# QSC 2019

## Program

**Monday 14**

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

**10:00 - 10:45 F. Wilhelm-Mauch: ***Understanding and engineering decoherence for quantum annealers*

Adiabatic quantum computing and quantum annealing are two closely related paradigms for quantum computing alternative to the circuit model. They have a number of attractive protperties, such as direct compatibility with economically important optimization problems and relatively simple control, allowing to aggressively scale quantum annealing hardware. It also appears that the role of decoherence is quite distinct from that in gate-based quantum computing, as temporal superpositions between energy eigensates need not be maintained, making the usual definition of dephasing unimportant. We will discuss here how decoherence in large quantum annealers, under the assumption of one fixed-strength heat bath per qubit, can affect the coherence of the instantaneous state in an annealing schedule and limit its reachable entanglement [1]. We will also describe how adding transversal noise can assist removing spurious excitations should they occur when the minimum gap is lower than the bath temperature [2]. Finally, we will discuss how qubits can be read-out with high fidelity in a fixed basis, irrespective of the qubit bias point [3].

[1] Tobias Chasseur, Stefan Kehrein, Frank K. Wilhelm, arXiv:1809.08897

[2] L. S. Theis, Peter K. Schuhmacher, M. Marthaler, F. K. Wilhelm, arXiv:1808.09873

[3] Marius Schöndorf, Adrian Lupascu, Frank K. Wilhelm, arXiv:1904.13157

**10:45 - 11:30 P. Schindler: ***Characterizing ion-trap quantum computers*

A major challenge towards practically useful quantum computing is characterizing and reducing the various errors that accumulate during an algorithm running on large-scale processors. Most characterization techniques are unable to adequately account for the exponentially large set of potential errors, including cross-talk and other correlated noise sources. We experimentally demonstrate cycle benchmarking to quantify such errors in non-entangling and entangling operations on an ion-trap quantum computer with up to 10 qubits [1,2].

[1] P. Schindler et al, New. J. Phys. 15, 123012 (2013)

[2] A. Erhard, J. Wallman, et al, arXiv:1902.08543

**12:00 - 12:45 F. Deppe***: Optimal control of a compact 3D quantum memory*

Quantum memories are of high relevance in the context of quantum computing and quantum communication. In view of the tremendous publicly-funded and commercial efforts to build scalable architectures based on superconducting quantum circuits, 3D cavities are promising candidates for a quantum memory. Recently, a compact layout exploiting the multimode structure of a rectangular 3D cavity has been demonstrated [1]. In that work, the fidelity of the transfer process reached 80% and was limited by a trade-off originating from the requirement to minimize both energy relaxation and state leakage at the same time. Here, we first review full tomography results. Then, we discuss optimal control experiments promising increased fidelities with otherwise unchanged system parameters.

We acknowledge support by the Germany’s Excellence Strategy EXC-2111-390814868, Elite Network of Bavaria through the program ExQM, and the European Union via the Quantum Flagship project QMiCS (Grant No. 820505).

[1] E. Xie *et al.*, Appl. Phys. Lett. **112**, 202601 (2018).

**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. Morais Smith ***Atom-by-atom engineering of electronic states of matter*

Feynman’s original idea of using one quantum system that can be manipulated at will to simulate the behavior of another more complex one has flourished during the last decades in the field of cold atoms. More recently, this concept started to be developed in nanophotonics and in condensed matter. In this talk, I will discuss a few recent experiments, in which 2D electron lattices were engineered on the nanoscale. The first is the Lieb lattice [1,2], and the second is a Sierpinski gasket [3], which has dimension D = 1.58. The realization of fractal lattices opens up the path to electronics in fractional dimensions. Finally, I will show how to realize topological states of matter using the same procedure. We investigate the robustness of the zero modes in a breathing Kagome lattice, which is the first experimental realization of a designed electronic higher-order topological insulator [4]. Then, we investigate the importance of the sample termination in determining the existence of topological edge modes in crystalline topological insulators. We focus on the breathing Kekule lattice, with two different types of termination [5]. In all cases, we observe an excellent agreement between the theoretical predictions and the experimental results.

[1] M.R. Slot, T.S. Gardenier, P.H. Jacobse, G.C.P. van Miert, S.N. Kempkes, S.J.M. Zevenhuizen, C. Morais Smith, D. Vanmaekelbergh, and I. Swart, “Experimental realisation and characterisation of an electronic Lieb lattice”, Nature Physics 13, 672 (2017).

[2] M. R. Slot et al., “p-band engineering in artificial electronic lattices”, Phys. Rev. X 9, 011009 (2019).

