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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 tri-snRNP 27K protein is a component of the human U4/U6-U5 tri-snRNP and contains an N-terminal phosphorylated RS domain. In a forward genetic screen in C. elegans, we previously identified a dominant mutation, M141T, in the highly-conserved C-terminal region of this protein. The mutant allele promotes changes in cryptic 5′ splice site choice. To better understand the function of this poorly characterized splicing factor, we performed high-throughput mRNA sequencing analysis on worms containing this dominant mutation. Comparison of alternative splice site usage between the mutant and wild-type strains led to the identification of 26 native genes whose splicing changes in the presence of the snrp-27mutation. The changes in splicing are specific to alternative 5′ splice sites. Analysis of new alleles suggests that snrp-27is an essential gene for worm viability. We performed a novel directed-mutation experiment in which we used the CRISPR-cas9 system to randomly generate mutations specifically at M141 of SNRP-27. We identified eight amino acid substitutions at this position that are viable, and three that are homozygous lethal. All viable substitutions at M141 led to varying degrees of changes in alternative 5′ splicing of native targets. We hypothesize a role for this SR-related factor in maintaining the position of the 5′ splice site as U1snRNA trades interactions at the 5′ end of the intron with U6snRNA and PRP8 as the catalytic site is assembled.

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.

Proline accumulation in two different bean (Phaseolus vulgarisL.) cultivars, one drought-sensitive (Canario 60) and one drought-resistant (Pinto Villa) was investigated. Both tolerated salt concentrations up to 150 mM NaCl, but the sensitive Canario 60 did not survive at 400 mM NaCl. In response to salt stress, both cvs. accumulated proline in all the analyzed tissues, the lowest contents were detected in roots. Pinto Villa accumulated higher proline concentrations than Canario 60 only at 400 mM NaCl. The addition of polyamines or ornithine increased proline content in plant tissues without stress, while they decreased it under salt stress.Proline accumulation in two different bean (Phaseolus vulgarisL.) cultivars, one drought-sensitive (Canario 60) and one drought-resistant (Pinto Villa) was investigated. Both tolerated salt concentrations up to 150 mM NaCl, but the sensitive Canario 60 did not survive at 400 mM NaCl. In response to salt stress, both cvs. accumulated proline in all the analyzed tissues, the lowest contents were detected in roots. Pinto Villa accumulated higher proline concentrations than Canario 60 only at 400 mM NaCl. The addition of polyamines or ornithine increased proline content in plant tissues without stress, while they decreased it under salt stress.

Partial cDNAs sequences for arginine decarboxylase (Pvadc), S-adenosylmethionine decarboxylase (Pvsamdc) and spermidine synthase (Pvspds) were isolated from the bean Phaseolus vulgarisusing primers designed from conserved regions of enzymes belonging to plant species. Sequence analysis showed that the Pvadc, Pvsamdcand Pvspdsgenes were most closely related to the orthologous genes from Glycine max, Phaseolus lunatusand Pisum sativum, respectively. The expression patterns of the genes, together with that of ornithine decarboxylase (Pvodc), were analysed in young and mature leaves, stems, roots, root tips, petals, stigma, ovaries, filaments and anthers of bean plants. Pvsamdcwas found to be expressed at similar levels in all tissues. The other transcripts showed tissue specific expression. Pvadcwas barely expressed in petals and not at all in roots tips, Pvspdswas mainly expressed in roots, stigma and filaments, and Pvodcwas detected only in roots.Partial cDNAs sequences for arginine decarboxylase (Pvadc), S-adenosylmethionine decarboxylase (Pvsamdc) and spermidine synthase (Pvspds) were isolated from the bean Phaseolus vulgarisusing primers designed from conserved regions of enzymes belonging to plant species. Sequence analysis showed that the Pvadc, Pvsamdcand Pvspdsgenes were most closely related to the orthologous genes from Glycine max, Phaseolus lunatusand Pisum sativum, respectively. The expression patterns of the genes, together with that of ornithine decarboxylase (Pvodc), were analysed in young and mature leaves, stems, roots, root tips, petals, stigma, ovaries, filaments and anthers of bean plants. Pvsamdcwas found to be expressed at similar levels in all tissues. The other transcripts showed tissue specific expression. Pvadcwas barely expressed in petals and not at all in roots tips, Pvspdswas mainly expressed in roots, stigma and filaments, and Pvodcwas detected only in roots.

We present a method to optimize qubit control parameters during error detection which is compatible with large-scale qubit arrays. We demonstrate our method to optimize single or two-qubit gates in parallel on a nine-qubit system. Additionally, we show how parameter drift can be compensated for during computation by inserting a frequency drift and using our method to remove it. We remove both drift on a single qubit and independent drifts on all qubits simultaneously. We believe this method will be useful in keeping error rates low on all physical qubits throughout the course of a computation. Our method is O(1) scalable to systems of arbitrary size, providing a path towards controlling the large numbers of qubits needed for a fault-tolerant quantum computer. [ABSTRACT FROM AUTHOR]