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The development of noisy intermediate-scale quantum (NISQ) devices has extended the scope of executable quantum circuits with high-fidelity single- and two-qubit gates. Equipping NISQ devices with three-qubit gates will enable the realization of more complex quantum algorithms and efficient quantum error correction protocols with reduced circuit depth. Several three-qubit gates have been implemented for superconducting qubits, but their use in gate synthesis has been limited due to their low fidelity. Here, using fixed-frequency superconducting qubits, we demonstrate a high-fidelity iToffoli gate based on two-qubit interactions, the so-called cross-resonance effect. As with the Toffoli gate, this three-qubit gate can be used to perform universal quantum computation. The iToffoli gate is implemented by simultaneously applying microwave pulses to a linear chain of three qubits, revealing a process fidelity as high as 98.26(2)%. Moreover, we numerically show that our gate scheme can produce additional three-qubit gates which provide more efficient gate synthesis than the Toffoli and iToffoli gates. Our work not only brings a high-fidelity iToffoli gate to current superconducting quantum processors but also opens a pathway for developing multi-qubit gates based on two-qubit interactions.

As superconducting quantum processors increase in complexity, techniques to overcome constraints on frequency crowding are needed. The recently developed method of laser-annealing provides an effective post-fabrication method to adjust the frequency of superconducting qubits. Here, we present an automated laser-annealing apparatus based on conventional microscopy components and demonstrate preservation of highly coherent transmons. In one case, we observe a two-fold increase in coherence after laser-annealing and perform noise spectroscopy on this qubit to investigate the change in defect features, in particular two-level system defects. Finally, we present a local heating model as well as demonstrate aging stability for laser-annealing on the wafer scale. Our work constitutes an important first step towards both understanding the underlying physical mechanism and scaling up laser-annealing of superconducting qubits., Comment: 11 pages, 7 figures

Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable $ZZ$ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off-resonantly. We show tunable coupling over one order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave crosstalk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of $99.43(1)\%$ as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors., Comment: 12 pages, 7 figures

As the size and complexity of a quantum computer increases, quantum bit (qubit) characterization and gate optimization become complex and time-consuming tasks. Current calibration techniques require complicated and verbose measurements to tune up qubits and gates, which cannot easily expand to the large-scale quantum systems. We develop a concise and automatic calibration protocol to characterize qubits and optimize gates using QubiC, which is an open source FPGA (field-programmable gate array) based control and measurement system for superconducting quantum information processors. We propose mutli-dimensional loss-based optimization of single-qubit gates and full XY-plane measurement method for the two-qubit CNOT gate calibration. We demonstrate the QubiC automatic calibration protocols are capable of delivering high-fidelity gates on the state-of-the-art transmon-type processor operating at the Advanced Quantum Testbed at Lawrence Berkeley National Laboratory. The single-qubit and two-qubit Clifford gate infidelities measured by randomized benchmarking are of $4.9(1.1) \times 10^{-4}$ and $1.4(3) \times 10^{-2}$, respectively., Comment: Added funding agency

Crosstalk is a leading source of failure in multiqubit quantum information processors. It can arise from a wide range of disparate physical phenomena, and can introduce subtle correlations in the errors experienced by a device. Several hardware characterization protocols are able to detect the presence of crosstalk, but few provide sufficient information to distinguish various crosstalk errors from one another. In this article we describe how gate set tomography, a protocol for detailed characterization of quantum operations, can be used to identify and characterize crosstalk errors in quantum information processors. We demonstrate our methods on a two-qubit trapped-ion processor and a two-qubit subsystem of a superconducting transmon processor., 20 pages, 8 figures, 6 tables

As quantum information processors grow in quantum bit (qubit) count and functionality, the control and measurement system becomes a limiting factor to large scale extensibility. To tackle this challenge and keep pace with rapidly evolving classical control requirements, full control stack access is essential to system level optimization. We design a modular FPGA (field-programmable gate array) based system called QubiC to control and measure a superconducting quantum processing unit. The system includes room temperature electronics hardware, FPGA gateware, and engineering software. A prototype hardware module is assembled from several commercial off-the-shelf evaluation boards and in-house developed circuit boards. Gateware and software are designed to implement basic qubit control and measurement protocols. System functionality and performance are demonstrated by performing qubit chip characterization, gate optimization, and randomized benchmarking sequences on a superconducting quantum processor operating at the Advanced Quantum Testbed at Lawrence Berkeley National Laboratory. The single-qubit and two-qubit process fidelities are measured to be 0.9980$\pm$0.0001 and 0.948$\pm$0.004 by randomized benchmarking. With fast circuit sequence loading capability, the QubiC performs randomized compiling experiments efficiently and improves the feasibility of executing more complex algorithms., Comment: Final published version on IEEE Transactions on Quantum Engineering

