Experimental Quantum Channel Discrimination Using Metastable States of a Trapped Ion.

We present experimental demonstrations of accurate and unambiguous single-shot discrimination between three quantum channels using a single trapped ^{40}Ca^{+} ion. The three channels cannot be distinguished unambiguously using repeated single channel queries, the natural classical analogue. We develop techniques for using the six-dimensional D_{5/2} state space for quantum information processing, and we implement protocols to discriminate quantum channel analogues of phase shift keying and amplitude shift keying data encodings used in classical radio communication. The demonstrations achieve discrimination accuracy exceeding 99% in each case, limited entirely by known experimental imperfections.

Bootstrap Embedding on a Quantum Computer.

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match─at little additional computational cost─full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation.

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 - δ while only requiring a single copy of the initial state. We subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: Θ‖H‖|t|+ln(1/ϵ)+ln(1/δ). Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H2 molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.

Pareto-Optimal Clustering with the Primal Deterministic Information Bottleneck.

At the heart of both lossy compression and clustering is a trade-off between the fidelity and size of the learned representation. Our goal is to map out and study the Pareto frontier that quantifies this trade-off. We focus on the optimization of the Deterministic Information Bottleneck (DIB) objective over the space of hard clusterings. To this end, we introduce the primal DIB problem, which we show results in a much richer frontier than its previously studied Lagrangian relaxation when optimized over discrete search spaces. We present an algorithm for mapping out the Pareto frontier of the primal DIB trade-off that is also applicable to other two-objective clustering problems. We study general properties of the Pareto frontier, and we give both analytic and numerical evidence for logarithmic sparsity of the frontier in general. We provide evidence that our algorithm has polynomial scaling despite the super-exponential search space, and additionally, we propose a modification to the algorithm that can be used where sampling noise is expected to be significant. Finally, we use our algorithm to map the DIB frontier of three different tasks: compressing the English alphabet, extracting informative color classes from natural images, and compressing a group theory-inspired dataset, revealing interesting features of frontier, and demonstrating how the structure of the frontier can be used for model selection with a focus on points previously hidden by the cloak of the convex hull.

Qudit-Basis Universal Quantum Computation Using χ

We prove that universal quantum computation can be realized-using only linear optics and χ^{(2)} (three-wave mixing) interactions-in any (n+1)-dimensional qudit basis of the n-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that χ^{(2)} Hamiltonians and photon-number operators generate the full u(3) Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-Z gate can be implemented with only linear optics and χ^{(2)} interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection or subtraction, a technique enabled by χ^{(2)} interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool, in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states.

Optimal Hamiltonian Simulation by Quantum Signal Processing.

The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d-sparse Hamiltonian H[over ^] for time-interval t with error ε is O[td∥H[over ^]∥_{max}+log(1/ε)/loglog(1/ε)], which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H[over ^] into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.

Realization of a scalable Shor algorithm.

Certain algorithms for quantum computers are able to outperform their classical counterparts. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer. For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev. We factor the number 15 by effectively employing and controlling seven qubits and four "cache qubits" and by implementing generalized arithmetic operations, known as modular multipliers. This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%.

Quantum imaging by coherent enhancement.

Conventional wisdom dictates that to image the position of fluorescent atoms or molecules, one should stimulate as much emission and collect as many photons as possible. That is, in this classical case, it has always been assumed that the coherence time of the system should be made short, and that the statistical scaling ∼1/√t defines the resolution limit for imaging time t. However, here we show in contrast that given the same resources, a long coherence time permits a higher resolution image. In this quantum regime, we give a procedure for determining the position of a single two-level system and demonstrate that the standard errors of our position estimates scale at the Heisenberg limit as ∼1/t, a quadratic, and notably optimal, improvement over the classical case.

Fixed-point quantum search with an optimal number of queries.

Grover's quantum search and its generalization, quantum amplitude amplification, provide a quadratic advantage over classical algorithms for a diverse set of tasks but are tricky to use without knowing beforehand what fraction λ of the initial state is comprised of the target states. In contrast, fixed-point search algorithms need only a reliable lower bound on this fraction but, as a consequence, lose the very quadratic advantage that makes Grover's algorithm so appealing. Here we provide the first version of amplitude amplification that achieves fixed-point behavior without sacrificing the quantum speedup. Our result incorporates an adjustable bound on the failure probability and, for a given number of oracle queries, guarantees that this bound is satisfied over the broadest possible range of λ.

Motional heating in a graphene-coated ion trap.

Electric field noise originating from metal surfaces is a hindrance for a variety of microengineered systems, including for ions in microtraps, but is not well understood at the microscopic level. For trapped ions, it is manifested as motional-state decoherence inexplicable by thermal noise of electrodes alone, but likely surface-dependent. Here, we investigate the role of surface properties in motional heating by creating an ion trap with a unique exterior. Using single trapped-ion probes, we characterize copper electrodes covered in monolayer graphene, a material free of surface charge and dangling bonds. Surprisingly, we measure an average heating rate of 1020 ± 30 quanta/s, which is ∼100 times higher than typical for an uncoated trap operated under similar conditions. This may be related to hydrocarbon deposits on the surface, which could be monitored on graphene to potentially elucidate the mechanisms of motional heating on the atomic scale.

Microfabricated surface ion trap on a high-finesse optical mirror.

