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Noise in existing quantum processors only enables an approximation to ideal quantum computation. However, these approximations can be vastly improved by error mitigation, for the computation of expectation values, as shown by small-scale experimental demonstrations. However, the practical scaling of these methods to larger system sizes remains unknown. Here, we demonstrate the utility of zero-noise extrapolation for relevant quantum circuits using up to 26 qubits, circuit depths of 60, and 1080 CNOT gates. We study the scaling of the method for canonical examples of product states and entangling Clifford circuits of increasing size, and extend it to the quench dynamics of 2-D Ising spin lattices with varying couplings. We show that the efficacy of the error mitigation is greatly enhanced by additional error suppression techniques and native gate decomposition that reduce the circuit time. By combining these methods, we demonstrate an accuracy in the approximate quantum simulation of the quench dynamics that surpasses the classical approximations obtained from a state-of-the-art 2-D tensor network method. These results reveal a path to a relevant quantum advantage with noisy, digital, quantum processors., 7 pages, 3 figures

The management of locally advanced muscle invasive bladder cancer (MIBC) often necessitates neo-adjuvant chemotherapy (NAC) to eliminate any micro-metastatic disease prior to definitive radical cystectomy (RC) and pelvic lymph node dissection (PLND). The most common imaging techniques traditionally used during this process are computerised tomography (CT) and magnetic resonance imaging (MRI), both of which lack a high sensitivity for nodal staging. In this paper, we attempt to review the evolving indications of F-fluoro-2-deoxy-D-glucose positron emission tomography/computerised tomography (FDG-PET/CT) imaging, in the pre-clinical and post-treatment staging of bladder cancer, with a focus on its ability to evaluate response to NAC. We concluded that use of FDG-PET/CT allows for improved nodal staging and metastatic disease detection, compared to traditional imaging modalities. This enabled earlier detection of tumour response to NAC and/or residual disease, impacting factors such as duration of chemotherapy, with its associated adverse effects, and timing of surgical intervention. However, further studies are required to reliably assess its impact on both overall and disease-free survival.

Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems. Yet, because of the inherent fragile nature of the physical computing elements, qubits, achieving quantum advantages over classical computation requires extremely low error rates for qubit operations as well as a significant overhead of physical qubits, in order to realize fault-tolerance via quantum error correction. However, recent theoretical work has shown that the accuracy of computation based off expectation values of quantum observables can be enhanced through an extrapolation of results from a collection of varying noisy experiments. Here, we demonstrate this error mitigation protocol on a superconducting quantum processor, enhancing its computational capability, with no additional hardware modifications. We apply the protocol to mitigate errors on canonical single- and two-qubit experiments and then extend its application to the variational optimization of Hamiltonians for quantum chemistry and magnetism. We effectively demonstrate that the suppression of incoherent errors helps unearth otherwise inaccessible accuracies to the variational solutions using our noisy processor. These results demonstrate that error mitigation techniques will be critical to significantly enhance the capabilities of near-term quantum computing hardware.

Improving two-qubit gate performance and suppressing crosstalk are major, but often competing, challenges to achieving scalable quantum computation. In particular, increasing the coupling to realize faster gates has been intrinsically linked to enhanced crosstalk due to unwanted two-qubit terms in the Hamiltonian. Here, we demonstrate a novel coupling architecture for transmon qubits that circumvents the standard relationship between desired and undesired interaction rates. Using two fixed frequency coupling elements to tune the dressed level spacings, we demonstrate an intrinsic suppression of the static $ZZ$, while maintaining large effective coupling rates. Our architecture reveals no observable degradation of qubit coherence ($T_1,T_2 > 100~��s$) and, over a factor of 6 improvement in the ratio of desired to undesired coupling. Using the cross-resonance interaction we demonstrate a 180~ns single-pulse CNOT gate, and measure a CNOT fidelity of 99.77(2)$\%$ from interleaved randomized benchmarking., 5 pages, 3 figures plus supplement (4 pages, 3 figures)

The computation of molecular excitation energies is essential for predicting photo-induced reactions of chemical and technological interest. While the classical computing resources needed for this task scale poorly, quantum algorithms emerge as promising alternatives. In particular, the extension of the variational quantum eigensolver algorithm to the computation of the excitation energies is an attractive option. However, there is currently a lack of such algorithms for correlated molecular systems that is amenable to near-term, noisy hardware. In this work, we propose an extension of the well-established classical equation of motion approach to a quantum algorithm for the calculation of molecular excitation energies on noisy quantum computers. In particular, we demonstrate the efficiency of this approach in the calculation of the excitation energies of the LiH molecule on an IBM Quantum computer., Physical Review Research, 2 (4), ISSN:2643-1564