Ternary quantum processors offer significant computational advantages over conventional qubit technologies, leveraging the encoding and processing of quantum information in qutrits (three-level systems). To evaluate and compare the performance of such emerging quantum hardware it is essential to have robust benchmarking methods suitable for a higher-dimensional Hilbert space. We demonstrate extensions of industry standard Randomized Benchmarking (RB) protocols, developed and used extensively for qubits, suitable for ternary quantum logic. Using a superconducting five-qutrit processor, we find a single-qutrit gate infidelity as low as $2.38 \times 10^{-3}$. Through interleaved RB, we find that this qutrit gate error is largely limited by the native (qubit-like) gate fidelity, and employ simultaneous RB to fully characterize cross-talk errors. Finally, we apply cycle benchmarking to a two-qutrit CSUM gate and obtain a two-qutrit process fidelity of $0.82$. Our results demonstrate a RB-based tool to characterize the obtain overall performance of a qutrit processor, and a general approach to diagnose control errors in future qudit hardware., 6 pages (+ 2 pages supplement), 5 figures

It has been proposed that there are new degrees of freedom intrinsic to quantum critical points that contribute to quantum critical physics. We study 2 + 1 D antiferromagnets in order to explore possible new quantum critical physics arising from nontrivial topological effects. We show that skyrmion excitations are stable at criticality and have nonzero probability at arbitrarily low temperatures. To include quantum critical skyrmion effects, we find a class of exact solutions composed of skyrmion and antiskyrmion superpositions, which we call topolons. We include the topolons in the partition function and renormalize by integrating out small size topolons and short wavelength spin waves. We obtain a correlation length critical exponent ν = 0.9297 and anomalous dimension η = 0.3381 .

Within the last decade, artificially engineered Bose Einstein Condensation has been achieved in atomic systems. Bose Einstein Condensates are superfluids just like bosonic Helium is and all interacting bosonic fluids are expected to be at low enough temperatures. One difference between the two systems is that superfluid Helium exhibits roton excitations while Bose Einstein Condensates have never been observed to have such excitations. The reason for the roton minimum in Helium is its proximity to a solid phase. The roton minimum is a consequence of enhanced density fluctuations at the reciprocal lattice vector of the stillborn solid. Bose Einstein Condensates in atomic traps are not near a solid phase and therefore do not exhibit roton minimum. We conclude that if Bose Einstein Condensates in an optical lattice are tuned near a transition to a Mott insulating phase, a roton minimum will develop at a reciprocal lattice vector of the lattice. Equivalently, a peak in the structure factor will appear at such a wavevector. The smallness of the roton gap or the largeness of the structure factor peak are experimental signatures of the proximity to the Mott transition., Comment: 4 pages, 5 figures

An array of Cooper paired planes will not have long-range phase coherence at any finite temperature owing to an infrared divergence of phase fluctuations when the coherence length perpendicular to the plane is small enough to prevent leakage of the superconducting order parameter within the planes. The phase correlations decay in a sufficiently slow manner to provide enough local phase coherence to make possible the nucleation of vortices. The planes then acquire Kosterlitz–Thouless topological order with its intrinsic rigidity and concomitant superfluidity. We conclude that the high-temperature superconducting cuprates are topologically ordered superconductors rather than phase-ordered superconductors since the large insulating layer between the copper–oxygen planes prevents effective leakage of the superfluid order parameter. For low enough superfluid densities, as in the underdoped cuprates studied by Uemura, the transition temperature T c will be proportional to the superfluid density corresponding to...

It is proposed that the event horizon of a black hole is a quantum phase transition of the vacuum of space-time analogous to the liquid-vapor critical point of a bose fluid. The equations of classical general relativity remain valid arbitrarily close to the horizon yet fail there through the divergence of a characteristic coherence length. The integrity of global time, required for conventional quantum mechanics to be defined, is maintained. The metric inside the event horizon is different from that predicted by classical general relativity and may be de Sitter space. The deviations from classical behavior lead to distinct spectroscopic and bolometric signatures that can, in principle, be observed at large distances from the black hole.