[3] S.N. Kempkes, M.R. Slot, S.E. Freeney, S.J.M. Zevenhuizen, D. Vanmaekelbergh, I. Swart, and C. Morais Smith, “Design and characterization of electronic fractals”, Nature Physics 15, 127(2019).

[4] S.N. Kempkes, M. R. Slot, J. J. van den Broeke, P. Capiod, W. A. Benalcazar, D. Vanmaekelbergh, D. Bercioux, I. Swart, and C. Morais Smith “Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice”, ArXiv: 1905.06053, in print in Nature Materials (2019).

[5] S. E. Freeney, J. J. van den Broeke, A. J. J. Harsveld van der Veen, I. Swart, and C. Morais Smith, “Edge dependent topology in Kekulé lattices”, submitted (2019).

**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 J. Martinis**

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

**Tuesday 15**

**10:00 - 10:45 T. Esslinger: ***Non-classical gauge fields in lattices and a twist to dissipation*

The coupling between gauge and matter fields plays an important role in many models of high-energy and condensed matter physics. In these models, the gauge fields are dynamical quantum degrees of freedom in the sense that they are influenced by the spatial configuration and motion of the matter field. So far, synthetic magnetic fields for atoms in optical lattices were intrinsically classical, as these did not feature back-action from the atoms. I will report on a scheme realizing the fundamental ingredient for a density-dependent gauge field by engineering non-trivial Peierls phases that depend on the site occupation of fermions in a Hubbard model. [F. Görg, K. Sandholzer, J. Minguzzi, R. Desbuquois, M. Messer, and T. Esslinger, Nat. Phys. https://doi.org/10.1038/s41567-019-0615-4(2019).]

Dissipative and unitary processes define the evolution of a many-body system. We discovered a non-stationary state of chiral nature in a synthetic many-body system with independently controllable unitary and dissipative couplings. Our experiment is based on a spinor Bose gas interacting with an optical resonator. Orthogonal quadratures of the resonator field coherently couple the Bose-Einstein condensate to two different atomic spatial modes whereas the dispersive effect of the resonator losses mediates a dissipative coupling between these modes. In a regime of dominant dissipative coupling we observe a chiral evolution with regimes reminiscent of limit cycles [N. Dogra, M. Landini, K. Kroeger, L. Hruby, T. Donner, and T. Esslinger, arXiv:1901.05974]

**10:45 - 11:30 M.A. Martin-Delgado: ***Topological Heat Transport and Symmetry-Protected Boson Currents*

The study of non-equilibrium properties in topological systems is of practical and fundamental importance. We analyze the stationary properties of a two-dimensional bosonic Hofstadter lattice coupled to two thermal baths in the quantum open-system formalism. Novel phenomena appear like chiral edge heat currents that are the out-of-equilibrium counterparts of the zero-temperature edge currents. They support a new concept of dissipative symmetry-protection, where a set of discrete symmetries protects topological heat currents, differing from the symmetry-protection devised in closed systems and zero-temperature. Remarkably, one of these currents flows opposite to the decreasing external temperature gradient. As the starting point, we consider the case of a single external reservoir already showing prominent results like thermal erasure effects and topological thermal currents. Our results are experimentally accessible with platforms like photonics systems and optical lattices.

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

**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 ***Entanglement Stabilization using Parity Detection and Real-Time Feedback in Superconducting Circuits*

Superconducting circuits are a prime contender both for realizing universal quantum computation in fault-tolerant processors and for solving noisy intermediate-scale quantum (NISQ) problems without error correction. Superconducting circuits also play an important role in state of the art quantum optics experiments and provide interfaces in hybrid systems. In this talk, as one of two examples of our research, I will present an experiment in the area of fault tolerant quantum computing in which we stabilize the entanglement of a pair of superconducting qubits using parity detection and real-time feedback [1]. In quantum-error-correction codes, measuring multi-qubit parity operators and subsequently conditioning operations on the observed error syndrome is quintessential. We perform experiments in a multiplexed device architecture [2], which enables fast, high fidelity, single-shot qubit read-out [3], unconditional reset [4], and high fidelity single and two-qubit gates. As a second example, I will present the realization of a deterministic state transfer and entanglement generation protocol aimed at extending monolithic chip-based architectures for quantum information processing in a modular approach. Our all-microwave protocol exchanges time-symmetric itinerant single photons between individually packaged chips connected by transmission lines to achieve on demand state transfer and remote entanglement [5]. We foresee that sharing information coherently between physically separated chips in a network of quantum computing modules is essential for realizing a viable extensible quantum information processing architecture.