Reducing measurement errors in multi-qubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical post-processing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parameterizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error mitigation overhead, including the the number of measurements and the cost of the classical post-processing, is exponential in $\epsilon n$, where $\epsilon$ is the maximum error rate and $n$ is the number of qubits. We report experimental demonstration of our error mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\le 12$ qubits and entangled 20-qubit states generated by low-depth random Clifford circuits., Comment: 13 pages, 7 figures

We improve the quality of quantum circuits on superconducting quantum computing systems, as measured by the quantum volume, with a combination of dynamical decoupling, compiler optimizations, shorter two-qubit gates, and excited state promoted readout. This result shows that the path to larger quantum volume systems requires the simultaneous increase of coherence, control gate fidelities, measurement fidelities, and smarter software which takes into account hardware details, thereby demonstrating the need to continue to co-design the software and hardware stack for the foreseeable future., Comment: Fixed typo in author list. Added references [38], [49] and [52]

Implementing topological insulators as elementary units in quantum technologies requires a comprehensive understanding of the dephasing mechanisms governing the surface carriers in these materials, which impose a practical limit to the applicability of these materials in such technologies requiring phase coherent transport. To investigate this, we have performed magnetoresistance (MR) and conductance fluctuations (CF) measurements in both exfoliated and molecular beam epitaxy grown samples. The phase breaking length (${l}_{\ensuremath{\phi}}$) obtained from MR shows a saturation below sample dependent characteristic temperatures, consistent with that obtained from CF measurements. We have systematically eliminated several factors that may lead to such behavior of ${l}_{\ensuremath{\phi}}$ in the context of TIs, such as finite size effect, thermalization, spin-orbit coupling length, spin-flip scattering, and surface-bulk coupling. Our work indicates the need to identify an alternative source of dephasing that dominates at low $T$ in topological insulators, causing saturation in the phase breaking length and time.

The concept of quantum computing has inspired a whole new generation of scientists, including physicists, engineers, and computer scientists, to fundamentally change the landscape of information technology. With experimental demonstrations stretching back more than two decades, the quantum computing community has achieved a major milestone over the past few years: the ability to build systems that are stretching the limits of what can be classically simulated, and which enable cloud-based research for a wide range of scientists, thus increasing the pool of talent exploring early quantum systems. While such noisy near-term quantum computing systems fall far short of the requirements for fault-tolerant systems, they provide unique test beds for exploring the opportunities for quantum applications. Here, we highlight an IBM-specific perspective of the facets associated with these systems, including quantum software, cloud access, benchmarking quantum systems, error correction and mitigation in such systems, understanding the complexity of quantum circuits, and how early quantum applications can run on near-term quantum computers.

Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to these interacting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. These limitations of classical computational methods have made even few-atom molecular structures problems of practical interest for medium-sized quantum computers. Yet, thus far experimental implementations have been restricted to molecules involving only Period I elements. Here, we demonstrate the experimental optimization of up to six-qubit Hamiltonian problems with over a hundred Pauli terms, determining the ground state energy for molecules of increasing size, up to BeH2. This is enabled by a hardware-efficient variational quantum eigensolver with trial states specifically tailored to the available interactions in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We further demonstrate the flexibility of our approach by applying the technique to a problem of quantum magnetism. Across all studied problems, we find agreement between experiment and numerical simulations with a noisy model of the device. These results help elucidate the requirements for scaling the method to larger systems, and aim at bridging the gap between problems at the forefront of high-performance computing and their implementation on quantum hardware., 6 pages, 4 figures in main text. 18 pages, 9 figures in supplementary information

Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits., Comment: Contribution to the special issue of Quantum Science & Technology on "What would you do with 1000 qubits"

