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Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution, $P(\mathcal{M})$, of the magnetization transferred across the chain's center. The first two moments of $P(\mathcal{M})$ show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.

Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.

Undesired coupling to the surrounding environment destroys long-range correlations on quantum processors and hinders the coherent evolution in the nominally available computational space. This incoherent noise is an outstanding challenge to fully leverage the computation power of near-term quantum processors. It has been shown that benchmarking Random Circuit Sampling (RCS) with Cross-Entropy Benchmarking (XEB) can provide a reliable estimate of the effective size of the Hilbert space coherently available. The extent to which the presence of noise can trivialize the outputs of a given quantum algorithm, i.e. making it spoofable by a classical computation, is an unanswered question. Here, by implementing an RCS algorithm we demonstrate experimentally that there are two phase transitions observable with XEB, 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 varying the strength of noise versus coherent evolution. Furthermore, by presenting an RCS experiment with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers, even when accounting for the inevitable presence of noise. 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. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth. Here, we study physical simulation within the seniority-zero electron pairing subspace, which affords both a computational stepping stone to a fully correlated model, and an opportunity to validate recently introduced ``purification-based'' error-mitigation strategies. We compare the performance of error mitigation based on doubling quantum resources in time (echo verification) or in space (virtual distillation), 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 (e.g. post-selection); the gain from error mitigation is seen to increase with the system size. Employing these error mitigation strategies enables the implementation of the largest variational algorithm for a correlated chemistry system to-date. Extrapolating performance from these results allows us to estimate minimum requirements for a beyond-classical simulation of electronic structure. We find that, despite the impressive gains from purification-based error mitigation, significant hardware improvements will be required for classically intractable variational chemistry simulations., Comment: 10 pages, 13 page supplementary material, 12 figures. Experimental data available at https://doi.org/10.5281/zenodo.7225821

The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy near the expected value of $\ln2$, and simulate anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigate key aspects of the surface code, including logical state injection and the decay of the non-local order parameter. Our results demonstrate the potential for quantum processors to provide key insights into topological quantum matter and quantum error correction., Comment: 6 pages 4 figures, plus supplementary materials

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using eighteen superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to probe 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 arrive at an accuracy in measuring energy eigenvalues of this wire with an error of ~0.01 rad, whereas typical energy scales are of order 1 rad. Insight into this unprecedented algorithm fidelity is gained by highlighting robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 1e-4 rad. Furthermore, we synthesize magnetic flux and disordered local potentials, two key tenets of a condensed-matter system. When sweeping the magnetic flux, we observe avoided level crossings in the spectrum, a detailed fingerprint of the spatial distribution of local disorder. Combining these methods, we reconstruct electronic properties of the eigenstates where we observe persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation and paves the way to study novel quantum materials with superconducting qubits.

Quantum algorithms offer a dramatic speedup for computational problems in machine learning, material science, and chemistry. However, any near-term realizations of these algorithms will need to be heavily optimized to fit within the finite resources offered by existing noisy quantum hardware. Here, taking advantage of the strong adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a 3x reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an iSWAP-like gate to attain an arbitrary swap angle, $\theta$, and a CPHASE gate that generates an arbitrary conditional phase, $\phi$. Using one of each of these gates, we can perform an arbitrary two-qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic Simulation, or fSim, gate set. We benchmark the fidelity of the iSWAP-like and CPHASE gate families as well as 525 other fSim gates spread evenly across the entire fSim($\theta$, $\phi$) parameter space achieving purity-limited average two-qubit Pauli error of $3.8 \times 10^{-3}$ per fSim gate., Comment: 20 pages, 17 figures

The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modification of the dynamics, making their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two qubit density matrices allowed us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here measure affirmative correlations and allow us to exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter., Comment: 5+28 pages, 5+22 figures, updated version

Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number of logical qubits is the same as the number of qubits on the device. The hardware determines which pairs of qubits can be addressed by unitary operators. The goal is to build quantum states that solve computational problems such as maximizing a combinatorial objective function or minimizing a Hamiltonian. These problems may not fit naturally on the physical layout of the qubits. Our algorithms use a sequence of parameterized unitaries that sit on the qubit layout to produce quantum states depending on those parameters. Measurements of the objective function (or Hamiltonian) guide the choice of new parameters with the goal of moving the objective function up (or lowering the energy). As an example we consider finding approximate solutions to MaxCut on 3-regular graphs whereas the hardware is physical qubits laid out on a rectangular grid. We prove that the lowest depth version of the Quantum Approximate Optimization Algorithm will achieve an approximation ratio of at least 0.5293 on all large enough instances which beats random guessing (0.5). We open up the algorithm to have different parameters for each single qubit $X$ rotation and for each $ZZ$ interaction associated with the nearest neighbor interactions on the grid. Small numerical experiments indicate that an enveloping classical algorithm can be used to find the parameters which sit on the grid to optimize an objective function with a different connectivity. We discuss strategies for finding good parameters but offer no evidence yet that the proposed approach can beat the best classical algorithms. Ultimately the strength of this approach will be determined by running on actual hardware., Comment: 20 pages, 6 figures

We have investigated experimentally the pressure dependence of the production of ultracold neutrons (UCN) in superfluid helium in the range from saturated vapor pressure to 20bar. A neutron velocity selector allowed the separation of underlying single-phonon and multiphonon pro- cesses by varying the incident cold neutron (CN) wavelength in the range from 3.5 to 10{\AA}. The predicted pressure dependence of UCN production derived from inelastic neutron scattering data was confirmed for the single-phonon excitation. For multiphonon based UCN production we found no significant dependence on pressure whereas calculations from inelastic neutron scattering data predict an increase of 43(6)% at 20bar relative to saturated vapor pressure. From our data we conclude that applying pressure to superfluid helium does not increase the overall UCN production rate at a typical CN guide., Comment: 18 pages, 8 figures Version accepted for publication in PRC

Accurate knowledge of the single-molecule (self) translational dynamics of liquid para-H2 is an essential requirement for the calculation of the neutron scattering properties of this important quantum liquid. We show that, by using Centroid Molecular Dynamics (CMD) quantum simulations of the velocity autocorrelation function, calculations of the total neutron cross section (TCS) remarkably agree with experimental data at the thermal and epithermal incident neutron energies where para-H2 dynamics is actually dominated by the self contributions. This result shows that a proper account of the quantum nature of the fluid, as provided by CMD, is a necessary and very effective condition to obtain the correct absolute-scale cross section values directly from first-principle computations of the double differential cross section, and without the need of introducing any empirically adjusted quantity. At subthermal incident energies, appropriate modeling of the para-H2 intermolecular (distinct) dynamics also becomes crucial, but quantum simulations are not yet able to cope with it. Existing simple models which account for the distinct part provide an appropriate correction of self-only calculations and bring the computed results in reasonable accord with TCS experimental data available until very recently. However, if just published cross section measurements in the cold range are considered, the agreement turns out to be by far superior and very satisfactory. The possible origin of slight residual differences will be commented and suggest further computational and experimental efforts. Nonetheless, the ability to reproduce the total cross section in the wide range between 1 and 900 meV represents an encouraging and important validation step of the CMD method and of the present simple algorithm.

We consider a (1+1) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now lose energy, but at a rate that is exponentially small when the expansion rate is slow. We also show numerically that a universe that starts with (almost) thermal initial conditions will cool to a final state where a significant fraction of the energy of the universe -- on the order of 50% -- is stored in oscillons. If this phenomenon persists in realistic models, oscillons may have cosmological consequences., Comment: 13 pages, 4 .eps figures, uses RevTeX4; v2: clarified details of expansion, added references

We give a quantum algorithm for the binary NAND tree problem in the Hamiltonian oracle model. The algorithm uses a continuous time quantum walk with a run time proportional to sqrt N. We also show a lower bound of sqrt N for the NAND tree problem in the Hamiltonian oracle model., Comment: 16 pages, 15 figures, v2 with run time improved to sqrt N by slight sharpening of estimates in section 3

