properties of topological quantum devices.
We proposed a straightforward approach to detect non-local properties of Majorana zero modes in topological superconducting islands. A novel coherent non-local electron transport process, termed "double Majorana-assisted teleportation," exhibits anomalous universal conductance behavior. The conductance shows a transition from T^6 to T^3 power-law at low energies. Above the Andreev bound state energy, the conductance decreases with temperature, following a 1/T behavior. This non-monotonic temperature dependence distinguishes it from conventional local transport, confirming the non-local nature of remote transport in topological quantum devices.
Related Publications: Yiru Hao, Gu Zhang, Donghao Liu, Dong E. Liu, Nature Communications 13, 6699 (2022)
2. Decoherence and noise in quantum computations
Noise-resilient phase estimation with randomized compiling
Quantum phase estimation is a key step in many quantum algorithms, such as Shor's algorithm for factorization, the HHL algorithm for solving systems of linear equations, and the estimation of Hamiltonian energy spectra. However, phase estimation algorithms based on quantum Fourier transform require many auxiliary qubits and need quantum error correction to resist noise. Both of these requirements are difficult to achieve in the current era of noisy intermediate-scale (NISQ) quantum computing. In order to reduce qubit consumption, a phase estimation that does not require a controlled unitary operator was proposed by S. Kimmel, G. H. Low, and T. J. Yoder. However, this algorithm is still affected by noise during actual operation. To get meaningful results, it is necessary to develop corresponding error mitigation techniques.
We developed a novel error mitigation method tailored for control-free phase estimation in quantum computing. We have confirmed through theoretical proof that the phases of a unitary operator are immune to noise channels, provided the channels have only Hermitian Kraus operators under first-order correction. This revelation enables the identification of certain benign types of noise specifically for phase estimation. By additionally incorporating a randomized compiling protocol [Proposed by J. J. Wallman and J. Emerson], we can effectively transformed generic noise in the phase estimation circuits into stochastic Pauli noise. The significance of this transformation is that it aligns with the conditions of their theorem, thereby facilitating a noise-resilient phase estimation without any quantum resource overhead.
Related Publications: Yanwu Gu, Yunheng Ma, Nicolo Forcellini, Dong E. Liu, Phys. Rev. Lett. 130, 250601 (2023)
Channel Spectrum Benchmarking
Noise is the primary hindrance to the evolution of scalable quantum computation. Understanding and mitigating this noise through quantum benchmarking is crucial for developing advanced quantum processors. The current benchmarking protocols have had their limitations, mainly restricted to a particular set of quantum gates or unable to describe the individual target gate’s performance accurately. However, current benchmarking methods are either limited to a specific subset of quantum gates or cannot directly describe the performance of the individual target gate. To overcome these limitations, we propose channel spectrum benchmarking (CSB), a method to infer the noise properties of the target gate, including process fidelity, stochastic fidelity, and some unitary parameters, from the eigenvalues of its noisy channel.
We compare our CSB protocol with other benchmarking protocols under three aspects: (1) what gates they can benchmark; (2) what type of fidelity they actually measure; (3) under what conditions they can be scalable to many-qubit systems.
The procedures of channel spectrum benchmarking protocol.
CSB allows for the precise analysis of process fidelity, stochastic fidelity, and various unitary parameters by examining the eigenvalues of a gate's noisy channel. Distinctively, CSB can benchmark a wide array of universal gates and is scalable to multiple qubit systems, making it a versatile tool for various quantum computing applications. Its methodology, involving a specially chosen initial state and control-free phase estimation circuits, ensures simplified data processing and accurate results, ultimately aiding in the development of robust and advanced quantum processors.
Related Publications: Yanwu Gu, Wei-Feng Zhuang, Xudan Chai, Dong E. Liu, Nature Communications 14, 5880 (2023)
Coherent Deviations and error threshold theorem in realistic quantum error corrections
A key concept of fault tolerance and QEC is the “error threshold theorem”, which states that if the physical error rate is below an error threshold, quantum computation with arbitrary logical accuracy can be implemented in the noisy quantum devices. Although enjoying widespread acceptance within the quantum computing community, this theorem can only be considered well-established if the quantum devices are solely susceptible to independent stochastic noise of a classical nature. However, actual quantum devices suffer from imperfect calibration and control in gate operations, causing quantum deviation or coherent noise, which is a more practical type of noise. On the other hand, understanding this quantum or coherent error in QEC is exceedingly challenging due to the lack of analytical and numerical tools. This motivates us to develop a theoretical framework to study the elusive and unavoidable coherent error problems in QEC and establish a more practical error threshold theorem.
