The task of finding a correctable encoding that protects against some physical quantum process is in general hard. Two main obstacles are that an exponential number of experiments are needed to gain complete information about the quantum process, and known algorithmic methods for finding correctable encodings involve operations on exponentially large matrices. However, we show that in some cases it is possible to find such encodings with only partial information about the quantum process. Such useful partial information can be systematically extracted by averaging the channel under the action of a set of unitaries in a process known as "twirling". In this paper we prove that correctable encodings for a twirled channel are also correctable for the original channel. We investigate the particular case of twirling over the set of Pauli operators and qubit permutations, and show that the resulting quantum operation can be characterized experimentally in a scalable manner. We also provide a postprocessing scheme for finding unitarily correctable codes for these twirled channels which does not involve exponentially large matrices.
To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in p…
By interpreting the well-known, qualitative criteria for the existence of quantum error correction (QEC) codes by Knill and Laflamme from a quantitative perspective, we propose a figure of merit for assessing a QEC scheme based on the average fidelity between codewords. This enables us to quantify the performance of a protocol as a whole, including errors beyond the correctable set. Various examples are calculated for photonic qubit codes dealing with the experimentally relevant case of photon loss, demonstrating the advantages of the new measure. In the context of continuous-variable QEC, our…
We propose a new quantum-computing scheme using ultracold neutral ytterbium atoms in an optical lattice. The nuclear Zeeman sublevels define a qubit. This choice avoids the natural phase evolution due to the magnetic dipole interaction between qubits. The Zeeman sublevels with large magnetic moments in the long-lived metastable state are also exploited to address individual atoms and to construct a controlled-multiqubit gate. Estimated parameters required for this scheme show that this proposal is scalable and experimentally feasible.
Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons
Korea Institute of Science and Technology (KIST)（韩国科学技术院）；Seoul National University（首尔大学）；Korea University（高丽大学）；The University of Sydney（悉尼大学）；Pritzker School of Molecular Engineering, The University of Chicago（芝加哥大学普里茨克分子工程学院）
Universität Innsbruck（因斯布鲁克大学）；University of Gdańsk（格但斯克大学）；The University of Queensland（昆士兰大学）；Macquarie University（麦考瑞大学）；Alpine Quantum Technologies GmbH（阿尔卑斯量子技术有限公司）；Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
We study experimentally demonstrated single-electron ${}^{12}$C CNT QD with significant spin-orbit interaction as a scalable quantum computer candidate. Both electron spin and orbital angular momentum can serve as a logical qubit for quantum processing. We introduce macroscopic quantum memory for the system in a form of injected either magnetic or spin carrying atomic ensemble into the nanotube. CNT provides with a stable atomic trap in finite temperature and with one-dimensional nuclear spin lattice in an external magnetic field. The electron is coupled to the atomic ensemble through either m…
The Kitaev honeycomb model is a system allowing for experimentally realisable quantum computation with topological protection of quantum information. Practical implementation of quantum information processing typically relies on adiabatic, i.e. slow dynamics. Here we show that the restriction to adiabatic dynamics can be overcome with optimal control theory, enabled by an extension of the fermionization of the Kitaev honeycomb model to the time-dependent case. Moreover we present a quantum control method that is applicable to large lattice models due to sub-exponential scaling.
Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and a well-defined experimental procedure for estimating the distinguishability measure. Here, we propose the average measurement fidelity and error between quantum measurements as distinguishability measures. We present protocols for obtaining bounds on these quantities that are both estimable using experimentally accessible quantities and scalable in the size …
Scalable high-fidelity and near-deterministic preparation of large photon-number states
College of Physics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学物理学院）；China Mobile (Suzhou) Software Technology Co., Ltd.（中国移动（苏州）软件技术有限公司）
We experimentally demonstrate novel structures for the realisation of registers of atomic qubits: We trap neutral atoms in one and two-dimensional arrays of far-detuned dipole traps obtained by focusing a red-detuned laser beam with a microfabricated array of microlenses. We are able to selectively address individual trap sites due to their large lateral separation of 125 mu m. We initialize and read out different internal states for the individual sites. We also create two interleaved sets of trap arrays with adjustable separation, as required for many proposed implementations of quantum gate…
Creation of entanglement is considered theoretically and numerically in an ensemble of spin chains with dipole-dipole interaction between the spins. The unwanted effect of the long-range dipole interaction is compensated by the optimal choice of the parameters of radio-frequency pulses implementing the protocol. The errors caused by (i) the influence of the environment,(ii) non-selective excitations, (iii) influence of different spin chains on each other, (iv) displacements of qubits from their perfect locations, and (v) fluctuations of the external magnetic field are estimated analytically an…
We propose a floating tunable coupler that does not rely on direct qubit-qubit coupling capacitances to achieve the zero-coupling condition. We show that the polarity of the qubit-coupler couplings can be engineered to offset the otherwise constant qubit-qubit coupling and attain the zero-coupling condition when the coupler frequency is above or below the qubit frequencies. We experimentally demonstrate these two operating regimes of the tunable coupler by implementing symmetric and asymmetric configurations of the coupler's superconducting pads with respect to the qubits. Such a floating tuna…
Atomic ensembles, comprising clouds of atoms addressed by laser fields, provide an attractive system for both the storage of quantum information, and the coherent conversion of quantum information between atomic and optical degrees of freedom. In a landmark paper, Duan et al. (DLCZ) [1] showed that atomic ensembles could be used as nodes of a quantum repeater network capable of sharing pairwise quantum entanglement between systems separated by arbitrarily large distances. In recent years, a number of promising experiments have demonstrated key aspects of this proposal [2-7]. Here, we describe …
We propose and experimentally demonstrate a new scheme for measuring high-dimensional phase states using a two-photon interference technique, which we refer to as quantum-controlled measurement. Using this scheme, we implement a $d$-dimensional time-phase quantum key distribution (QKD) system and achieve secret key rates of 5.26 and 8.65 Mbps using $d = 2$ and $d = 8$ quantum states, respectively, for a 4~dB channel loss, illustrating that high-dimensional time-phase QKD protocols are advantageous for low-loss quantum channels. This work paves the way for practical high-dimensional QKD protoco…
Robust and high-precision quantum control is crucial but challenging for scalable quantum computation and quantum information processing. Traditional adiabatic control suffers severe limitations on gate performance imposed by environmentally induced noise because of a quantum system's limited coherence time. In this work, we experimentally demonstrate an alternative approach {to quantum control} based on deep reinforcement learning (DRL) on a trapped $^{171}\mathrm{Yb}^{+}$ ion. In particular, we find that DRL leads to fast and robust {digital quantum operations with running time bounded by sh…
We theoretically investigate the use of fast pulsed two-qubit gates for trapped ion quantum computing in a two-dimensional microtrap architecture. In one dimension, such fast gates are optimal when employed between nearest neighbours, and we examine the generalisation to a two-dimensional geometry. We demonstrate that fast pulsed gates are capable of implementing high-fidelity entangling operations between ions in neighbouring traps faster than the trapping period, with experimentally demonstrated laser repetition rates. Notably, we find that without increasing the gate duration, high-fidelity…
An experimentally feasible scheme for generating a 12-qubit hyperentangled state via four photons, entangled in polarization, frequency and spatial mode, is proposed. We study the nature of quantum non-locality of this hyperentangled state by evaluating its violation degree to a Bell-type inequality, and find that the result agrees well with quantum mechanics prediction while extremely contradicts to the local realism constraint.
