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Quantum process tomography is a pivotal technique in fully characterizing quantum dynamics. However, exponential scaling of the Hilbert space with the increasing system size extremely restrains its experimental implementations. Here, we put forward a more efficient, flexible, and error-mitigated method: variational entanglement-assisted quantum process tomography with arbitrary ancillary qubits. Numerically, we simulate up to eight-qubit quantum processes and show that this tomography with m ancillary qubits (0≤m≤n) alleviates the exponential costs on state preparation (from 4^{n} to 2^{n-m}), measurement settings (at least a 1 order of magnitude reduction), and data postprocessing (efficient and robust parameter optimization). Experimentally, we first demonstrate our method on a silicon photonic chip by rebuilding randomly generated one-qubit and two-qubit unitary quantum processes. Further using the error mitigation method, two-qubit quantum processes can be rebuilt with average gate fidelity enhanced from 92.38% to 95.56%. Our Letter provides an efficient and practical approach to process tomography on the noisy quantum computing platforms.

The increasing control complexity of Noisy Intermediate-Scale Quantum (NISQ) systems underlines the necessity of integrating quantum hardware with quantum software. While mapping heterogeneous quantum-classical computing (HQCC) algorithms to NISQ hardware for execution, we observed a few dissatisfactions in quantum programming languages (QPLs), including difficult mapping to hardware, limited expressiveness, and counter-intuitive code. In addition, noisy qubits require repeatedly performed quantum experiments, which explicitly operate low-level configurations, such as pulses and timing of operations. This requirement is beyond the scope or capability of most existing QPLs. We summarize three execution models to depict the quantum-classical interaction of existing QPLs. Based on the refined HQCC model, we propose the Quingo framework to integrate and manage quantum-classical software and hardware to provide the programmability over HQCC applications and map them to NISQ hardware. We propose a six-phase quantum program life-cycle model matching the refined HQCC model, which is implemented by a runtime system. We also propose the Quingo programming language, an external domain-specific language highlighting timer-based timing control and opaque operation definition, which can be used to describe quantum experiments. We believe the Quingo framework could contribute to the clarification of key techniques in the design of future HQCC systems.

As the condensed matter analog of Majorana fermion, the Majorana zero-mode is well known as a building block of fault-tolerant topological quantum computing. This review focuses on the recent progress of Majorana experiments, especially experiments about semiconductor-superconductor hybrid devices. We first sketch Majorana zero-mode formation from a bottom-up view, which is more suitable for beginners and experimentalists. Then, we survey the status of zero-energy state signatures reported recently, from zero-energy conductance peaks, the oscillations, the quantization, and the interactions with extra degrees of freedom. We also give prospects of future experiments for advancing one-dimensional semiconductor nanowire-superconductor hybrid materials and devices.

Programmable silicon photonics realizes universal control over quantum walks., Applications of quantum walks can depend on the number, exchange symmetry and indistinguishability of the particles involved, and the underlying graph structures where they move. Here, we show that silicon photonics, by exploiting an entanglement-driven scheme, can realize quantum walks with full control over all these properties in one device. The device we realize implements entangled two-photon quantum walks on any five-vertex graph, with continuously tunable particle exchange symmetry and indistinguishability. We show how this simulates single-particle walks on larger graphs, with size and geometry controlled by tuning the properties of the composite quantum walkers. We apply the device to quantum walk algorithms for searching vertices in graphs and testing for graph isomorphisms. In doing so, we implement up to 100 sampled time steps of quantum walk evolution on each of 292 different graphs. This opens the way to large-scale, programmable quantum walk processors for classically intractable applications.

Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of a variational quantum circuit and this state. The number of parameters of the variational quantum circuit grows linearly with the number of qubits and the circuit depth, so that only polynomial measurements are required, even for highly-entangled states. After that, a subsequent classical circuit simulator is used to transform the information of the target quantum state from the variational quantum circuit into a familiar format. We demonstrate our method by performing numerical simulations for the tomography of the ground state of a one-dimensional quantum spin chain, using a variational quantum circuit simulator. Our method is suitable for near-term quantum computing platforms, and could be used for relatively large-scale quantum state tomography for experimentally relevant quantum states., 7 pages, 3 figures

We present a novel route to realizing topological superconductivity using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core. In the destructive Little-Parks regime, reentrant regions of superconductivity are associated with integer number of phase windings in the shell. Tunneling into the core reveals a hard induced gap near zero applied flux, corresponding to zero phase winding, and a gapped region with a discrete zero-energy state around one applied flux quantum, {\Phi}_0 = h/2e, corresponding to 2{\pi} phase winding. Theoretical analysis indicates that in the presence of radial spin-orbit coupling in the semiconductor, the winding of the superconducting phase can induce a transition to a topological phase supporting Majorana zero modes. Realistic modeling shows a topological phase persisting over a wide range of parameters, and reproduces experimental tunneling conductance data. Further measurements of Coulomb blockade peak spacing around one flux quantum in full-shell nanowire islands shows exponentially decreasing deviation from 1e periodicity with device length, consistent with Majorana modes at the ends of the nanowire., Comment: NBI QDEV CMT 2020. Supersedes previous separate theory (arXiv:1809.05512) and experiment (arXiv:1809.05513) versions

Being a key component on a photonic chip, the microring usually specializes in a certain nonlinear optical process and can not simultaneously meet different working conditions for different processes. Here, we theoretically and experimentally investigate a reconfigurable silicon microring resonator to act as a optimization strategy for both classical four-wave mixing and quantum light sources. Experimental results show that the four-wave mixing efficiency with continuous wave and pulsed pump can be both optimized to a high value well matching numerical analysis. A variety of quantum light sources – including the heralded single-photon source, two-photon source and multi-photon source – are demonstrated to present a high performance and their key parameters including the pair generation rates (PGR), the heralding efficiency (HE) and the coincidence-to-accidental ratio (CAR) are controllable and optimizable. Such tunable nonlinear converter is immune to fabrication variations and can be popularized to other nonlinear optical materials, providing a simple and compact post-fabrication trimming strategy for on-chip all-optical signal processing and photonic quantum technologies.

Details of experimental setups, principles, and results.

The unremitting pursuit for quantum advantages gives rise to the discovery of a quantum-enhanced randomness processing named quantum Bernoulli factory (QBF). This quantum enhanced process can show its priority over the corresponding classical process through readily available experimental resources, thus in the near term it may be capable of accelerating the applications of classical Bernoulli factories, such as the widely used sampling algorithms. In this work, we provide the framework analysis of the QBF. We thoroughly analyze the quantum state evolution in this process, discovering the field structure of the constructible quantum states. Our framework analysis shows that naturally, the previous works can be described as specific instances of this framework. Then, as a proof of principle, we experimentally demonstrate this framework via an entangled two-photon source along with a reconfigurable photonic logic, and show the advantages of the QBF over the classical model through a classically infeasible instance. These results may stimulate the discovery of advantages of the quantum randomness processing in a wider range of tasks, as well as its potential applications., Comment: 9 pages, 4 figures

Recent advances on quantum computing hardware have pushed quantum computing to the verge of quantum supremacy. Random quantum circuits are outstanding candidates to demonstrate quantum supremacy, which could be implemented on a quantum device that supports nearest-neighbour gate operations on a two-dimensional configuration. Here we show that using the Projected Entangled-Pair States algorithm, a tool to study two-dimensional strongly interacting many-body quantum systems, we can realize an effective general-purpose simulator of quantum algorithms. This technique allows to quantify precisely the memory usage and the time requirements of random quantum circuits, thus showing the frontier of quantum supremacy. With this approach we can compute the full wave-function of the system, from which single amplitudes can be sampled with unit fidelity. Applying this general quantum circuit simulator we measured amplitudes for a $7\times 7$ lattice of qubits with depth $1+40+1$ and double-precision numbers in 31 minutes using less than $93$ TB memory on the Tianhe-2 supercomputer., Comment: 10 pages, 6 figures, 1 table