Here, we consider topological surface code, with both stochastic Pauli noise and coherent noise on the multi-qubit entanglement gates during both code space preparation and stabilizer checks. We map a multi-round error detection protocol to a 3D lattice gauge theory coupled to a 2D lattice gauge model [1]. Therefore, for the first time, we provide a theoretical tool to study both the coherent and the stochastic error problems for QEC and threshold theorem. Remarkably, our findings indicate that in the limit of large code distance [Middle Figure], imperfect initial state preparation may result in the failure of QEC even below a theoretical threshold, contradicting the commonly held notion that logical errors should be completely suppressed [Left Figure]. What is not excessively frustrating is that: With a finite code size , the effectiveness of the pragmatic QEC remains viable when the error rate associated with the state preparation is below a size-dependent crossover scale [Right Figure]. For the first time, we obtain a practical error threshold theorem which do not follow the commonly held notion, notably identifying that coherent deviation in the initial QEC state preparations could cause a critical problem.
Related Publications: Yuanchen Zhao, Dong E. Liu, "Lattice gauge theory and topological quantum error correction with quantum deviations in the state preparation and error detection", arXiv:2301.12859 (2023)
3. Dissipation and noise in non-equilibrium quantum systems
Unified Theoretical Framework connecting Measurements and Disorders
In recent years, there has been a growing fascination with many-body systems and random circuits subjected to measurements, commonly referred to as monitored quantum systems. Notably, considerable attention has been devoted to investigating the phenomenon of subsystem entanglement transition within such systems. Nonetheless, the existing body of research primarily centers on this specific aspect, while other properties of monitored quantum systems remain largely unexplored. Consequently, the comprehensive understanding of these systems and the identification of potential applications hinge upon unraveling the currently uncharted characteristics. Moreover, a significant gap persists in establishing the intrinsic relationship between entanglement transitions induced by measurements and those arising from disorders, despite the resemblances exhibited by both phenomena.
The unification of measurements and disorders, seemingly distinct concepts, is achieved through the adoption of the Keldysh nonlinear sigma model as a theoretical framework. This unexpected and pioneering unification, elucidated by the functional Keldysh field theory, represents a significant advancement in the field. By incorporating the perspectives and methodologies of disordered systems, a well-established research domain since Anderson's seminal work, we are empowered to investigate monitored systems more comprehensively.
Related Publications: Qinghong Yang, Yi Zuo, Dong E. Liu, "Keldysh Nonlinear Sigma Model for a Free-Fermion Gas under Unconditional Continuous Measurements", Phys. Rev. Research 5, 033174 (2023) Link
Dissipative Floquet Majorana Modes in Proximity-Induced Topological Superconductors
Floquet engineering manipulates quantum systems using periodic driving, holding promise for realizing topological nontrivial band structures and exotic quantum states. However, system-bath couplings introduce complex statistical behaviors in open Floquet systems, necessitating self-consistent treatments and consideration of realistic conditions to comprehend such elusive nonequilibrium systems. For instance, periodically driven topological superconductors, such as Floquet Majorana modes, typically rely on proximity-induced effects. However, under external driving, it becomes essential to treat the superconductor as an external bath, contributing both Cooper pair tunneling and dissipative effects, leading to nonequilibrium steady states. Those concerns raise questions about the validity of the Floquet picture under interplay between nonequilibrium conditions and strong dissipations.
We study a realistic Floquet topological superconductor, a periodically driven nanowire proximitized to an equilibrium s-wave superconductor. In particular, we find that the Floquet Majorana zero and π modes become dissipative, and can no longer be simply described by the Floquet topological band theory. We also propose an effective model to simplify the calculation of the lifetime of these Floquet Majoranas and find that the lifetime can be engineered by the external driving field.
Related Publications: Zhesen Yang, Qinghong Yang, Jiangping Hu, Dong E. Liu, Phys. Rev. Lett. 126, 086801 (2021)