Session P39: Quantum Advantage in Near-term Systems

Probing many-body dynamics on a large-scale quantum simulator

We demonstrate a method for the creation of controlled many-body quantum matter that combines deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. We realize a programmable Ising-type quantum spin model with tunable interactions and system sizes up to 51 qubits. Using this approach, we observe transitions into ordered states that break various discrete symmetries, verify their high-fidelity preparation, and investigate dynamics across the phase transition . In particular, we observe novel, robust many-body dynamics corresponding to persistent oscillations of the order after a sudden quantum quench, investigate quantum critical regimes with different universality classes and probe entanglement dynamics within this system. Finally, prospects for realization and testing of quantum optimization algorithms will be discussed.   

Optimal quantum algorithms to simulate strongly correlated fermionic systems

We discuss quantum simulation of strongly correlated fermionic lattice models with nearest-neighbor interacting qubit arrays. We improve an existing quantum algorithm to prepare arbitrary Slater determinants by exploiting a symmetry in their representations. We present a quantum algorithm to prepare an arbitrary fermionic Gaussian state with O(N²) gates and O(N) circuit depth. This algorithm---unlike existing ones that rely on translational symmetry---is completely general and is useful to simulating disordered systems and quantum impurity models. These two algorithms are optimal because the numbers of gates equal to the numbers of parameters to describe the quantum states to be prepared. We also present an algorithm to implement the 2-dimensional (2D) fermionic Fourier transformation on a 2D qubit array with O(N^1.5) gates and O(N^1/2) circuit depth. Both scalings are optimal because they represent the minimum cost for quantum information to travel through the qubit array. We also present methods to simulate each time step in the evolution of the 2D Hubbard model---again on a 2D qubit array---with O(N) gates and O(N^1/2) circuit depth. Finally, we discuss the physical significance of these algorithms using the Fermi-Hubbard model as an example.   

Boson sampling of multiple quantum random walkers on a lattice

A quantum device capable of performing an information-processing task more efficiently than current state of the art classical computers is said to demonstrate “quantum supremacy”. One path to achieving this in the short term is via “sampling complexity;” random samples are drawn from a probability distribution by measuring a complex quantum state in a defined basis. Surprisingly, a gas of identical noninteracting bosons can yield sampling complexity due solely to quantum statistics, as shown by Aaronson and Arkhipov, dubbed “boson sampling,” in the context of identical photons scattering from a linear optical network. We generalize this to noninteracting bosonic quantum random walkers on a 1D lattice. We study the quantum complexity of the probability distribution obtained through a discrete-time quantum random walk. Here the goal is to approximate a Haar-random unitary map on a single boson, and quantum statistics yields the many-body complexity. We consider a physical realization based on controlled transport of ultra-cold atoms in a spinor optical lattice. We quantify the degree of randomness (and thus complexity) of the unitarity map using different techniques from random matrix theory, unitary t-designs, and Renyi entropy.   

Feeding the multitude: A polynomial-time algorithm to improve sampling of degenerate optimization problems

A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution space tends to be favored while, in the worst case, some solutions can never be accessed by the employed algorithm. Here we present a simple post-processing technique that improves sampling for any optimization technique. Starting from a pool of known optima, the algorithm generates potentially new solutions via rejection-free cluster updates at zero temperature. Although the method is not ergodic and there is no guarantee that any new states can be found, the solution pool is typically increased. We illustrate our results on exponentially-biased data produced on the D-Wave 2X quantum annealer.   

Noise-resilient quantum circuits

Certain quantum circuits are shown to be surprisingly resilient to noise. The circuit depth scales with the system size, but even without error correction, low-order correlation functions are perturbed at most by an amount comparable to the noise strength, independent of the system size. These circuits can be run on a noisy quantum computer of moderate size to assist variational calculations of various tensor networks. In particular, the dependence of the computational cost on the variational parameters can be exponentially reduced by the quantum computer. We estimate the computational cost based on realistic physical parameters, and find that it is far smaller than the cost of classical computation.   