Gate-tunable semiconductor-superconductor nanowires with superconducting leads form exotic Josephson junctions that are a highly desirable platform for two types of qubits: those with topological superconductivity (Majorana qubits) and those based on tunable anharmonicity (gatemon qubits). Controlling their behavior, however, requires understanding their electrostatic environment and electronic structure. Here we study gated InAs nanowires with epitaxial aluminum shells. By measuring current-phase relations (CPR) and comparing them with analytical and numerical calculations, we show that we can tune the number of modes, determine the transparency of each mode, and tune into regimes in which electron-electron interactions are apparent, indicating the presence of a quantum dot. To take into account electrostatic and geometrical effects, we perform microscopic self-consistent Schrodinger-Poisson numerical simulations, revealing the energy spectrum of Andreev states in the junction as well as their spatial distribution. Our work systematically demonstrates the effect of device geometry, gate voltage and phase bias on mode behavior, providing new insights into ongoing experimental efforts and predictive device design., Comment: Main: 16 pages, 4 figures. Supplement: 8 pages, 4 figures

Boson sampling is a promising candidate for quantum supremacy. It requires to sample from a complicated distribution, and is trusted to be intractable on classical computers. Among the various classical sampling methods, the Markov chain Monte Carlo method is an important approach to the simulation and validation of boson sampling. This method however suffers from the severe sample loss issue caused by the autocorrelation of the sample sequence. Addressing this, we propose the sample caching Markov chain Monte Carlo method that eliminates the correlations among the samples, and prevents the sample loss at the meantime, allowing more efficient simulation of boson sampling. Moreover, our method can be used as a general sampling framework that can benefit a wide range of sampling tasks, and is particularly suitable for applications where a large number of samples are taken., 5 pages, 4 figures

Selective area epitaxy (SAE) can be used to grow highly uniform III–V nanostructure arrays in a fully controllable way and is thus of great interest in both basic science and device applications. Here, an overview of this promising technique is presented, focusing on the growth fundamentals, formation of III–V nanowire arrays, monolithic integration of III–V nanowire arrays on silicon, the growth of nanowire heterostructures, and networks of various shapes. The applications of these III–V nanostructure arrays in photonics, electronics, optoelectronics, and quantum science are also reviewed. Finally, the current challenges and opportunities provided by SAE are discussed.

High-dimensional entanglement provides valuable resources for quantum technologies, including quantum communication, quantum optical coherence tomography, and quantum computing. Obtaining a high brightness and dimensional entanglement source has significant value. Here we utilize a tunable asymmetric Mach–Zehnder interferometer coupled silicon microring resonator with 100 GHz free spectral range to achieve this goal. With the strategy of the tunable coupler, the dynamical and extensive tuning range of quality factors of the microring can be obtained, and then the biphoton pair generation rate can be optimized. By selecting and characterizing 28 pairs from a more than 30-pair modes biphoton frequency comb, we obtain a Schmidt number of at least 23.4 and on-chip pair generation rate of 19.9 MHz/mW2 under a low on-chip pump power, which corresponds to 547 dimensions Hilbert space in frequency freedom. These results will prompt the wide applications of quantum frequency comb and boost the further large density and scalable on-chip quantum information processing.

Quantum entanglement enables measurement on one party to affect the other’s state. Based on this peculiar feature, we propose a model of remote-controlled quantum computing and design an optical scheme to realize this model for a single qubit. As an experimental demonstration of this scheme, we further implement three Pauli operators, Hardmard gate, phase gate, and π / 8 gate. The minimal fidelity obtained by quantum process tomography reaches 82%. Besides, as a potential application, our model contributes to secure remote quantum information processing.

Multipartite entanglement is one of the most prominent features of quantum mechanics and is the key ingredient in quantum information processing. Seeking for an advantageous way to generate it is of great value. Here we propose two different schemes to prepare multiphoton entangled states on a quantum photonic chip that are both based on the theory of entanglement on the graph. The first scheme is to construct graphs for multiphoton states by the network of spatially anti-bunching two-photon sources. The second one is to construct graphs by the linear beam-splitter network, which can generate W and Dicke states efficiently with simple structure. Both schemes can be scaled up in the photon number and can be reconfigured for different types of multiphoton states. This study supplies a systematic solution for the on-chip generation of multiphoton entangled states and will promote the practical development of multiphoton quantum technologies.

