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Undesired coupling to the surrounding environment destroys long-range correlations in quantum processors and hinders coherent evolution in the nominally available computational space. This noise is an outstanding challenge when leveraging the computation power of near-term quantum processors1. It has been shown that benchmarking random circuit sampling with cross-entropy benchmarking can provide an estimate of the effective size of the Hilbert space coherently available2–8. Nevertheless, quantum algorithms’ outputs can be trivialized by noise, making them susceptible to classical computation spoofing. Here, by implementing an algorithm for random circuit sampling, we demonstrate experimentally that two phase transitions are observable with cross-entropy benchmarking, which we explain theoretically with a statistical model. The first is a dynamical transition as a function of the number of cycles and is the continuation of the anti-concentration point in the noiseless case. The second is a quantum phase transition controlled by the error per cycle; to identify it analytically and experimentally, we create a weak-link model, which allows us to vary the strength of the noise versus coherent evolution. Furthermore, by presenting a random circuit sampling experiment in the weak-noise phase with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers. Our experimental and theoretical work establishes the existence of transitions to a stable, computationally complex phase that is reachable with current quantum processors.

An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Before fault-tolerant quantum computing, robust error-mitigation strategies were necessary to continue this growth. Here, we validate recently introduced error-mitigation strategies that exploit the expectation that the ideal output of a quantum algorithm would be a pure state. We consider the task of simulating electron systems in the seniority-zero subspace where all electrons are paired with their opposite spin. This affords a computational stepping stone to a fully correlated model. We compare the performance of error mitigations on the basis of doubling quantum resources in time or in space on up to 20 qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques such as postselection. We study how the gain from error mitigation scales with the system size and observe a polynomial suppression of error with increased resources. Extrapolation of our results indicates that substantial hardware improvements will be required for classically intractable variational chemistry simulations.

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2–9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform1–4. 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 10−4rad. 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 simulation5,6and paves the way to study new quantum materials with superconducting qubits.

The intriguing many-body phases of quantum matter arise from the interplay of particle interactions, spatial symmetries, and external fields. Generating these phases in an engineered system could provide deeper insight into their nature. Using superconducting qubits, we simultaneously realize synthetic magnetic fields and strong particle interactions, which are among the essential elements for studying quantum magnetism and fractional quantum Hall phenomena. The artificial magnetic fields are synthesized by sinusoidally modulating the qubit couplings. In a closed loop formed by the three qubits, we observe the directional circulation of photons, a signature of broken time-reversal symmetry. We demonstrate strong interactions through the creation of photon vacancies, or ‘holes’, which circulate in the opposite direction. The combination of these key elements results in chiral ground-state currents. Our work introduces an experimental platform for engineering quantum phases of strongly interacting photons.

A digitized approach to adiabatic quantum computing, combining the generality of the adiabatic algorithm with the universality of the digital method, is implemented using a superconducting circuit to find the ground states of arbitrary Hamiltonians.

Quercetin (Qu) is a powerful flavanol antioxidant that is naturally found in plants and is part of the flavonoid family. Qu has a wide range of biological properties, such as neuroprotective, anti-cancer, anti-diabetic, anti-inflammatory, and radical scavenging capabilities. However, the in vivo application of QU is limited by its poor water solubility and low bioavailability. These issues could be addressed by utilizing Qu nanoformulations. Cyclophosphamide (CP) is a potent chemotherapeutic agent that causes severe neuronal damage and cognitive impairment due to reactive oxygen species (ROS) overproduction. The present study aimed to explore the proposed neuroprotective mechanism of quercetin (Qu) and quercetin-loaded Chitosan nanoparticles (Qu-Ch NPs) against the brain oxidative damage induced by CP in male albino rats. For this aim, thirty-six adult male rats were randomly divided into six groups (n=6). Rats were pretreated with Qu and Qu-Ch NPs orally in doses of 10mg/kg bwt/day for 2 weeks, and CP (75mg/kg bwt) was administered intraperitoneally 24hours before the termination of the experiment. After 2 weeks, some neurobehavioral parameters were evaluated, and then euthanization was done to collect the brain and blood samples. Results showed that CP induces neurobehavioral deteriorations and impaired brain neurochemical status demonstrated by a significant decrease in brain glutathione (GSH), serum total antioxidant capacity (TAC), and serotonin (5-HT) levels while malondialdehyde (MDA), nitric oxide (NO), Tumor necrosis factor α (TNFα), and choline esterase (ChE) concentrations increased significantly compared to the control group. Pretreatment with Qu and Qu-Ch NPs showed a significant anti-oxidative, anti-depressive, and neuroprotective effect through modification of the above-mentioned parameters. The results were further validated by assessing the expression levels of selected genes in brain homogenates and histopathological investigations were done to pinpoint the exact brain-altered regions. It could be concluded that Qu and Qu-Ch NPs can be useful neuroprotective adjunct therapy to overcome neurochemical damage induced by cyclophosphamide.