It is proposed that the infinite-red-shift surface of a black hole is a quantum phase transition of the vacuum of space-time analogous to the liquid-vapour critical point of a Bose fluid. The equations of classical general relativity remain valid arbitrarily close to the horizon yet fail there through the divergence of a characteristic coherence length E. The integrity of global time, required for conventional quantum mechanics to be defined, is maintained. The metric inside the event horizon is different from that predicted by classical general relativity and may be de Sitter space. The deviations from classical behaviour lead to distinct spectroscopic and bolometric signatures that can, in principle, be observed at large distances from the black hole.

In the present work we undertake a study of the quasi-static loop model and the observational consequences of the various solutions found. We obtain the most general solutions consistent with certain initial conditions. Great care is exercised in choosing these conditions to be physically plausible (motivated by observations). We show that the assumptions of previous quasi-static loop models, such as the models of Rosner, Tucker and Vaiana (1978) and Veseckey, Antiochos and Underwood (1979), are not necessarily valid for small loops at transition region temperatures. We find three general classes of solutions for the quasi-static loop model, which we denote, radiation dominated loops, conduction dominated loops and classical loops. These solutions are then compared with observations. Departures from the classical scaling law of RTV are found for the solutions obtained. It is shown that loops of the type that we model here can make a significant contribution to lower transition region emission via thermal conduction from the upper transition region.

The results of the Gravity Probe B relativity science mission published in Everitt et al (2011 Phys. Rev. Lett. 106 221101) required a rather sophisticated analysis of experimental data due to several unexpected complications discovered on-orbit. We give a detailed description of the Gravity Probe B data reduction. In the first paper (Silbergleit et al Class. Quantum Grav. 22 224018) we derived the measurement models, i.e., mathematical expressions for all the signals to analyze. In the third paper (Conklin et al Class. Quantum Grav. 22 224020) we explain the estimation algorithms and their program implementation, and discuss the experiment results obtained through data reduction. This paper deals with the science data preparation for the main analysis yielding the relativistic drift estimates.

During the last few years, investigations of Rare-Earth materials have made clear that not only the heavy fermion phase in these systems provides interesting physics, but the quantum criticality where such a phase dies exhibits novel phase transition physics not fully understood. Moreover, attempts to study the critical point numerically face the infamous fermion sign problem, which limits their accuracy. Effective action techniques and Callan-Symanzik equations have been very popular in high energy physics, where they enjoy a good record of success. Yet, they have been little exploited for fermionic systems in condensed matter physics. In this work, we apply the RG effective action and Callan-Symanzik techiques to the heavy fermion problem. We write for the first time the effective action describing the low energy physics of the system. The f-fermions are replaced by a dynamical scalar field whose nonzero expected value corresponds to the heavy fermion phase. This removes the fermion sign problem, making the effective action amenable to numerical studies as the effective theory is bosonic. Renormalization group studies of the effective action can be performed to extract approximations to nonperturbative effects at the transition. By performing one-loop renormalizations, resummed via Callan-Symanzik methods, we describe the heavy fermion criticality and predict the heavy fermion critical dynamical susceptibility and critical specific heat. The specific heat coefficient exponent we obtain (0.39) is in excellent agreement with the experimental result at low temperatures (0.4)., Comment: 5 pages. In the replacement, the numerical value for the specific heat coefficient exponent has been included explicitly in decimal form, and has been compared with the experimental results