A novel approach to optics integration in ion traps is demonstrated based on a surface electrode ion trap that is microfabricated on top of a dielectric mirror. Additional optical losses due to fabrication are found to be as low as 80 ppm for light at 422 nm. The integrated mirror is used to demonstrate light collection from, and imaging of, a single Sr88(+) ion trapped 169±4 µm above the mirror.

Quantum codes give counterexamples to the unique preimage conjecture of the N-representability problem.

It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N-representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle preimage, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.

Cavity sideband cooling of a single trapped ion.

We report a demonstration and quantitative characterization of one-dimensional cavity cooling of a single trapped (88)Sr(+) ion in the resolved-sideband regime. We measure the spectrum of cavity transitions, the rates of cavity heating and cooling, and the steady-state cooling limit. The cavity cooling dynamics and cooling limit of 22.5(3) motional quanta, limited by the moderate coupling between the ion and the cavity, are consistent with a simple model [Phys. Rev. A 64, 033405 (2001)] without any free parameters, validating the rate equation model for cavity cooling.

Gapped two-body hamiltonian whose unique ground state is universal for one-way quantum computation.

Many-body entangled quantum states studied in condensed matter physics can be primary resources for quantum information, allowing any quantum computation to be realized using measurements alone, on the state. Such a universal state would be remarkably valuable, if only it were thermodynamically stable and experimentally accessible, by virtue of being the unique ground state of a physically reasonable Hamiltonian made of two-body, nearest-neighbor interactions. We introduce such a state, composed of six-state particles on a hexagonal lattice, and describe a general method for analyzing its properties based on its projected entangled pair state representation.

Temperature dependence of electric field noise above gold surfaces.

Electric field noise from fluctuating patch potentials is a significant problem for a broad range of precision experiments, including trapped ion quantum computation and single spin detection. Recent results demonstrated strong suppression of this noise by cryogenic cooling, suggesting an underlying thermal process. We present measurements characterizing the temperature and frequency dependence of the noise from 7 to 100 K, using a single Sr+ ion trapped 75 mum above the surface of a gold plated surface electrode ion trap. The noise amplitude is observed to have an approximate 1/f spectrum around 1 MHz, and grows rapidly with temperature as T;{beta} for beta from 2 to 4. The data are consistent with microfabricated cantilever measurements of noncontact friction but do not extrapolate to the dc measurements with neutral atoms or contact potential probes.

Suppression of heating rates in cryogenic surface-electrode ion traps.

Dense arrays of trapped ions provide one way of scaling up ion trap quantum information processing. However, miniaturization of ion traps is currently limited by sharply increasing motional state decoherence at sub-100 mum ion-electrode distances. We characterize heating rates in cryogenically cooled surface-electrode traps, with characteristic sizes in the 75 to 150 mum range. Upon cooling to 6 K, the measured rates are suppressed by 7 orders of magnitude, 2 orders of magnitude below previously published data of similarly sized traps operated at room temperature. The observed noise depends strongly on the fabrication process, which suggests further improvements are possible.

Ultra-small-sample molecular structure detection using microslot waveguide nuclear spin resonance.

We here report on the design of a planar microslot waveguide NMR probe with an induction element that can be fabricated at scales from centimeters to nanometers to allow analysis of biomolecules at nano- or picomole quantities, reducing the required amount of materials by several orders of magnitude. This device demonstrates the highest signal-to-noise ratio for a planar detector to date, measured by using the anomeric proton signal from a 15.6-nmol sample of sucrose. This probe had a linewidth of 1.1 Hz for pure water without susceptibility matching. Analysis of 1.57 nmol of ribonuclease-A shows high sensitivity in one- and two-dimensional NMR spectra. Along with reducing required sample volumes, this integrated geometry can be packed in parallel arrays and combined with microfluidic systems. Further development of this device may have broad implications not only for advancing our understanding of many intractable protein structures and their folding, molecular interactions, and dynamic behaviors, but also for high-sensitivity diagnosis of a number of protein conformational diseases.

Compact, filtered diode laser system for precision spectroscopy.

Stable, narrow-linewidth optical sources are necessary in modern atomic physics. An appealing approach to achieving approximately 10 kHz frequency stability is optical feedback. We have designed a compact external cavity diode laser with optical feedback to a filter cavity mounted on a single baseplate and enclosed inside a vacuum sealed box. The design was implemented for three wavelengths addressing the 422 nm cooling, 1091 nm repumping, and 674 nm clock transition lines of Sr(+). We are able to cool a single, trapped strontium ion to approximately 2 mK and observe motional sidebands of the 5S(1/2) <--> 4D(5/2) transition.

Wave scattering and splitting by magnetic metamaterials.

We study experimentally propagation of electromagnetic waves through a slab of uniaxial magnetic metamaterial. We observe a range of novel phenomena including partial focusing and splitting into multiple transmitted beams.We demonstrate that while some of these experimentally observed effects can be described within the approximation of an effective medium, a deeper understanding of the experimental results requires a rigorous study of internal eigenmodes of the lattice of resonators.

Efficient quantum circuits for Schur and Clebsch-Gordan transforms.

The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient {size poly[n,d,log(1/epsilon)] for accuracy epsilon} quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. Our circuits provide explicit efficient methods for solving such diverse problems as estimating the spectrum of a density operator, quantum hypothesis testing, and communicating without a shared reference frame. We thus render tractable a large series of methods for extracting resources from quantum systems and for numerous quantum information protocols.