Spatial separation of Majorana zero modes distinguishes trivial from topological midgap states and is key to topological protection in quantum computing applications. Although signatures of Majorana zero modes in tunneling spectroscopy have been reported in numerous studies, a quantitative measure of the degree of separation, or nonlocality, of the emergent zero modes has not been reported. Here, we present results of an experimental study of nonlocality of emergent zero modes in superconductor-semiconductor hybrid nanowire devices. The approach takes advantage of recent theory showing that nonlocality can be measured from splitting due to hybridization of the zero mode in resonance with a quantum dot state at one end of the nanowire. From these splittings as well as anticrossing of the dot states, measured for even and odd occupied quantum dot states, we extract both the degree of nonlocality of the emergent zero mode, as well as the spin canting angles of the nonlocal zero mode. Depending on the device measured, we obtain either a moderate degree of nonlocality, suggesting a partially separated Andreev subgap state, or a highly nonlocal state consistent with a well-developed Majorana mode., Comment: As published version

We introduce selective area grown hybrid InAs/Al nanowires based on molecular beam epitaxy, allowing arbitrary semiconductor-superconductor networks containing loops and branches. Transport reveals a hard induced gap and unpoisoned 2e-periodic Coulomb blockade, with temperature dependent 1e features in agreement with theory. Coulomb peak spacing in parallel magnetic field displays overshoot, indicating an oscillating discrete near-zero subgap state consistent with device length. Finally, we investigate a loop network, finding strong spin-orbit coupling and a coherence length of several microns. These results demonstrate the potential of this platform for scalable topological networks among other applications., The research was supported by Microsoft, the Danish National Research Foundation, and the European Commission. C. M. M. acknowledges support from the Villum Foundation. M. T. D. acknowledges support from State Key Laboratory of High Performance Computing, China. S. M.-S. acknowledges funding from “Programa Internacional de Becas ‘la Caixa’- Severo Ochoa.” ICN2 acknowledges support from the Severo Ochoa Programme (MINECO, Grant No. SEV2013-0295) and is funded by the CERCA Programme/Generalitat de Catalunya.

The combination of strong spin-orbit coupling, large $g$-factors, and the coupling to a superconductor can be used to create a topologically protected state in a semiconductor nanowire. Here we report on growth and characterization of hybrid epitaxial InAsSb/Al nanowires, with varying composition and crystal structure. We find the strongest spin-orbit interaction at intermediate compositions in zincblende InAs$_{1-x}$Sb$_{x}$ nanowires, exceeding that of both InAs and InSb materials, confirming recent theoretical studies \cite{winkler2016topological}. We show that the epitaxial InAsSb/Al interfaces allows for a hard induced superconducting gap and 2$e$ transport in Coulomb charging experiments, similar to experiments on InAs/Al and InSb/Al materials, and find measurements consistent with topological phase transitions at low magnetic fields due to large effective $g$-factors. Finally we present a method to grow pure wurtzite InAsSb nanowires which are predicted to exhibit even stronger spin-orbit coupling than the zincblende structure., 10 pages and 5 figures

Semiconductor nanowires with superconducting leads are considered promising for quantum computation. The current–phase relation is systematically explored in gate-tunable InAs Josephson junctions, and is shown to provide a clean handle for characterizing the transport properties of these structures. Gate-tunable semiconductor nanowires with superconducting leads have great potential for quantum computation1,2,3 and as model systems for mesoscopic Josephson junctions4,5. The supercurrent, I, versus the phase, φ, across the junction is called the current–phase relation (CPR). It can reveal not only the amplitude of the critical current, but also the number of modes and their transmission. We measured the CPR of many individual InAs nanowire Josephson junctions, one junction at a time. Both the amplitude and shape of the CPR varied between junctions, with small critical currents and skewed CPRs indicating few-mode junctions with high transmissions. In a gate-tunable junction, we found that the CPR varied with gate voltage: near the onset of supercurrent, we observed behaviour consistent with resonant tunnelling through a single, highly transmitting mode. The gate dependence is consistent with modelled subband structure that includes an effective tunnelling barrier due to an abrupt change in the Fermi level at the boundary of the gate-tuned region. These measurements of skewed, tunable, few-mode CPRs are promising both for applications that require anharmonic junctions6,7 and for Majorana readout proposals8.

