Session E33: Applications with Near-Term Superconducting Quantum Devices

Applications of restricted near-term superconducting qubit architectures: Using quantum control to reach quantum advantage

While universal quantum computers certainly will have to be fault tolerant, there is the alternative line of thinking to demonstrate quantum advantage on near-term hardware, with limited number of gates, qubits, and connectivity. This can be achieved by careful co-design of hardware, algorithms, and controls.
I will describe a specific application of this idea, a quantum subroutine to the classical variational Cluster algorithm for the Fermi Hubbard model [1] . This approach can simulate an infinite Hubbard lattice at nonzero temperature with limited resources [2].
One way to make this algorithm maximally effective is the judicious use of one-shot implementations of important gate. To this end, we introduce the iFREDKIN [3] - a three qubit gate that is important in this type of application and that can be implemented in one shot in superconducting qubits with the aid of pulse shaping [4]. We will show further application of exchange-based gates in 1d architectures [5].
inspired by classical computational physics, we will show how to benchmark conservation laws efficiently [6].

[1] P.-L. Dallaire-Demers and F. K. Wilhelm, Phys. Rev. A. 93, 032303 (2016)
[2] P.-L. Dallaire-Demers and F. K. Wilhelm, Phys. Rev. A. 94, 062304 (2016)
[3] P.J. Liebermann, P.-L. Dallaire-Demers, F.K. Wilhelm, arXiv:1701.07870
[4] S. Machnes, D.J. Tannor, F. K. Wilhelm and E. Assémat, arXiv:1507.04261
[5] F. Motzoi, M. P. Kaicher, and F. K. Wilhelm, Phys. Rev. Lett. 119, 160503 (2017)
[6] T. Chasseur, F. Motzoi, M. Kaicher, P.-L. Dallaire-Demers, F.K. Wilhelm, arXiv:1710.04563   

Training a classifier with a superconducting quantum processor

Recent theoretical and experimental progress in quantum information suggests that there may be advantages in quantum-assisted heuristic algorithms for near-term devices, even at relatively shallow circuit depths. In the particular case of machine learning, in the light of increasing dataset sizes there is basis to hold the concern that traditional computational resources will become increasingly inefficient to growing challenges. In this talk, I will explore potential solutions to some of these problems by using quantum support to classical optimizers in solving classification problems.   

Linear and Logarithmic Time Compositions of Quantum Many-Body Operators

We develop a generalized framework for constructing many-body-interaction operations either in linear time or in logarithmic time with a linear number of ancilla qubits. Exact gate decompositions are given for Pauli strings, many-control Toffoli gates, number- and parity-conserving interactions, unitary coupled cluster operations, and sparse matrix generators. We provide a linear time protocol that works by creating a superposition of exponentially many different possible operator strings and then uses dynamical
decoupling methodology to undo all the unwanted terms. A logarithmic time protocol overcomes the speed limit of the first by using ancilla registers to condition evolution to the support of the desired many-body interaction before using parallel chaining operations to expand the string length. The two techniques improve substantially on current strategies (reductions in time and space ranging from linear to
exponential), are applicable to different physical interaction mechanisms such as CNOT , XX, and XX+YY, and generalize to a wide range of many-body operators.   

Sampling and scrambling on a chain of superconducting qubits

We study a circuit, the Josephson sampler, that embeds a real vector into an entangled state of n qubits, and optionally samples from it. We measure its fidelity and entanglement on the 16-qubit ibmqx5 chip. To assess its expressiveness, we also measure its ability to generate Haar random unitaries and quantum chaos, as measured by Porter-Thomas statistics and out-of-time-order correlation functions. The circuit requires nearest-neighbor CZ gates on a chain and is especially well suited for first-generation superconducting architectures.   

Tensor-network based variational approach to calculating ground state properties of interacting quantum systems with superconducting qubits

Variational quantum-classical hybrid algorithms have recently emerged as a promising application for near-term quantum devices. In superconducting circuits, recent demonstrations of this algorithm with up to four qubits have probed the energy landscapes of simple molecules and spin chains. As these devices scale to increasingly larger numbers of qubits, the choice of ansatz for the variationally-optimized wavefunction becomes more important. An ideal ansatz combines two desiderata: the ability to represent a large portion of the n-qubit Hilbert space, specifically highly-entangled states; and a circuit depth which scales polynomially with the qubit number. Recently, classical methods based on tensor networks have become popular for compactly handling wavefunctions of interacting systems which possess a high degree of entanglement. Motivated by their successes, we apply tensor network ansatze to the variational quantum eigensolver in an experimental setting: an superconducting quantum processor comprising eight transmon qubits. Our approach is intended to study ground-state properties of interacting systems, e.g. spin chains. Here we detail the experimental protocol and present preliminary data.   