We report neutron scattering measurements on bcc solid $^{4}$% He. We studied the phonon branches and the recently discovered ''optic-like'' branch along the main crystalline directions. In addition, we discovered another, dispersionless "optic-like'' branch at an energy around 1 meV ($\sim$~11K). The properties of the two "optic-like" branches seem different. Since one expects only 3 acoustic phonon branches in a monoatomic cubic crystal, these new branches must represent different type of excitations. One possible interpretation involves localized excitations unique to a quantum solid., Comment: 4 pages, 3 figures, accepted by PRB, Rapid Communications

We study classical dynamics in the spherical ansatz for the SU(2) gauge and Higgs fields of the electroweak Standard Model in the absence of fermions and the photon. With the Higgs boson mass equal to twice the gauge boson mass, we numerically demonstrate the existence of oscillons, extremely long-lived localized configurations that undergo regular oscillations in time. We have only seen oscillons in this reduced theory when the masses are in a two-to-one ratio. If a similar phenomenon were to persist in the full theory, it would suggest a preferred value for the Higgs mass., Comment: 7 pages, 6 .eps figures, uses revtex4 and epsfig

We report neutron diffraction studies of low density bcc and hcp solid 4He. In the bcc phase, we observed a continuous dynamical behaviour involving macroscopic structural changes of the solid. The dynamical behaviour takes place in a cell full of solid, and therefore represents a solidsolid transformation. The structural changes are consistent with a gradual rotation of macroscopic grains separated by low angle grain boundaries. We suggest that these changes are triggered by random momentary vibrations of the experimental system. An analysis of Laue diffraction patterns indicates that in some cases these structural changes, once initiated by a momentary impulse, seem to proceed at a constant rate over times approaching an hour. The energy associated with these macroscopic changes appears to be on the order of kT. Under similar conditions (temperature and pressure), these effects were absent in the hcp phase., Comment: 14 pages, 6 figure, accepted for PRB

We explore the effects of a heavy fermion doublet in a simplified version of the standard electroweak theory. We integrate out the doublet and compute the exact effective energy functional of spatially varying gauge and Higgs fields. We perform a variational search for a local minimum of the effective energy and do not find evidence for a soliton carrying the quantum numbers of the decoupled fermion doublet. The fermion vacuum polarization energy offsets the gain in binding energy previously argued to be sufficient to stabilize a fermionic soliton. The existence of such a soliton would have been a natural way to maintain anomaly cancellation at the level of the states. We also see that the sphaleron energy is significantly increased due to the quantum corrections of the heavy doublet. We find that when the doublet is slightly heavier than the quantum--corrected sphaleron, its decay is exponentially suppressed owing to a new barrier. This barrier exists only for an intermediate range of fermion masses, and a heavy enough doublet is indeed unstable., Comment: 30 pages LaTeX, 3 eps-figures

We report neutron scattering measurements of the phonons in bcc solid 4He. In general, only 3 accoustic phonon branches should exist in a monoatomic cubic crystal. In addition to these phonon branches, we found a new ''optic-like'' mode along the [110] direction. One possible interpretation of this new mode is in terms of localized excitations unique to a quantum solid., Comment: Text and 4 figures, to appear in Phys. Rev. Lett

We search for static solitons stabilized by heavy fermions in a 3+1 dimensional Yukawa model. We compute the renormalized energy functional, including the exact one-loop quantum corrections, and perform a variational search for configurations that minimize the energy for a fixed fermion number. We compute the quantum corrections using a phase shift parameterization, in which we renormalize by identifying orders of the Born series with corresponding Feynman diagrams. For higher-order terms in the Born series, we develop a simplified calculational method. When applicable, we use the derivative expansion to check our results. We observe marginally bound configurations at large Yukawa coupling, and discuss their interpretation as soliton solutions subject to general limitations of the model., Comment: 27 pp., 7 EPS files; email correspondence to jaffe@mit.edu

