Explore the vast range of titles available.

The central challenge in building a quantum computer is error correction. Unlike classical bits, which are susceptible to only one type of error, quantum bits (qubits) are susceptible to two types of error, corresponding to flips of the qubit state about the X and Z  directions. Although the Heisenberg uncertainty principle precludes simultaneous monitoring of X - and Z -flips on a single qubit, it is possible to encode quantum information in large arrays of entangled qubits that enable accurate monitoring of all errors in the system, provided that the error rate is low 1 . Another crucial requirement is that errors cannot be correlated. Here we characterize a superconducting multiqubit circuit and find that charge noise in the chip is highly correlated on a length scale over 600 micrometres; moreover, discrete charge jumps are accompanied by a strong transient reduction of qubit energy relaxation time across the millimetre-scale chip. The resulting correlated errors are explained in terms of the charging event and phonon-mediated quasiparticle generation associated with absorption of γ-rays and cosmic-ray muons in the qubit substrate. Robust quantum error correction will require the development of mitigation strategies to protect multiqubit arrays from correlated errors due to particle impacts. Cosmic-ray particles and γ-rays striking superconducting circuits can generate qubit errors that are spatially correlated across several millimetres, hampering current error-correction approaches.

In bulk materials, superconductivity is remarkably robust with respect to non-magnetic disorder. In the two-dimensional limit, however, disorder and electron correlations both tend to destroy the quantum condensate. Here we study, both experimentally and theoretically, the effect of structural disorder on the local spectral response of crystalline superconducting monolayers of lead on silicon. In a direct scanning tunnelling microscopy measurement, we reveal how the local superconducting spectra lose their conventional character and show variations at scales significantly shorter than the coherence length. We demonstrate that the precise atomic organization determines the robustness of the superconducting order with respect to structural defects, such as single atomic steps, which may disrupt superconductivity and act as native Josephson barriers. We expect that our results will improve the understanding of microscopic processes in surface and interface superconductivity, and will open a new way of engineering atomic-scale superconducting quantum devices. The effect of structural disorder on superconductivity can be subtle: for two crystalline arrangements of superconducting lead monolayers deposited on silicon, there are unexpected spatial variations that result in macroscopically different behaviour.

All physical implementations of quantum bits (or qubits, the logical elements in a putative quantum computer) must overcome conflicting requirements: the qubits should be manipulable through external signals, while remaining isolated from their environment. Proposals based on quantum optics emphasize optimal isolation 1 , 2 , 3 , while those following the solid-state route exploit the variability and scalability of nanoscale fabrication techniques 4 , 5 , 6 , 7 , 8 . Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation 9 , 10 , 11 , however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task. Protecting qubits from decoherence by exploiting topological stability is a qualitatively new proposal 12 that holds promise for long decoherence times, but its physical implementation has remained unclear. Here we show how strongly correlated systems developing an isolated twofold degenerate quantum dimer liquid ground state can be used in the construction of topologically stable qubits; we discuss their implementation using Josephson junction arrays. Although the complexity of their architecture challenges the technology base available today, such topological qubits greatly benefit from their built-in fault-tolerance.

Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of the dimension 4 gluon condensate. The moments Mn(Q2) of the polarization operator of the vector charm currents are calculated and compared with the experimental data. The three-loop (\\(_s^2\\)) perturbative corrections, the contribution of the gluon condensate with \\(_s\\) corrections and the contribution of the dimension 6 operator G3 are accounted. It is shown that the sum rules for the moments do not work at Q2 = 0, where the perturbation series diverges and the G3 contribution is large. The domain in the (n, Q2) plane where the sum rules are legitimate is found. A strong correlation of the values of gluon condensate and \\(MS\\) charm quark mass is determined. The absolute limits are found to be for the gluon condensate \\( (_s /) G^2 = 0.009 0.007GeV^4\\) and for the charm quark mass \\( m( m) = 1.275 0.015 GeV\\) in the \\(MS\\) scheme.

