# QSC 2019

## Program

**Monday 14**

**09:30 - 10:00 REGISTRATION**

**10:00 - 10:45 F. Wilhelm-Mauch**

**10:45 - 11:30 P. Schindler**

**12:00 - 12:45 F. Deppe**

**12:45 - 13:15 A. Gonzalez-Tudela**: *Analog quantum chemistry simulation with ultra-cold atoms*

Solving quantum chemistry problems with a quantum computer is one of the most exciting applications of future quantum technologies. Current efforts are focused on finding on algorithms that allow the efficient simulation of chemistry problems in a digital way. In this talk, I will present a complementary approach to the problem which consists in simulating quantum chemistry problems using ultra-cold atoms [1]. I will first show how to simulate the different parts of the Hamiltonian, and then benchmark it with simple molecules.

[1] arXiv:1807.09228

**15:00 - 15:45 C. M. Smith**

**15:45 - 16:15 R. Babbush***: Reducing the measurements required for accurate variational quantum simulations*

Many applications of quantum simulation require that one prepare and then characterize quantum states by performing an efficient partial tomography to estimate observables corresponding to k-body reduced density matrices (k-RDMs). For instance, variational algorithms for the quantum simulation of chemistry usually require that one measure the fermionic 2-RDM. While such marginals provide a tractable description of quantum states from which many important properties can be computed, their determination often requires a prohibitively large number of circuit repetitions. First, we will discuss techniques introduced in arXiv:1907.13117 that cubically reduces the number of unique circuits required to estimate the energy of molecular systems in a variational context while also enabling a power form of error-mitigation. Then, we describe techniques introduced in arXiv:1908.05628 that enable one to measure all elements of k-body qubit RDMs acting on N qubits with a number of circuits scaling as O(3^k log^{k−1} N), an exponential improvement in N over prior art. We expect these results will improve the viability of many proposals for near-term quantum simulation.

**16:45 - 17:30 C. Hempel**

**17:30 - 18:15 POSTER SESSION**

**Tuesday 15**

**10:00 - 10:45 T. Esslinger**

**10:45 - 11:30 M.A. Martin-Delgado**

**12:00 - 12:45 S. Bravyi**

**12:45 - 13:15 A. Vrajitoarea**: *Quantum simulation in a field-programmable cavity array*

Superconducting circuits extensively rely on the Josephson junction as a nonlinear electronic element for manipulating quantum information and mediating interactions between microwave photons. In this talk, we will present a new paradigm in exploiting the Josephson nonlinearity for the purpose of tailoring the Hilbert space of harmonic oscillators using a parametrically activated three-wave interaction with an ancillary mode. This dynamical capability has been demonstrated for a single microwave resonator [1], where the one-photon manifold is addressed as an isolated two-level system, offering a promising pathway to designing long-lived qubits. This novel approach of engineering oscillators with stimulated nonlinearity can be extended to an array of coupled cavities for studying non-equilibrium physics with photons. We will present a proposal for a hardware-efficient simulator, whereby a single nonlinear Josephson circuit is coupled to a cavity lattice allowing independent control of photon hopping and interactions via frequency-selective flux modulation. Theoretical investigations show that for strong stimulated nonlinearities, the driven-dissipative steady state develops spatial density-density correlations indicating that photons crystallise in the lattice.

[1] A. Vrajitoarea et al., Quantum control of an oscillator using stimulated nonlinearity [arXiv:1810.10025]

**15:00 - 15:45 S. Filipp**:* Computing molecular spectra on superconducting near-term quantum devices*

A key requirement for performing useful computations on current quantum processors is the design of quantum algorithms with short circuit depth. This can be achieved by gates that are tailored to the problem at hand and which can be directly implemented in hardware. In our experiments we implement exchange-type gates realized by parametrically-driven couplers on a superconducting qubit platform. Such gates preserve the number of qubit excitations corresponding to the fixed number of electrons in a molecule and are thus ideally suited for quantum chemistry computations. We determine the energy spectrum of molecular hydrogen using the variational quantum eigensolver (VQE) algorithm combined with the equations-of-motion method to compute its excited states. We compute the eigenstates within an accuracy of 50 mHartree on average, a good starting point for near-term applications with scientific and commercial relevance.