The authors present fabrication and electrical measurements of InSb nanowire field-effect transistors (FETs) and quantum dots. The devices are made on a SiO2-capped Si substrate from InSb segments of InAs/InSb heterostructured nanowires, which are grown by metalorganic vapor phase epitaxy. For the FETs, both single- and dual-gate devices are fabricated. The Si substrate is employed as the back gate in both the single- and dual-gate devices, while a top metal gate is employed as a second gate in the dual-gate devices. This top gate is made either as a global gate or as a local finger gate by using a thin HfO2 layer grown by atomic layer deposition as a gate dielectric. The measurements reveal that the fabricated devices show the desired transistor characteristics. The measurements also demonstrate the possibility of realizing ambipolar transistors using InSb nanowires. For InSb nanowire quantum dots, both contact-induced Schottky-barrier-defined devices and top-finger-gate-defined devices are fabricated, and the Si substrate is used as a gate to tune the electron number in the quantum dots. The electrical measurements of these fabricated quantum-dot devices show the Coulomb-blockade effect at 4.2 K. A Fabry-Perot-like interference effect is also observed in a Schottky-barrier-defined quantum device. The authors also discuss in a comparative way, the results of measurements for the InSb nanowire devices made by different fabrication technologies employed in this study.

We report on realization and transport spectroscopy study of single quantum dots (QDs) made from InSb nanowires grown by molecular beam epitaxy (MBE). The nanowires employed are 50-80 nm in diameter and the QDs are defined in the nanowires between the source and drain contacts on a Si/SiO$_2$ substrate. We show that highly tunable QD devices can be realized with the MBE-grown InSb nanowires and the gate-to-dot capacitance extracted in the many-electron regimes is scaled linearly with the longitudinal dot size, demonstrating that the devices are of single InSb nanowire QDs even with a longitudinal size of ~700 nm. In the few-electron regime, the quantum levels in the QDs are resolved and the Land\'e g-factors extracted for the quantum levels from the magnetotransport measurements are found to be strongly level-dependent and fluctuated in a range of 18-48. A spin-orbit coupling strength is extracted from the magnetic field evolutions of a ground state and its neighboring excited state in an InSb nanowire QD and is on the order of ~300 $\mu$eV. Our results establish that the MBE-grown InSb nanowires are of high crystal quality and are promising for the use in constructing novel quantum devices, such as entangled spin qubits, one-dimensional Wigner crystals and topological quantum computing devices., Comment: 19 pages, 5 figures

We explore the signatures of Majorana fermions in a nanowire based topological superconductor-quantum dot-topological superconductor hybrid device by charge transport measurements. The device is made from an epitaxially grown InSb nanowire with two superconductor Nb contacts on a Si/SiO$_2$ substrate. At low temperatures, a quantum dot is formed in the segment of the InSb nanowire between the two Nb contacts and the two Nb contacted segments of the InSb nanowire show superconductivity due to the proximity effect. At zero magnetic field, well defined Coulomb diamonds and the Kondo effect are observed in the charge stability diagram measurements in the Coulomb blockade regime of the quantum dot. Under the application of a finite, sufficiently strong magnetic field, a zero-bias conductance peak structure is observed in the same Coulomb blockade regime. It is found that the zero-bias conductance peak is present in many consecutive Coulomb diamonds, irrespective of the even-odd parity of the quasi-particle occupation number in the quantum dot. In addition, we find that the zero-bias conductance peak is in most cases accompanied by two differential conductance peaks, forming a triple-peak structure, and the separation between the two side peaks in bias voltage shows oscillations closely correlated to the background Coulomb conductance oscillations of the device. The observed zero-bias conductance peak and the associated triple-peak structure are in line with the signatures of Majorana fermion physics in a nanowire based topological superconductor-quantum dot-topological superconductor system, in which the two Majorana bound states adjacent to the quantum dot are hybridized into a pair of quasi-particle states with finite energies and the other two Majorana bound states remain as the zero-energy modes located at the two ends of the entire InSb nanowire., 6 pages, 4 figures