Boson Sampling in the Frequency Domain

We present a scheme to perform Boson sampling using frequency modes that results in significantly reduced losses and experimental complexity as compared to existing spatial mode implementations. Boson sampling is computationally intractable on a classical computer but can be efficiently performed using a linear optical network. Our scheme uses Bragg-scattering four wave mixing (BS-FWM), a third-order nonlinear process to achieve coherent interaction between a large number of frequency modes mediated by strong classical pumps and has distinct advantages over spatial mode implementations. While spatial beam splitters couple only nearest neighbors, it is straightforward to create highly delocalized non-nearest neighbor couplings using BS-FWM, leading to complex unitary interaction with fewer resources. Moreover, the interaction takes place in a single nonlinear fiber, resulting in fixed loss independent of the number of modes. To demonstrate experimental feasibility, we show Hong-Ou-Mandel interference between correlated photons of distinct frequencies, using BS-FWM as a frequency beam splitter. We believe our scheme addresses multiple challenges to scale Boson Sampling to the regime of 20-30 photons, which could provide confirmation for quantum speedup over classical simulations.   

Randomized Benchmarking with Restricted Gate Sets

Standard randomized benchmarking protocols require sampling from a unitary 2-design, which is not always practical. In this talk I examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2-designs. I show in a variety of cases that one can benchmark the error probability to within a small factor that rapidly approaches unity as the number of qubits in the benchmarking experiment grows.   

The Effect of Coherent Errors in Error Correction

The first threshold theorems for fault tolerant quantum computation assumed a stochastic error model. More recently there has been interest in coherent errors, because under these errors the error rate can grow quadratically instead of linearly. Even with the same error rate per gate, a coherent error model could have orders of magnitude larger error for the whole computation. Past work on coherent errors has focused on a constant single-qubit coherent error as a simple case. This work treats coherent, Markovian noise with arbitrary correlations in space using a random ensemble approach. The noise at each time step is drawn from some distribution on the space of channels. We work with an arbitrary family of stabilizer codes paired with a family of ensemble noise models and prove that if the correlations for the noise models satisfy a bound, the logical error rate and the residual logical noise approach the incoherent answer. We present a modified threshold theorem that gives conditions on the noise models such that an arbitrary length computation can be successfully performed.   

General error-transparent quantum gates for fault-tolerant quantum computation

Error-transparent (ET) quantum gates have recently been proposed for small logical qubit architectures [arXiv:1703.09762]. The key idea is to design the Hamiltonian evolution for an ET logical quantum gate, so that it commutes with all first order error processes which may occur anytime during the evolution. Even if the error occurs in the mid of the evolution, it will be detected/corrected at the end of the evolution without compromising the encoded quantum information. We provide a general construction of ET logical quantum gates for any quantum error correction code. In addition, we investigate practical implementation of ET logical quantum gates with circuit QED systems.   

Quantum inspired tempering

We introduce a replica exchange heuristic based on the Shin Smith Smolin
Vazirani semi-classical approximation of quantum annealing
(arXiv:1401.7087), combined with algorithmic accelerators from the study
of spin glasses. The algorithm is benchmarked against current
state of the art classical heuristics, as well as quantum optimization
machines using synthetic spin-glass benchmarks.   

Imaging incoherent point sources with quantum-inspired measurements

Every imaging technique has a resolution limit. The ability to image closely-separated point sources faces the diffraction limit, or “Rayleigh’s curse”. However, recent progress by Tsang et al. [Phys. Rev. X 6, 031033 (2016), New Journ. Phys. 19, 023054 (2017)] has dispelled the curse: the separation of two incoherent point sources has a non-vanishing Fisher information even as the separation goes to zero. The separation, and any statistical moment of the source distribution, can be estimated using quantum-information-inspired measurements that address information contained in the full electromagnetic field rather than the intensity alone. There has been an upstart of experiments showing this advantage over direct imaging techniques. In this talk I will review the recent experimental progress in our group [Phys. Rev. Lett. 118, 070801 (2017)] which demonstrates an improved ability to estimate the separation distance between two sources, and our continuing efforts towards implementing these measurements in realistic imaging scenarios.

  

Searching for Axion Dark Matter using Superconducting Qubits

A transmon qubit can be operated in a resonant cavity as a sensor of a single microwave photon produced by the interaction between axion dark matter and a laboratory magnetic field. The axion is a potential solution to the strong CP problem in QCD and could account for the abundance of dark matter observed in the universe. In the presence of an applied magnetic field, the axion field will source a current that can be harnessed to drive a resonant cavity to single photon occupation. When weakly coupled to the detection cavity through a dipole interaction, the qubit transition frequency shift is used to measure the cavity photon number. The use of a direct dispersive quantum non-demolition measurement of the photon number decouples the measurement induced back action from the experimental uncertainties.