**15:45 - 16:15 C. Wunderlich**: *Quantum Information Processing using Trapped Atomic Ions and MAGIC*

Trapped atomic ions are a very well characterized physical system for quantum information science (QIS) and its applications. When considering the scalability of trapped ions, the use of laser light for coherent operations turns out to give rise to technological issues, and to difficulties rooted in the physics related to trapped ions. In suitably modified ion traps that allow for magnetic gradient induced coupling (MAGIC) [1], laser light can be replaced by long wavelength radiation in the radio-frequency (RF) regime, thus facilitating scalability. Recent experimental results obtained using a freely programmable quantum computer (QC) based on MAGIC will be summarized first. In particular, we will report on a proof-of-principle experimental demonstration of the deliberation process in the framework of reinforcement learning on a quantum computer [2]. This experiment at the boundary between QIS and machine learning shows that decision making for reinforcement learning is sped up quadratically on a QC as compared to a classical agent. In addition, by varying the initial relative probabilities for obtaining a desired action over a wide range, we show that this experiment preserves these relative probabilities during the deliberation process. RF-driven atomic ions and MAGIC, as used in these experiments, are a promising approach for realizing scalable quantum computing using interconnected modules containing quantum processors [3]. Transport of trapped ions is a prerequisite for this and other scalable strategies for quantum computing with trapped ions [4]. We have shown, by shuttling a single 171Yb+ ion 22 x 106 times and quantifying the coherence of its hyperfine qubit, that the quantum information stored in this qubit is preserved with a fidelity of 99.9994(+6 -7)% during transport of the ion over a distance of 250 µm [5]. Then we will report on the experimental progress in realizing fast 2-qubit RF gates that are robust against variations in the secular trap frequency and Rabi frequency.

[1] C. Piltz, T. Sriarunothai, S.S. Ivanov, S. Wölk, C. Wunderlich, “Versatile microwave-driven trapped ion spin system for quantum information processing”, Science Advances 2, e1600093 (2016).

[2] Th. Sriarunothai, S. Wölk, G.S. Giri, N. Friis, V. Dunjko, H. J. Briegel, and Ch. Wunderlich, „Speeding-up the decision making of a learning agent using an ion trap quantum processor”, Quantum Science and Technology 4, 015014 (2019).

[3] B. Lekitsch, S. Weidt, A. G. Fowler, K. Molmer, S. J. Devitt, C. Wunderlich and W. K. Hensinger, “Blueprint for a microwave trapped ion quantum computer”, Science Advances 3, e1601540 (2017).

[4] D. Kielpinski, C. Monroe and D. J. Wineland, “Architecture for a large-scale ion-trap quantum computer” Nature 417, 709 (2002).

[5] P. Kaufmann, T. F. Gloger, D. Kaufmann, M. Johanning and Ch. Wunderlich, „High-Fidelity Preservation of Quantum Information During Trapped-Ion Transport”, Phys. Rev. Lett. 120, 010501 (2018).

**16:45 - 17:30 C. Savoie**

**17:30 - 18:15 ROUND TABLE**

**Wednesday 16**

**10:00 - 10:45 A. Wallraff**

**10:45 - 11:30 A. Amo**

**12:00 - 12:45 F. Brandao**

**12:45 - 13:15 A. King**: *Dynamics of quantum and classical simulations of a quantum magnet*

Programmable simulation of quantum magnets has been established as a promising and natural early application of quantum annealing (QA) processors, as demonstrated in 3D spin glasses (Science 165, 2018) and geometrically frustrated 2D lattices (Nature 560, 2018). Here we study relaxation dynamics in the second case, comparing QA in a lower-noise D-Wave prototype with path-integral QMC. Although this Hamiltonian is sign-problem free, QMC dynamics remain many orders of magnitude slower than QA even when tailored cluster updates and imaginary-time discretisation are incorporated. More importantly, our results show scaling in both temperature and system size: the advantage of using quantum hardware increases as the systems become larger and colder. This is a key validation of the ability of flux qubits to efficiently simulate systems in the transverse field Ising model.