The description of the complex separability structure of quantum states in terms of partially ordered sets has been recently put forward. In this work, we address the question of how to efficiently determine these structures for unknown states. We propose an experimentally accessible and scalable iterative methodology that identifies, on solid statistical grounds, sufficient conditions for non-separability with respect to certain partitions. In addition, we propose an algorithm to determine the minimal partitions (those that do not admit further splitting) consistent with the experimental obse…
Unwanted $ZZ$ interaction is a quantum-mechanical crosstalk phenomenon which correlates qubit dynamics and is ubiquitous in superconducting qubit systems. It adversely affects the quality of quantum operations and can be detrimental in scalable quantum information processing. Here we propose and experimentally demonstrate a practically extensible approach for complete cancellation of residual $ZZ$ interaction between fixed-frequency transmon qubits, which are known for long coherence and simple control. We apply to the intermediate coupler that connects the qubits a weak microwave drive at a p…
Experimental demonstration of scalable cross-entropy benchmarking to detect measurement-induced phase transitions on a superconducting quantum processor
Multi-mode NOON states have been attracting increasing attentions recently for their abilities of obtaining supersensitive and superresolved measurements for simultaneous multiple-phase estimation. In this paper, four different methods of generating multi-mode NOON states with high photon number are proposed. The first method is a linear optical approach that makes use of the Fock state filtration to reduce lower-order Fock state terms from the coherent state inputs, which are jointly combined to produce a multi-mode NOON state with the triggering of single-photon coincidence detections (SPCD)…
We propose a hypercube switching architecture for the perfect state transfer (PST) where we prove that it is always possible to find an induced hypercube in any given hypercube of any dimension such that PST can be performed between any two given vertices of the original hypercube. We then generalise this switching scheme over arbitrary number of qubits where also this routing feature of PST between any two vertices is possible. It is shown that this is optimal and scalable architecture for quantum computing with the feature of routing. This allows for a scalable and growing network of qubits.…
The quantum statistical fluctuations of the electromagnetic field establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broa…
Quantum information processing with multi-level systems (qudits) provides additional features and applications than the two-level systems. However, qudits are more prone to dephasing and dynamical decoupling for qudits has never been experimentally demonstrated. Here, as a proof-of-principle demonstration, we experimentally apply dynamical decoupling to protect superpositions with three levels of a trapped $^9\rm{Be}^+$ ion from ambient noisy magnetic field, prolonging coherence by up to approximately an order of magnitude. Our demonstration, straightforwardly scalable to more levels, may open…
Heralded single-photon sources with on-demand readout are promising candidates for quantum repeaters enabling long-distance quantum communication. The need for scalability of such systems requires simple experimental solutions, thus favouring room-temperature systems. For quantum repeater applications, long delays between heralding and single-photon readout are crucial. Until now, this has been prevented in room-temperature atomic systems by fast decoherence due to thermal motion. Here we demonstrate efficient heralding and readout of single collective excitations created in warm caesium vapou…
Fast robust two-qubit gate operation with low susceptibility to crosstalk are the key to scalable quantum information processing. Parametrically driven gate is inherently insensitive to crosstalk while superadiabatic control can speed up the gate without losing accuracy. We propose and experimentally implement superadiabatic two-qubit gates using parametric modulation on superconducting quantum circuits. Our results demonstrate the preservation of adiabaticity at a gate speed close to the quantum limit, in addition to robustness against control instability. We demonstrate a CZ gate with error …
Non-stabilizerness or magic resource characterizes the amount of non-Clifford operations needed to prepare quantum states. It is a crucial resource for quantum computing and a necessary condition for quantum advantage. However, quantifying magic resource beyond a few qubits has been a major challenge. Here, we introduce efficient measures of magic resource for pure quantum states with a sampling cost that is independent of the number of qubits. Our method uses Bell measurements over two copies of a state, which we implement in experiment together with a cost-free error mitigation scheme. We sh…
Deterministic and Programmable Fusion for Scalable Generation of Photonic Graph States
Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院量子信息中心）；Hefei National Laboratory（合肥国家实验室）
We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation. We use a programmable array of superconducting qubits to compute the energy surface of molecular hydrogen using two distinct quantum algorithms. First, we experimentally execute the unitary coupled cluster method using the variational quantum eigensolver. Our efficient implementation predicts the correct dissociation energy to within chemical accuracy of the numerically exact result. Second, we experimentally demonstrate the canonical quantum algorithm for chemistry…
Topological quantum error correcting codes have emerged as leading candidates towards the goal of achieving large-scale fault-tolerant quantum computers. However, quantifying entanglement in these systems of large size in the presence of noise is a challenging task. In this paper, we provide two different prescriptions to characterize noisy stabilizer states, including the surface and the color codes, in terms of localizable entanglement over a subset of qubits. In one approach, we exploit appropriately constructed entanglement witness operators to estimate a witness-based lower bound of local…
Scalable and Highly Fault-Tolerant Circular Quantum Byzantine Agreement
National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室、物理学院、先进微结构协同创新中心）；School of Physics and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学物理学院、量子态构建与操控教育部重点实验室）；MatricTime Digital Technology Co. Ltd.（迈特时间数字技术有限公司）
Quantum information systems are on a path to vastly exceed the complexity of any classical device. The number of entangled qubits in quantum devices is rapidly increasing and the information required to fully describe these systems scales exponentially with qubit number. This scaling is the key benefit of quantum systems, however it also presents a severe challenge. To characterize such systems typically requires an exponentially long sequence of different measurements, becoming highly resource demanding for large numbers of qubits. Here we propose a novel and scalable method to characterize q…