We present transport measurements in superconductor-nanowire devices with a gated constriction forming a quantum point contact. Zero-bias features in tunneling spectroscopy appear at finite magnetic fields, and oscillate in amplitude and split away from zero bias as a function of magnetic field and gate voltage. A crossover in magnetoconductance is observed: Magnetic fields above ~ 0.5 T enhance conductance in the low-conductance (tunneling) regime but suppress conductance in the high-conductance (multichannel) regime. We consider these results in the context of Majorana zero modes as well as alternatives, including Kondo effect and analogs of 0.7 structure in a disordered nanowire., Supplemental Material here: https://dl.dropbox.com/u/1742676/Churchill_Supplemental.pdf

We use the effective g factor of Andreev subgap states in an axial magnetic field to investigate how the superconducting density of states is distributed between the semiconductor core and the superconducting shell in hybrid nanowires. We find a steplike reduction of the Andreev g factor and an improved hard gap with reduced carrier density in the nanowire, controlled by gate voltage. These observations are relevant for Majorana devices, which require tunable carrier density and a g factor exceeding that of the parent superconductor.

This thesis focuses on charge transport in semiconductor InSb nanowire quantum devices, including the electron transport, the hole transport, and the Cooper pair transport. Devices in which InSb semiconductor nanowire quantum dots are coupled with normal metals, superconductors or the proximity effect induced topological superconductors are fabricated and measured. Firstly, we have fabricated and measured normal metal contacted InSb nanowire devices. In each of these devices, a quantum dot is formed in the InSb nanowire between the contacts. We report on the magnetotransport measurements performed to these quantum dot devices, and reveal several novel transport features. First, we demonstrate the ambipolar quantum dot devices in which the quantum dots can be tuned from the n-type regime to the p-type regime. The transport measurements in both of the n-type regime and the p-type regime are performed. We also show that two methods can be used to estimate the effective g-factor of the quantum dot, but they can give very different estimation in the presence of a Kondo effect. In the p-type regime of an ambipolar quantum dot, we observe conductance peaks in the stability diagram which can be attributed to the quasi-1D lead states. Secondly, we have fabricated and characterized the superconductor coupled InSb nanowire quantum dots. We probe the density of states of the quasi-particles in the superconductor contacts, via a weakly coupled InSb quantum dot. In the strongly coupled InSb nanowire-superconductor junctions, dissipationless Josephson currents are observed. A SQUIDS device is also fabricated and measured, in which an anomalous modulation of the Josephson current in the magnetic field is observed. In the medium coupling regime, we observe the signatures of the multiple Andreev reflections, the sub-gab bound states, and the Josephson current, interplaying with the Kondo effect. By adjusting the gate voltages, we can control the dot-lead coupling strength and asymmetry. Here, we report the quantum phase transition induced by tuning the dot-lead coupling and the quantum phase transition induced by a magnetic field. We have also found the coupling asymmetry is very important for the observation of the Josephson current. In the magnetic field, the evolution of the Kondo effect enhanced Josephson current is found to be strongly dependent on the energy ratio of Kondo energy and superconducting gap. Finally, an anomalous low-field suppression of the zero-bias conductance peak in the Kondo regime is observed. In the last part of the thesis, we report on our efforts to search for Majorana fermions in solid state systems. Nb-InSb nanowire quantum dot-Nb hybrid devices were fabricated and the transport measurements were performed at low temperatures for these devices. We have observed anomalous zero-bias conductance peaks emerging in finite magnetic fields in the Nb-InSb nanowire quantum dot-Nb hybrid devices as a signature of the Majorana bound states in such hybrid devices. We have also found that the zero-bias conductance peak are independent of the even-odd parity of the quasi-particle number in the quantum dots and are associated with interesting fine structures. As a validation, a Au-InSb nanowire quantum dot-Nb device is fabricated and measured. Here, signatures of Majorana bound states, i.e., the zero-bias conductance peaks in finite magnetic fields are also observed. In addition, we analyze several other mechanisms that can lead to the emergence of zero-bias conductance peaks in finite magnetic fields, and discuss the results in comparison with the signatures of Majorana bound states.