**15:00 - 15:45 J. Bermejo-Vega**: *Quantum advantage from short-time Hamiltonian dynamics*

A near-term goal in quantum computation and simulation is to realize a quantum device showing a computational advantage. The goal here is to perform a quantum experiment whose outcome cannot be efficiently predicted on a classical computer. A hope of this program is that performing such an experiment may be simpler than building a universal quantum computer. Candidate quantum devices for this task include boson samplers and Google-AI’s random quantum circuits.

In this talk, we will review the current approaches towards demonstrating superior quantum computational power, as well as associated challenges concerning scalability, verifiability and complexity theoretic soundness. We will introduce a new proposal based on short-time evolutions of 2D Ising models [1-3]. Our proposal has the benign features of being hard to simulate classically (assuming plausible complexity theoretic conjectures) while being reasonably close to cold-atomic quantum implementations, and admitting an efficient simple quantum verification protocol. We will also present recent complexity-theoretic results (on anti-concentration and average-case hardness) [3], giving the strongest evidence to date that Hamiltonian quantum simulation architectures are classically intractable. Our work shows that realistic quantum simulators can demonstrate reliable quantum advantages.

[1] J. Bermejo-Vega, D. Hangleiter, M. Schwarz, R. Raussendorf, and J. Eisert, Architectures for quantum simulation showing a quantum speedup, Phys. Rev. X 8, 021010, https://arxiv.org/abs/1703.00466

[2] D. Hangleiter, J. Bermejo-Vega, M. Schwarz, and J. Eisert, Anti-concentration theorems for schemes showing a quantum speedup, Quantum 2, 65 (2018), https://arxiv.org/abs/1706.03786

[3] Jonas Haferkamp, Dominik Hangleiter, Adam Bouland, Bill Fefferman, Jens Eisert, Juani Bermejo-Vega, Closing gaps of a quantum advantage with short-time Hamiltonian dynamics, https://arxiv.org/abs/1908.08069

**15:45 - 16:15 D. Mills**

The search for an application of near-term quantum devices is widespread. Quantum Machine Learning is touted as a potential utilisation of such devices, particularly those which are out of the reach of the simulation capabilities of classical computers. In this work, we propose a generative Quantum Machine Learning Model, called the Ising Born Machine (IBM), which we show cannot, in the worst case, and up to suitable notions of error, be simulated efficiently by a classical device. We also show this holds for all the circuit families encountered during training. In particular, we explore quantum circuit learning using non-universal circuits derived from Ising Model Hamiltonians, which are implementable on near term quantum devices. We propose two novel training methods for the IBM by utilising the Stein Discrepancy and the Sinkhorn Divergence cost functions. We show numerically, both using a simulator within Rigetti's Forest platform and on the Aspen-1 16Q chip, that the cost functions we suggest outperform the more commonly used Maximum Mean Discrepancy (MMD) for differentiable training. We also propose an improvement to the MMD by proposing a novel utilisation of quantum kernels which we demonstrate provides improvements over its classical counterpart. We discuss the potential of these methods to learn `hard' quantum distributions, a feat which would demonstrate the advantage of quantum over classical computers, and provide the first formal definitions for what we call `Quantum Learning Supremacy'. Finally, we propose a novel view on the area of quantum circuit compilation by using the IBM to `mimic' target quantum circuits using classical output data only.

**16:45 - 17:30 G. Pagano**

**17:30 - 18:00 T. O’Brien**: *Calculating energy derivatives for quantum chemistry on a quantum computer*

Modelling chemical reactions and complicated molecular systems has been proposed as the `killer application' for a future quantum computer. Accurate calculations of derivatives of eigenenergies are essential towards this end, allowing for geometry optimisation, transition state search, prediction of the response to applied electric and magnetic fields, and dynamical molecular simulations. In this work we survey previous methods to calculate energy derivatives, and present two new methods: one based on quantum phase estimation, the other on the quantum subspace expansion. We calculate asymptotic error bounds and approximate computational scalings for the methods presented. We implement these methods, performing the world's first geometry optimisation on an experimental quantum processor, estimating the equilibrium bond length of the dihydrogen molecule to within 0.014 Angstrom of the full configuration interaction value. Within the same experiment, we estimate the polarisability of the H2 molecule, finding agreement at the equilibrium bond length to within 0.06 a.u. (2% relative error).