Motivated by heavy ion collision experiments, we study the hydrodynamic properties of non-Abelian systems. These issues arise in condensed matter physics in the context of transport of spins in the presence of spin orbit coupling: the Pauli Hamiltonian governing the leading relativistic corrections in condensed matter systems can be rewritten in a language of SU(2) covariant derivatives, where the role of the non-Abelian gauge fields is taken by the physical electromagnetic fields. Taking a similar perspective as Jackiw and coworkers, we show that non-abelian hydrodynamical currents can be factored in a non-coherent 'classical' part, and a coherent part requiring macroscopic non-abelian quantum entanglement. Non-abelian flow being thus a much richer affair than familiar hydrodynamics, permits us to classify the various spin transport phenomena in in condensed matter physics in a unifying framework.In semiconductor spintronics, the absence of hydrodynamics is well known, but in our formulation it is directly associated with the fact that non-abelian currents are only covariantly conserved.We analyze the quantum mechanical single particle currents of relevance to mesoscopic transport with as highlight the Aharonov-Casher effect, where we demonstrate that the non-abelian transport structure renders it much more fragile than its abelian counterpart, the Aharonov-Bohm effect. We subsequently focus on spin flows protected by order parameters, of which the spin-spiral magnets and the spin superfluids are important examples. The surprising bonus is that the presence of an order parameter, being single-valued, restores hydrodynamics. We demonstrate a new effect: the trapping of electrical line charge, being the 'fixed frame' non-Abelian analogue of the familiar magnetic flux trapping by superconductors., Comment: 23 pages, 7 figures

It has been proposed that there are degrees of freedom intrinsic to quantum critical points that can contribute to quantum critical physics. We point out that this conclusion is quite general below the upper critical dimension. We show that in (2+1)D antiferromagnets Skyrmion excitations are stable at criticality and identify them as the critical excitations. We find exact solutions composed of Skyrmion and anti-Skyrmion superpositions, which we call topolons. We include the topolons in the partition function and renormalize by integrating out small size topolons and short wavelength spin waves. We obtain a correlation length exponent nu=0.690 666 and anomalous dimension eta=0.0166.

We show that the suppression of light scattering off a Bose Einstein Condensate is equivalent to the Landau argument for superfluidity and thus is a consequence of the {\it Principle of Superfluidity}. The superfluid ground state of a BEC contains nonseparable, nontrivial correlations between the bosons that make up the system, i. e., it is entangled. The correlations in the ground state entangle the bosons into a coherent state for the lowest energy state. The entanglement is so extreme that the bosons that make up the system cannot be excited at long wavenumbers. Their existence at low energies is impossible. Only quantum sound can be excited, i.e. the excitations are Bogolyubov quasiparticles which do not resemble free bosons whatsoever at low energies. This means that the system is superfluid by the Landau argument and the superfluidity is ultimately the reason for suppressed scattering at low wavelengths., 4 pages

Recently, a new phenomenological Hamiltonian has been proposed to describe the superconducting cuprates. This so-called Gossamer Hamiltonian is an apt model for a superconductor with strong on-site Coulomb repulsion between the electrons. It is shown that at half-filling the Gossamer superconductor with strong repulsion is unstable toward an antiferromagnetic insulator. The superconducting state undergoes a quantum phase transition to an antiferromagnetic insulator as one increases the on-site Coulomb repulsion. Near the transition the Gossamer superconductor becomes spectroscopically indistinguishable from the insulator.

The phase diagram of a single component Bose system in a lattice at zero temperature is obtained. We calculate the variational energies for the Mott insulating and superfluid phases. Below a certain critical density, which depends monotonically on the well depth of the lattice, the Mott insulating phase is stable over the superfluid phase for low enough tunelling amplitude regardless of whether the number of bosons is or is not incommensurate with the lattice. The transition is discontinuous as the superfluid order parameter jumps from a finite value to zero at the Mott transition., Comment: 4 pages, 2 figures

A set of new exact analytical General Relativity (GR) solutions with time-dependent and spatially inhomogeneous quintessence demonstrate 1) a static non-empty space-time with a horizon-type singular surface; 2) time-dependent spatially homogeneous `spheres' which are completely different in geometry from the Friedmann isotropic models; 3) infinitely strong anti-gravity at a `true' singularity where the density is infinitely large. It is also found that 4) the GR solutions allow for an extreme `density-free' form of energy that can generate regular space-time geometries.

In the current standard viewpoint small black holes are believed to emit radiation as black bodies at the Hawking temperature, at least until they reach Planck size, after which their fate is open to conjecture. A cogent argument against the existence of remnants is that, since no evident quantum number prevents it, black holes should radiate completely away to photons and other ordinary stable particles and vacuum, like any unstable quantum system. Here we argue the contrary, that the generalized uncertainty principle may prevent their total evaporation in exactly the same way that the uncertainty principle prevents the hydrogen atom from total collapse: the collapse is prevented, not by symmetry, but by dynamics, as a minimum size and mass are approached., Comment: 11 pages, 4 figures; Winner of 3rd Place in the 2001 Gravity Research Foundation Essay Competition

Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring theory, but the derivation given here is based on simpler and rather general considerations with either Newtonian gravitational theory or general relativity theory., Gravity Research Foundation essay. 14 pages Minor typos were corrected

We study the dynamical description of gravity, the appropriate definition of the scalar field energy-momentum tensor, and the interrelation between them in scalar-tensor theories of gravity. We show that the quantity which one would naively identify as the energy-momentum tensor of the scalar field is not appropriate because it is spoiled by a part of the dynamical description of gravity. A new connection can be defined in terms of which the full dynamical description of gravity is explicit, and the correct scalar field energy-momentum tensor can be immediately identified. Certain inequalities must be imposed on the two free functions (the coupling function and the potential) that define a particular scalar-tensor theory, to ensure that the scalar field energy density never becomes negative. The correct dynamical description leads naturally to the Einstein frame formulation of scalar-tensor gravity which is also studied in detail., Submitted to Phys. Rev D15, 10 pages. Uses ReVTeX macros

We discuss a recent provocative suggestion by Amelino-Camelia and others that classical spacetime may break down into ``quantum foam'' on distance scales many orders of magnitude larger than the Planck length, leading to effects which could be detected using large gravitational wave interferometers. This suggestion is based on a quantum uncertainty limit obtained by Wigner using a quantum clock in a gedanken timing experiment. Wigner's limit, however, is based on two unrealistic and unneccessary assumptions: that the clock is free to move, and that it does not interact with the environment. Removing either of these assumptions makes the uncertainty limit invalid, and removes the basis for Amelino-Camelia's suggestion., Comment: Submitted to Phys. Lett. B

We give a complete description of the asymptotic behavior of a Friedmann-Robertson-Walker Universe with ``normal'' matter and a minimally coupled scalar field. We classify the conditions under which the Universe is or is not accelerating. In particular, we show that only two types of large time behavior exist: an exponential regime, and a subexponential expansion with the logarithmic derivative of the scale factor tending to zero. In the case of the subexponetial expansion the Universe accelerates when the scalar field energy density is dominant and the potential behaves in a specified manner, or if matter violates the strong energy conditon $\rho + 3p >0$. When the expansion is exponential the Universe accelerates, and the scalar field energy density is dominant. We also find that the existence of the Big Bang and a never ending expansion of the Universe constrain the equation of state of matter at large and small densities, respectively., Comment: Submitte to Phys. Lett. A. Minor changes were made to clarify some points

We study the asymptotic behavior at late times of Friedmann-Robertson-Walker (uniform density) cosmological models within scalar-tensor theories of gravity. Particularly, we analyze the late time behavior in the present (matter dominated) epoch of the universe. The result of Damour and Nordtvedt that for a massless scalar in a flat cosmology the Universe evolves towards a state indistinguishable from general relativity is generalized. We first study a massless scalar field in an open universe. It is found that, while the universe tends to approach a state with less scalar contribution to gravity, the attractor mechanism is not effective enough to drive the theory towards a final state indistinguishable from general relativity. For the self-interacting case it is found that the scalar field potential dominates the late time behavior. In most cases this makes the attractor mechanism effective, thus resulting in a theory of gravity with vanishingly small scalar contribution even for the open Universe., Comment: 23 pages, no figures. Submitted for publicatiom in Phys. Rev, D15

We study the cosmological evolution of massless single-field scalar-tensor theories of gravitation from the time before the onset of $e^+e^-$ annihilation and nucleosynthesis up to the present. The cosmological evolution together with the observational bounds on the abundances of the lightest elements (those mostly produced in the early universe) place constraints on the coefficients of the Taylor series expansion of $a(\phi)$, which specifies the coupling of the scalar field to matter and is the only free function in the theory. In the case when $a(\phi)$ has a minimum (i.e., when the theory evolves towards general relativity) these constraints translate into a stronger limit on the Post-Newtonian parameters $\gamma$ and $\beta$ than any other observational test. Moreover, our bounds imply that, even at the epoch of annihilation and nucleosynthesis, the evolution of the universe must be very close to that predicted by general relativity if we do not want to over- or underproduce $^{4}$He. Thus the amount of scalar field contribution to gravity is very small even at such an early epoch., Comment: 15 pages, 2 figures, ReVTeX 3.1, submitted to Phys. Rev. D15