Background: Polycystic ovarian syndrome (PCOS) is a reproductive disorder associated with several endocrine and metabolic alterations. The mechanism underlying this syndrome is controversial. On the other hand, drugs used for the treatment are associated with several side effects and poor in controlling PCOS phenotype. l-Carnitine (LC) has been reported to have a significant regulatory function on the redox and metabolic status of female reproductive system. Nevertheless, its regulatory pathways to regulate PCOS are still under investigation. Therefore, this study aimed to evaluate the effects of LC on the steroidogenic pathways, oxidative stress markers and metabolic profile in letrozole (LTZ)-induced PCOS rat model. Methods: For this aim, animals were divided into four groups (n= 6). Control group, untreated letrozole-induced PCOS group (1 mg/kg bwt) for 21 days, PCOS group treated with l-Carnitine (100 mg/kg bwt) for 14 days and PCOS group treated with clomiphene citrate (2 mg/kg bwt) for 14 days. Finally, body and ovarian weight, metabolic state(glucose and lipid profile), hormonal assays (testosterone, 17 β estradiol, LH and FSH levels), intraovarian relative gene expression (CYP17A1, StAR, CYP11A1and CYP19A1genes), ovarian redox state (malondialdehyde (MDA), reduced glutathione content (GSH) and catalase enzyme activity (CAT)) as well as serum total antioxidant capacity (TAC) were detected. Also, histomorphometric ovarian evaluation (number and diameter of cystic follicles, granulosa cell thickness and theca cell thickness) as well as immune expression of caspase-3 of granulosa cells of cystic follicles were determined. Results: LC significantly improved ovarian redox state (GSH, MDA and CAT), steroidogenic pathways gene expression (CYP17A1, StAR, CYP11A1and CYP19A1genes), hormonal profile (Follicle stimulating hormone (FSH) and luteinizing hormone (LH), testosterone and estradiol), metabolic state (Glucose and lipid profile) histomorphometric alterations and decreased caspase 3 immune reaction of granulosa cells. Conclusion: l-Carnitine supplementation can ameliorate the PCOS phenotype through its energetic, antioxidant and antiapoptotic functions as well as steroidogenesis regulatory role. This protocol could be modified to produce the best therapeutic benefits, and it could be regarded as a prospective therapeutic intervention for PCOS.

Recent results have demonstrated the successful applications of quantum-classical hybrid methods to train quantum circuits for a variety of machine learning tasks. A natural question to ask is consequentially whether we can also train such quantum circuits to discriminate quantum data, i.e., perform classification on data stored in form of quantum states. Although quantum mechanics fundamentally forbids deterministic discrimination of non-orthogonal states, we show in this work that it is possible to train a quantum circuit to discriminate such data with a trade-off between minimizing error rates and inconclusiveness rates of the classification tasks. Our approach achieves at the same time a performance which is close to the theoretically optimal values and a generalization ability to previously unseen quantum data. This generalization power hence distinguishes our work from previous circuit optimization results and furthermore provides an example of a quantum machine learning task that has inherently no classical analogue.