Low Depth Quantum Simulation of Electronic Structure

The majority of quantum algorithms for solving the electronic structure problem encode the wavefunction using N Gaussian orbitals, leading to Hamiltonians with O(N^4) second-quantized terms. We avoid this overhead and extend methods to the condensed phase by utilizing a dual form of the plane wave basis which diagonalizes the potential operator, leading to a Hamiltonian representation with O(N^2) second-quantized terms. Using this representation we can implement single Trotter steps of the Hamiltonians with linear gate depth on a planar lattice. Properties of the basis allow us to deploy Trotter and Taylor series based simulations with respective circuit depths of O(N^{7/2}) and O(N^{8/3}) for fixed charge densities - both large asymptotic improvements over all prior results. Variational algorithms also require significantly fewer measurements to find the mean energy in this basis, ameliorating a primary challenge of that approach. We conclude with a proposal to simulate the uniform electron gas (jellium) using a low depth variational ansatz realizable on near-term quantum devices. From these results we identify simulations of low density jellium as a promising first setting to explore quantum supremacy in electronic structure.   

Quantum chemistry algorithms for efficient quantum computing

Quantum chemistry is definitely one of the most promising application areas of near term quantum computers. The exponentially large Hilbert space of molecular systems can be efficiently mapped into the spin configuration space of available quantum computers offering a unique opportunity for the solution of interesting electronic structure problems with unprecedented accuracy. To achieve this goal, new quantum algorithms need to be develop that are able to best exploit the potential of quantum speed-up. While this effort should target the design of quantum algorithms for the future fault-tolerant quantum hardware, there is pressing need to develop algorithms, which can be implemented in present-day non-fault tolerant quantum hardware with limited coherence time. In this talk, we will discuss (i) ways to derive efficient trial wavefunctions based on known quantum chemistry solutions (like e.g., Moller-Plesset perturbation theory and Unitary Coupled Cluster), (ii) schemes to map states to available quantum computer architectures, and (iii) procedures to reduce the overall circuit depths in quantum chemistry calculations and experiments. These methods will be applied to a set of model systems (e.g., the Hubbard model) and molecules.   

Adiabatic Quantum Chemistry Simulations with Superconducting Qubits

Quantum technology is improving fast and quantum devices with more than 50 qubits appear feasible soon. The quest for systems which profit of exponential speed-up and cannot be calculated on classical computers has recently triggered a lot of attention. Quantum chemistry is among the best candidates for exploiting such exponential speed-up. Quantum chemistry Hamiltonians can be directly mapped on quantum devices based on superconducting qubits. However, the controlled realization of different types of interactions between qubits without compromising their coherence is essential. A coupling method between fixed-frequency transmon qubits can be achieved with the frequency modulation of an auxiliary capacitively coupled quantum bus. An adiabatic protocol for the hydrogen molecule can be implemented on such a coupled qubit system. We show that the electronic ground state of the molecule can be reached within the typical coherence time of a superconducting qubit. Hence, the quantum system of the hydrogen molecule can directly be mapped to the quantum system of a qubit device.   

Spectral signatures of many-body localization of interacting photons

Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization, but, can interacting systems always equilibrate regardless of parameter values? The energy spectrum of a system can answer this question and reveal the nature of the underlying phases. However, most experimental techniques only indirectly probe the many-body energy spectrum. Using a chain of nine superconducting qubits, we implement a novel technique for directly resolving the energy levels of interacting photons. We benchmark this method by capturing the intricate energy spectrum predicted for 2D electrons in a magnetic field, the Hofstadter butterfly. By increasing disorder, the spatial extent of energy eigenstates at the edge of the energy band shrink, suggesting the formation of a mobility edge. At strong disorder, the energy levels cease to repel one another and their statistics approaches a Poisson distribution -the hallmark of transition from the thermal to the many-body localized phase. Our work introduces a new many-body spectroscopy technique to study quantum phases of matter.   

Experimental implementation of error mitigation for short-depth quantum circuits

Quantum simulation is believed to be one of the near-term applications of early quantum computers. These simulations involve the preparation of a quantum state using a short-depth quantum circuit and the measurement of expectation values of observables of interest. The accuracy of these expectation values is however affected by decoherence during state preparation. While the implementation of a fully-fault tolerant architecture is beyond the scope of near-term hardware, a technique for mitigating such errors that requires no additional quantum resources was recently proposed [arXiv:1612.02058]. In this approach, the quantum state preparation is stretched in time, and the associated measurements of the expectation values are used to extrapolate to their noise-free values, thereby improving the fidelity of the chosen observable, without error-correcting the quantum state. We present our progress towards the experimental implementation of this technique.   

Realization of a Quantum Random Generator Certified with the Kochen-Specker Theorem

Random numbers are required for a variety of applications from secure communications to Monte-Carlo simulation. Yet randomness is an asymptotic property and no output string generated by a physical device can be strictly proven to be random. I will present an experimental realization of a quantum random number generator (QRNG) with randomness certified by quantum contextuality and the Kochen-Specker theorem. The certification is not performed in a device-independent way but through a rigorous theoretical proof of each outcome being value indefinite even in the presence of experimental imperfections. Our realization is based on cavity QED and transmon type qutrit. The coherent control and the single-shot quantum non-demolition readout enabled by the Josephson parametric amplifier has been recently used to demonstrate contextuality of the transmon based qutrit, the resource underlying the operation of the QNRG. We extend this technique to enable three-level single-shot non-demolition readout required by the protocol and we generate 10 GBit of raw data with the bitrate of 50 kBit/s. The generated data passes the standard statistical test suites. Analysis of the data with tests related to the algorithmic randomness of a sequence provides evidence of incomputable nature of the QNRG.