A striking prediction in topological insulators is the appearance of the quantized Hall resistance when the surface states are magnetized. The surface Dirac states become gapped everywhere on the surface, but chiral edge states remain on the edges. In an applied current, the edge states produce a quantized Hall resistance that equals the Chern number C = +1 or -1 (in natural units), even in zero magnetic field. This quantum anomalous Hall effect was observed by Chang et al. With reversal of the magnetic field, the system is trapped in a metastable state because of magnetic anisotropy. Here we investigate how the system escapes the metastable state at low temperatures (10-200 mK). When the dissipation (measured by the longitudinal resistance) is ultralow, we find that the system escapes by making a few, very rapid transitions, as detected by large jumps in the Hall and longitudinal resistances. Using the field at which the initial jump occurs to estimate the escape rate, we find that raising the temperature strongly suppresses the rate. From a detailed map of the resistance vs. gate voltage and temperature, we show that dissipation strongly affects the escape rate. We compare the observations with dissipative quantum tunneling predictions. In the ultralow dissipation regime, there exist two temperature scales T1 = 70 mK and T2 = 145 mK between which jumps can be observed. The jumps display a spatial correlation that extends over a large fraction of the sample., 18 pages, 9 figures

We propose two novel solar cell designs, tapping the advantages of semiconductor nanowires. A silicon (Si) tandem cell can be achieved by growing sub-5 nm p-n junction in the radial direction of the Si nanowires on a planar crystalline Si cell. For series connected sub-cells, based on a size-band gap dependence obtained from Quantum Monte Carlo calculations, we obtained the maximum detailed balance limit of efficiency to be 48% and 37% for concentrated and unconcentrated sunlight, respectively, for a nanowire diameter of 3.6 nm. The same efficiency would be obtained if the top tandem cell would be composed of AlGaAs nanowires, with an Al content of 19%. Ultra-high efficiencies could be achieved by a radial p-n junction nanowire tandem cell, since it could enable growth of lattice mismatched sub-cells whose band gap energies can be optimized and secondly, due to decoupling of carrier collection and light absorption. However, for a parallel connection of the sub cells, we show that the detailed balance limit of efficiency for the tandem cell will always be lower than an optimized single junction. Finally, we discuss future challenges and directions in realizing the designs.

The ferromagnetic state of topological insulators showing quantum anomalous Hall effect is surprisingly superparamagnetic., Quantized Hall conductance is a generic feature of two-dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is believed to be broken by long-range ferromagnetic order, with quantized resistance observed even at zero external magnetic field. We use scanning nanoSQUID (nano–superconducting quantum interference device) magnetic imaging to provide a direct visualization of the dynamics of the quantum phase transition between the two anomalous Hall plateaus in a Cr-doped (Bi,Sb)2Te3 thin film. Contrary to naive expectations based on macroscopic magnetometry, our measurements reveal a superparamagnetic state formed by weakly interacting magnetic domains with a characteristic size of a few tens of nanometers. The magnetic phase transition occurs through random reversals of these local moments, which drive the electronic Hall plateau transition. Surprisingly, we find that the electronic system can, in turn, drive the dynamics of the magnetic system, revealing a subtle interplay between the two coupled quantum phase transitions.

When a three-dimensional ferromagnetic topological insulator thin film is magnetized out-of-plane, conduction ideally occurs through dissipationless, one-dimensional (1D) chiral states that are characterized by a quantized, zero-field Hall conductance. The recent realization of this phenomenon, the quantum anomalous Hall effect, provides a conceptually new platform for studies of 1D transport, distinct from the traditionally studied quantum Hall effects that arise from Landau level formation. An important question arises in this context: how do these 1D edge states evolve as the magnetization is changed from out-of-plane to in-plane? We examine this question by studying the field-tilt-driven crossover from predominantly edge-state transport to diffusive transport in Crx(Bi,Sb)2−xTe3 thin films. This crossover manifests itself in a giant, electrically tunable anisotropic magnetoresistance that we explain by employing a Landauer–Büttiker formalism. Our methodology provides a powerful means of quantifying dissipative effects in temperature and chemical potential regimes far from perfect quantization., When magnetized out-of-plane, three-dimensional ferromagnetic topological insulator thin films exhibit the quantum anomalous Hall effect. Here, the authors follow the evolution of this dissipationless chiral edge transport effect as the magnetization is brought in-plane under an applied magnetic field.