**Thursday 17**

**10:00 - 10:45 J. Martinis**

**10:45 - 11:30 D. Aharonov**

**12:00 - 12:45 L. Vandersypen**

**12:45 - 13:15 J. Watson**

The field of Hamiltonian Complexity is concerned with the Local Hamiltonian problem, which asks for the ground state energy of a Hamiltonian to some precision. There have been a succession of results which prove hardness results for Hamiltonians with progressively more ``natural’’ parameters such as k-locality. We extend the field of Hamiltonian Complexity to the thermodynamic limit by introducing the `Ground State Energy Density Problem’ (GSED Problem). This asks whether the ground state energy density of a fixed Hamiltonian on a lattice in the thermodynamic limit is above or below a pair of parameters. The classical problem is shown to be NEEXP complete for a 2D, nearest neighbour, translationally invariant Hamiltonian. The quantum GSED problem is contained in QMA_EEXP, the quantum analogue of NEEXP for 2D, nearest neighbour, translationally invariant Hamiltonians. However, we give strong evidence that it is not QMA_EEXP-hard, making GSED a surprising natural example of a QMA_EEXP-intermediate problem. The problem is interesting not just because it applies to the thermodynamic limit, but also because we keep a fixed Hamiltonian. Therefore, for our hardness proof, we must encoded all NEEXP/QMA_EEXP instances in the ground state energy density of a single Hamiltonian. The result is that the only parameter we have is the precision to which we want the ground state.

**15:00 - 15:45 S. Boixo**

**15:45 - 16:15 E. Torrontegui**

We design protocols to implement ultra-fast two qubit gates with trapped ions allowing operations faster than the trapping period making the gate less sensitive to decoherence. Using optimisation techniques we design pulse sequences and shapes allowing high fidelity operations.

**16:45 - 17:30 S. Jordan**

**17:30 - 18:00 J. Gray**

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to tensor networks with irregular geometries. Finding the best possible contraction path for such networks is a central problem, with an exponential effect on the subsequent classical computational effort and memory footprint. In this work, we adapt a variety of tools from graph theory and network science to the contraction path problem and implement new randomised protocols that find very high quality contraction paths for arbitrary and large tensor networks. In some cases the paths found are more than a billion times better than the most established current approach. We find that different underlying geometries suit different methods and therefore suggest a hyper-optimisation approach, where both the method applied and its algorithmic parameters are tuned during the path finding. The increase in quality of contraction schemes found has significant practical implications for the simulation of quantum many-body systems, and further raises the barrier for practically demonstrating a quantum advantage.

**Friday 18**

**10:00 - 10:45 J. Eisert: ***Benchmarking quantum technologies*

At the same time as the development of quantum technologies progresses rapidly, new demands concerning the certification of their operation emerge. A question relevant for the application of various quantum technologies consequently is how the user can ensure the correct functioning of the quantum devices. In a number of instances, specifically in quantum simulation and quantum computing, challenges in appropriately benchmarking components or entire protocols constitute a widely acknowledged bottleneck. This talk will suggest several new takes to the problem at hand: We will see how data from SPAM-robust randomized benchmarking [1] can be used to perform process tomography of quantum gates in an experimentally-friendly and provably sample optimal fashion [2], making use of a machinery of compressed sensing and exploiting structure - that is to say, the components of a quantum circuit. We will see how qantum states can be characterizes provably even with imperfect detectors in what could be called semi-device-dependent tomography [3]. The issue becomes more challenging when one aims at certifying the functioning of an entire device. We will look at limitations to black-box verification for sampling problems that show a quantum advantage or "supremacy" [4], will have a fresh look at Hamiltonian learning [5] and will see that in some instances [6], one can ironically cerfify the correctness of a device even if one cannot efficiently predict its performance.

[1] Randomized benchmarking for individual quantum gates, E. Onorati, A. H. Werner, J. Eisert, Phys. Rev. Lett. 123, 060501 (2019).