Low-T Brillouin spectra of the incipient ferroelectric KTaO3 exhibit a broad central peak (CP), and additional Brillouin doublets (BD), that can both be related to phonon-density fluctuations. On the basis of new high-resolution neutron data obtained of low-lying phonon branches, we analysed the phonon-kinetics mechanisms that are possibly the origin of these unusual features. Firstly, transverse acoustic (TA) phonons whose normal damping is faster than the BD frequency can produce hydrodynamic second sound. Secondly, two-phonon difference scattering from low damping thermal transverse phonons contribute to the spectra with either a sharp or a broader doublet, depending on the phonon group velocity and anisotropy of dispersion surfaces. The position of the observed sharp doublet is consistent with both mechanisms, but a comparison of the computed and experimental anisotropies favours the second process., Comment: Ferroelectrics, in press (Aug 2000). 8 pages, 4 figures. EMF9 Proceedings. See http://www.ill.fr/

Monte-Carlo simulations of a focusing supermirror guide after the monochromator on the IN14 cold neutron three-axis spectrometer, I.L.L. were carried out using the instrument simulation programs RESTRAX and McSTAS. The simulations were compared to experiment to check their accuracy. Comparisons of the flux ratios over both a 100 mm2 and a 1600 mm2 area at the sample position compare well, and there is very close agreement between simulation and experiment for the energy spread of the incident beam., Comment: (3 pages, 2 figures) ECNS99 Proceedings

The incipient ferroelectric KTaO3 presents low-T Brillouin spectra anomalies,e.g. a broad central peak (CP), and some additional Brillouin doublets (BD), whose origin is interpreted in terms of phonon-density fluctuation processes. A parameterisation from new extensive high-resolution neutron-scattering measurements is used to show that hydrodynamic second sound from high damping (compared to BD frequency) TA phonons may exist in the crystal. Furthermore, low damping thermal phonons may scatter light through two-phonon difference processes and appear on the Brillouin spectra either as a sharp or a broader BD, depending on the phonon damping and group velocity . The comparison between computed anisotropies and experimental measurements favours the second process., Comment: 3 pages, 1 figure, ECNS99 Proceedings. See http://www.ill.fr/

High resolution data on low energy phonon branches (acoustic and soft optic) along the three principal symmetry axes in pure KTaO3 were obtained by cold neutron inelastic scattering between 10 and 80 K. Additional off-principal axis measurements were performed to characterize the dispersion anisotropy (away from the <100> and <110> axes). The parameters of the phenomenological model proposed by Vaks are refined in order to successfully describe the experimental low temperature (10 < T < 100 K) dispersion curves, over an appreciable reciprocal space volume around the zone center (|q| < 0.25 rlu). The refined model, which involves only 4 temperature-independent adjustable parameters, is intended to serve as a basis for quantitative computations of multiphonon processes., Comment: 15 2-columns pages, 11 figures, 2 tables see also

Optical mode crossing is not a plausible explanation for the new broad Brillouin doublet nor for the strong acoustic anomalies observed at low temperatures in SrTiO3. Data presented to support that explanation are also inconclusive., Comment: This is a comment to a paper from J.F. Scott (same ZFP volume)

We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a 1+1 dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions., Comment: 16 pages, uses RevTex, 1 figure; v2: minor corrections

We find static solitons stabilized by quantum corrections in a (1+1)-dimensional model with a scalar field chirally coupled to fermions. This model does not support classical solitons. We compute the renormalized energy functional including one-loop quantum corrections. We carry out a variational search for a configuration that minimizes the energy functional. We find a nontrivial configuration with fermion number whose energy is lower than the same number of free fermions quantized about the translationally invariant vacuum. In order to compute the quantum corrections for a given background field we use a phase-shift parameterization of the Casimir energy. We identify orders of the Born series for the phase shift with perturbative Feynman diagrams in order to renormalize the Casimir energy using perturbatively determined counterterms. Generalizing dimensional regularization, we demonstrate that this procedure yields a finite and unambiguous energy functional., Comment: 27 papes Latex, equation labels corrected, version to be published in Nucl. Phys. B