We report a detailed study on low-frequency 1/f-noise in large-area molecular-beam epitaxy grown thin (10 nm) films of topological insulators as a function of temperature, gate voltage, and magnetic field. When the Fermi energy is within the bulk valence band, the temperature dependence reveals a clear signature of generation-recombination noise in the defect states in the bulk band gap. However, when the Fermi energy is tuned to the bulk band gap, the gate voltage dependence of noise shows that the resistance fluctuations in surface transport are caused by correlated mobility-number density fluctuations due to the activated defect states present in the bulk of the topological insulator crystal with a density of D$_{it}=3.2\times10^{17}$ cm$^2$eV$^{-1}$. In the presence of a magnetic field, noise in these materials follows a parabolic dependence, which is qualitatively similar to mobility and charge-density fluctuation noise in non-degenerately doped trivial semiconductors. Our studies reveal that even in thin films of (Bi,Sb)$_2$Te$_3$ with thickness as low as 10 nm, the intrinsic bulk defects are the dominant source of noise., Comment: 15 pages, 4 figures

Periodic Aharonov–Bohm and Altshuler–Aronov–Spivak oscillations have traditionally been observed in lateral transport through patterned mesoscopic loops of diffusive conductors. However, our studies of perpendicular-to-plane magnetotransport in straight-channel, diffusive devices of epitaxial Bi2Se3 surprisingly reveal signatures of Aharonov–Bohm orbits, periodic conductance fluctuation magneto-fingerprints, even though the devices are not explicitly patterned into loops. We show that the length scale of these orbits corresponds to the typical perimeter of triangular terraces found on the surface of these thin film devices, strongly suggesting that the periodic magneto-fingerprint arises from coherent scattering of electron waves from the step-edges. Our interpretation is bolstered by control measurements in devices without such surface morphology that only show a conventional, aperiodic magneto-fingerprint. These results show that lithographically patterned Bi2Se3 devices provide a novel class of mesoscopic physical systems for systematic studies of coherent surface sensitive transport.

We report the integration of the insulating ferromagnet GdN with epitaxial films of the topological insulator Bi2Se3 and present detailed structural, magnetic and transport characterization of the heterostructures. Fabrication of multi-channel Hall bars with bare and GdN-capped sections enables direct comparison of magnetotransport properties. We show that the presence of the magnetic overlayer results in suppression of weak anti-localization at the top surface., The title and content of this manuscript have been significantly revised taking into account newly acquired data

The breaking of time-reversal symmetry by ferromagnetism is predicted to yield profound changes to the electronic surface states of a topological insulator. Here, we report on a concerted set of structural, magnetic, electrical and spectroscopic measurements of \MBS thin films wherein photoemission and x-ray magnetic circular dichroism studies have recently shown surface ferromagnetism in the temperature range 15 K $\leq T \leq 100$ K, accompanied by a suppressed density of surface states at the Dirac point. Secondary ion mass spectroscopy and scanning tunneling microscopy reveal an inhomogeneous distribution of Mn atoms, with a tendency to segregate towards the sample surface. Magnetometry and anisotropic magnetoresistance measurements are insensitive to the high temperature ferromagnetism seen in surface studies, revealing instead a low temperature ferromagnetic phase at $T \lesssim 5$ K. The absence of both a magneto-optical Kerr effect and anomalous Hall effect suggests that this low temperature ferromagnetism is unlikely to be a homogeneous bulk phase but likely originates in nanoscale near-surface regions of the bulk where magnetic atoms segregate during sample growth. Although the samples are not ideal, with both bulk and surface contributions to electron transport, we measure a magnetoconductance whose behavior is qualitatively consistent with predictions that the opening of a gap in the Dirac spectrum drives quantum corrections to the conductance in topological insulators from the symplectic to the orthogonal class., Comment: To appear in Phys. Rev. B

We report detailed temperature and gate-voltage dependence of 1/f resistance noise in magnetically doped topological insulators (TI) Crx(Bi,Sb)2−xTe3. The noise is remarkably sensitive to the gate voltage, increasing rapidly as the chemical potential is moved towards the charge neutrality point. Unlike in identically prepared (Bi,Sb)2Te3 films, where mobility-fluctuations in the surface states is the dominant mechanism, the noise in the magnetic Crx(Bi,Sb)2−xTe3 originates from transport in the localized band tail of the bulk valence band. A strong increase in noise with decreasing temperature supports this scenario. At higher temperature (≥10 K), we observed large noise peaks at gate voltage-dependent characteristic temperature scales. In line with similar observations in other non-magnetic TI systems, we attribute these peaks to generation-recombination in the Cr-impurity band.