[2] Recovering quantum gates from few average gate fidelities, I. Roth, R. Kueng, S. Kimmel, Y.-K. Liu, D. Gross, J. Eisert, M. Kliesch, Phys. Rev. Lett. 121, 170502 (2018).

[3] In preparation.

[4] Sample complexity of device-independently certified quantum supremacy, D. Hangleiter, M. Kliesch, J. Eisert, C. Gogolin, Phys. Rev. Lett. 122, 210502 (2019).

[5] In preparation.

[6] J. Haferkamp, D. Hangleiter, A. Bouland, B. Feﬀerman, J. Eisert, and J. Bermejo-Vega, arXiv:1908.08069.

**10:45 - 11:30 P. Forn-Diaz**

**12:00 - 12:45 J. Casanova**

**12:45 - 13:15 R. Orus**: *Forecasting financial crashes with quantum computing*

A key problem in financial mathematics is the forecasting of financial crashes: if we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem. Financial crashes are inherently difficult to predict, even for a regulator which has complete information about the financial system. In this talk we show how this problem can be handled by quantum annealers. More specifically, we map the equilibrium condition of a financial network to the ground-state problem of a spin-1/2 quantum Hamiltonian with 2-body interactions, i.e., a quadratic unconstrained binary optimisation (QUBO) problem. The equilibrium market values of institutions after a sudden shock to the network can then be calculated via adiabatic quantum computation and, more generically, by quantum annealers. We also show that our procedure can be implemented experimentally on near-term quantum processors such as the D-Wave 2000, providing a potentially more efficient way to predict financial crashes.

**15:00 - 15:30 O. Kyriienko**: *Ground state energy estimation by the quantum inverse iteration algorithm*

Quantum computing has the potential to revolutionise the fields of quantum chemistry and material science. Yet, modern quantum hardware cannot perform calculations in the fault-tolerant fashion, and is susceptible to errors and external noise. Given the rapid development of currently available quantum platforms, proposing efficient quantum software for near-term devices becomes the key to their successful operation. For instance, using the hybrid quantum-classical variational algorithms, which combine quantum gate operations and classical optimisation procedure, first experimental demonstrations of ground state energy estimation became possible. At the same time, more algorithmic developments are needed for tackling larger scale problems and exploiting analog quantum simulation.

In the talk, I will describe the quantum inverse iteration algorithm which allows to access the ground state properties of a quantum system (see details in [O. Kyriienko, arXiv:1901.09988 (2019)]). It relies on the simple evolution of the quantum state with a quantum simulator, followed by the measurement of overlap with the initial state. Designed to be run with imperfect noisy circuits, it does not require ancillary qubits and controlled operations, allows for the error mitigation, and favours analog quantum simulation.

When applied to quantum chemistry problems, the proposed protocol demonstrates an efficient performance for the present-day noisy circuits, and holds promise for intermediate scale computation. Given the ever-increasing scale of analog quantum simulators for material science models, it can offer capabilities to study ground state physics of highly correlated matter.

**15:30 - 16:00 T. Kohler**

Spin models are widely studied in the natural sciences, from investigating magnetic materials in condensed matter physics to studying neural networks. Previous work has demonstrated that there exist simple classical spin models that are universal: they can simulate -- in a precise and rigorous sense -- the complete physics of any other classical spin model, to any desired accuracy. However, all previously known universal models break translational invariance. In this paper we show that there exist translationally invariant universal models. Our main result is an explicit construction of a translationally invariant, 2D, nearest-neighbour, universal classical Hamiltonian with a single free parameter. The proof draws on techniques from theoretical computer science, in particular recent complexity theoretic results on tiling problems. Our results imply that there exists a single Hamiltonian which encompasses all classical spin physics, just by tuning a single parameter and varying the size of the lattice. We also prove that our construction is optimal in terms of the number of parameters in the Hamiltonian; there cannot exist a translationally invariant universal Hamiltonian with only the lattice size as a parameter. We discuss whether these results might generalise to the quantum case.

**16:30 - 17:15 J. Home**

**17:15 - 18:00 K. Temme**