The magnetic-flux analogue to coherent Josephson tunnelling of electric charge has been observed in a strongly disordered superconducting nanowire. Coherent quantum phase slip revealed Coherent quantum phase slip (CQPS) has not, until now, been observed experimentally. It is a phenomenon exactly dual to the Josephson effect, but whereas the latter is a coherent transfer of charges between superconducting contacts, CQPS is a coherent transfer of vortices or fluxes across a superconducting wire. This paper reports direct observation of CQPS in a strongly disordered indium oxide superconducting wire inserted in a loop; the effect manifests through the superposition of quantum states with different fluxes. The CQPS may — like the Josephson effect before it — lead to innovative applications in superconducting electronics and quantum metrology. A hundred years after the discovery of superconductivity, one fundamental prediction of the theory, coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual 1 to the Josephson effect; whereas the latter is a coherent transfer of charges between superconducting leads 2 , 3 , the former is a coherent transfer of vortices or fluxes across a superconducting wire. In contrast to previously reported observations 4 , 5 , 6 , 7 , 8 of incoherent phase slip, CQPS has been only a subject of theoretical study 9 , 10 , 11 , 12 . Its experimental demonstration is made difficult by quasiparticle dissipation due to gapless excitations in nanowires or in vortex cores. This difficulty might be overcome by using certain strongly disordered superconductors near the superconductor–insulator transition. Here we report direct observation of CQPS in a narrow segment of a superconducting loop made of strongly disordered indium oxide; the effect is made manifest through the superposition of quantum states with different numbers of flux quanta 13 . As with the Josephson effect, our observation should lead to new applications in superconducting electronics and quantum metrology 1 , 10 , 11 .

We predict the universal power-law dependence of the localization length on the magnetic field in the strongly localized regime. This effect is due to the orbital quantum interference. Physically, this dependence shows up in an anomalously large negative magnetoresistance in the hopping regime. The reason for the universality is that the problem of the electron tunneling in a random media belongs to the same universality class as the directed polymer problem even in the case of wave functions of random sign. We present numerical simulations that prove this conjecture. We discuss the existing experiments that show anomalously large magnetoresistance. We also discuss the role of localized spins in real materials and the spin polarizing effect of the magnetic field.

We demonstrate that chirality-violating condensates in massless QCD arise entirely from zero-mode solutions of the Dirac equation in arbitrary gluon fields. We propose a model in which the zero-mode solutions are the ones for quarks moving in the instanton field and calculate the quark condensate magnetic susceptibilities χ of dimension three and κ and ξ of dimension five based on this model. The good correspondence of the values of χ, κ, and ξ obtained using this approach with the values found from the hadronic spectrum is a serious argument that instantons are the only source of chirality-violating condensates in QCD. We discuss the temperature dependence of the quark condensate and show that the phase transition corresponding to the temperature dependence α(T) of the quark condensate as an order parameter is a crossover-type transition.

Faster algorithms for combinatorial optimization could prove transformative for diverse areas such as logistics, finance and machine learning. Accordingly, the possibility of quantum enhanced optimization has driven much interest in quantum technologies. Here we demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study performance for problems defined on the planar connectivity graph native to our hardware; however, we also apply the QAOA to the Sherrington–Kirkpatrick model and MaxCut, non-native problems that require extensive compilation to implement. For hardware-native problems, which are classically efficient to solve on average, we obtain an approximation ratio that is independent of problem size and observe that performance increases with circuit depth. For problems requiring compilation, performance decreases with problem size. Circuits involving several thousand gates still present an advantage over random guessing but not over some efficient classical algorithms. Our results suggest that it will be challenging to scale near-term implementations of the QAOA for problems on non-native graphs. As these graphs are closer to real-world instances, we suggest more emphasis should be placed on such problems when using the QAOA to benchmark quantum processors.It is hoped that quantum computers may be faster than classical ones at solving optimization problems. Here the authors implement a quantum optimization algorithm over 23 qubits but find more limited performance when an optimization problem structure does not match the underlying hardware.

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform 1 – 4 . However, the accuracy needed to outperform classical methods has not been achieved so far. Here, using 18 superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to investigate fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors, and measure the energy eigenvalues of this wire with an error of approximately 0.01 rad, whereas typical energy scales are of the order of 1 rad. Insight into the fidelity of this algorithm is gained by highlighting the robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 10 −4 rad. We also synthesize magnetic flux and disordered local potentials, which are two key tenets of a condensed-matter system. When sweeping the magnetic flux we observe avoided level crossings in the spectrum, providing a detailed fingerprint of the spatial distribution of local disorder. By combining these methods we reconstruct electronic properties of the eigenstates, observing persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation 5 , 6 and paves the way to study new quantum materials with superconducting qubits. As a blueprint for high-precision quantum simulation, an 18-qubit algorithm that consists of more than 1,400 two-qubit gates is demonstrated, and reconstructs the energy eigenvalues of the simulated one-dimensional wire to a precision of 1 per cent.

The temperature dependence of the c axis spectral weight (frequency integral of the interplane conductivity) of high transition temperature (high-T(c)) superconductors is shown to be a probe of thermal and quantal fluctuations of the phase of the superconducting order parameter. The behavior of underdoped cuprates is shown to be a natural consequence of superconducting pairing without long-ranged phase coherence. Very underdoped cuprates are found to have strong phase fluctuations, even for temperatures much less than the transition temperature.