We show that quantum effects can stabilize a soliton in a model with no soliton at the classical level. The model has a scalar field chirally coupled to a fermion in 1+1 dimensions. We use a formalism that allows us to calculate the exact one loop fermion contribution to the effective energy for a spatially varying scalar background. This energy includes the contribution from counterterms fixed in the perturbative sector of the theory. The resulting energy is therefore finite and unambiguous. A variational search then yields a fermion number one configuration whose energy is below that of a single free fermion., Comment: 10 pages, RevTeX, 2 figures composed from 4 .eps files; v2: fixed minor errors, added reference; v3: corrected reference added in v2

Suppose an oracle is known to hold one of a given set of D two-valued functions. To successfully identify which function the oracle holds with k classical queries, it must be the case that D is at most 2^k. In this paper we derive a bound for how many functions can be distinguished with k quantum queries., Comment: 5 pages. Lower bound on sorting n items improved to (1-epsilon)n quantum queries. Minor changes to text and corrections to references

We consider the problem of inserting a new item into an ordered list of N-1 items. The length of an algorithm is measured by the number of comparisons it makes between the new item and items already on the list. Classically, determining the insertion point requires log N comparisons. We show that, for N large, no quantum algorithm can reduce the number of comparisons below log N/(2 loglog N)., Comment: 5 pages

Consider a function f which is defined on the integers from 1 to N and takes the values -1 and +1. The parity of f is the product over all x from 1 to N of f(x). With no further information about f, to classically determine the parity of f requires N calls of the function f. We show that any quantum algorithm capable of determining the parity of f contains at least N/2 applications of the unitary operator which evaluates f. Thus for this problem, quantum computers cannot outperform classical computers., Comment: 9 pages, latex

We consider a variant of the standard electroweak theory in which the Higgs sector has been modified so that there is a classically stable weak scale soliton. We explore fermion number violating processes which involve soliton decay. A soliton can decay by tunnelling under the sphaleron barrier, or the decay can be collision induced if the energy is sufficient for the barrier to be traversed. We present a classical solution to the Minkowski space equations of motion in which a soliton is kicked over the barrier by an incoming pulse. This pulse corresponds to a quantum coherent state with mean number of $W$ quanta $\sim 2.5/g^2$ where $g$ is the $SU(2)$ gauge coupling constant. We also give a self-contained treatment of the relationship between classical solutions, including those in which solitons are destroyed, and tree-level quantum amplitudes. Furthermore, we consider a limit in which we can reliably estimate the amplitude for soliton decay induced by collision with a single $W$-boson. This amplitude depends on $g$ like $\exp (-cg^{-1/3})$, and is larger than that for spontaneous decay via tunnelling in the same limit. Finally we show that in soliton decays, light $SU(2)_L$ doublet fermions are anomalously produced. Thus we have a calculation of a two body process with energy above the sphaleron barrier in which fermion number is violated., Comment: 64 pages, revtex, epsf, all figures included. Revised version. Section V replaced with a corrected version. Qualitative conclusions unchanged. Numerical value of one exponent has changed

We investigate fermion production in the background of Minkowski space solutions to the equations of motion of $SU(2)$ gauge theory spontaneously broken via the Higgs mechanism. First, we attempt to evaluate the topological charge $Q$ of the solutions. We find that for solutions $Q$ is not well-defined as an integral over all space-time. Solutions can profitably be characterized by the (integer-valued) change in Higgs winding number $\Delta N_H$. We show that solutions which dissipate at early and late times and which have nonzero $\Delta N_H$ must have at least the sphaleron energy. We show that if we couple a quantized massive chiral fermion to a classical background given by a solution, the number of fermions produced is $\Delta N_H$, and is not related to $Q$., Comment: Version to be published. Argument showing that the topological charge of solutions is undefined has been strengthened and clarified. Conclusions unchanged