[1] C. Kraglund Andersen et al., npj Quantum Information 5, 69 (2019)

[2] J. Heinsoo et al., Phys. Rev. Applied 10, 034040 (2018)

[3] T. Walter et al., Phys. Rev. Applied 7, 054020 (2017)

[4] P. Magnard et al., Phys. Rev. Lett. 121, 060502 (2018)

[5] P. Kurpiers et al., Nature 558, 264-267 (2018)

**10:45 - 11:30 A. Amo:*** Emulation of Dirac Hamiltonians and artificial gauge fields with polaritons*

Microcavity polaritons present remarkable properties for the implementation of analogue Hamiltonians with drive and dissipation. Thanks to their hybrid light-matter nature, they combine the possibility of implementing lattices of arbitrary geometry with significant nonlienearities. Here we will present our latest experimental results on the engineering lattice Hamiltonians with exotic Dirac cones, artificial gauge fields and the nonlinear dynamics of polaritons in flat bands.

**12:00 - 12:45 K. Temme: ***Approximation algorithms for quantum many-body problems*

**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 Born Supremacy: Quantum Advantage and Training of an Ising Born Machine*

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**: *From Quantum Algorithms to Out-of-Equilibrium Phenomena in Interacting Trapped-Ion Spin Chains*

Laser cooled trapped ions offer unprecedented control over both internal and external degrees of freedom at the single-particle level. They are considered among the foremost candidates for realizing quantum simulation and computation platforms that can outperform classical computers at specific tasks. In this talk I will show how linear arrays of trapped 171Yb+ ions can be used as a versatile platform for studying out-of-equilibrium strongly correlated many-body quantum systems. In particular I will present our observation of a new type of out-of-equilibrium dynamical phase transition in a spin system with over 50 spins [1]. Moreover, I will show our latest efforts towards scaling up the trapped-ion quantum simulator [2] using a cryo-pumped vacuum chamber where we can trap more than 100 ions indefinitely. The reliable production and lifetime of large linear ion chains enabled us to use up to 40 trapped-ion qubits to observe real-time domain wall confinement in an interacting spin chain [3, 4] and to implement a Quantum Approximate Optimization Algorithm (QAOA) to approximate the ground state energy of a transverse field Ising model [5].

References:

[1] J. Zhang, G. Pagano, et al., Nature, 551, 601 (2017)

[2] G. Pagano et al., Quantum Sci. Technol., 4, 014004 (2019)

[3] F. Liu, et al., Phys. Rev. Lett. 122, 150601 (2018)

[4] W. L. Tan, P. Becker, et al. (in preparation)

[5] G. Pagano, et al., arXiv 1906.02700 (2019)

**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 C. Hempel: ***Quantum firmware - Ingredients and applications*

As we move to larger qubit counts and towards realizing the first logical qubit kept alive through quantum error correction, a layered approach to quantum computation becomes a necessity. Homogenization of error rates across time (circuit depth) and space as well as their correlations become important factors. Controls that adapt to both hardware and algorithm specifics come turn into a crucial ingredient, and resource efficient mapping of noise fields emerges as a need.

In this talk, I am going to discuss work that our group has done to address those needs. Specifically, I will be speaking about a way to identify and suppress error correlations across space and time using a deterministic approach. The second part of the talk will focus on entangling gates in a trapped ion system, where we use phase modulation to provide robustness to both static and time-varying errors as well as the means to scale up efficiently to larger qubit numbers. In a final part of the presentation, I will briefly touch on recent work to efficiently map noise in quantum architectures using an approach inspired by “simultaneous localization and mapping” techniques used, e.g., in navigation of autonomous vehicles.

**10:45 - 11:30 D. Aharonov: ***Stoquastic PCP vs. Randomness*

The derandomization of MA, the probabilistic version of NP, is a long standing and major open question in the classical theory of computer science. In this work, we show that this problem is surprisingly *equivalent* to the major open problem of quantum PCP, in the case of stoquastic Hamiltonians, Our starting point is the beautiful work of Bravyi and Terhal who devised a classical random walk based on stoquastic Hamiltonians, and used it to prove the MA-completeness of the stoqastic local Hamiltonian problem: deciding whether the groundenergy of a given (uniform) stoquastic local Hamiltonian is zero or at least inverse polynomial. We study the gapped version of this problem, and find much more structure; we use it prove that the gapped version of this problem is in NP. (thus, gap amplification of Bravyi and Terhal's problem, i.e. stoqaustic PCP, would put MA in NP!) We hope that this surprising connection between two seemingly unrelated areas might lead to progress on both quantum PCP and derandomization; hopefully, this will also have implications on the long standing question of whether adiabatic algorithms with stoquastic Hamiltonians can be simulated efficiently classically. I will explain the main ideas in the proof (light cone argument, expansion, PCPs...) and touch upon the many open questions. Joint work with Alex. B Grilo.

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

**12:45 - 13:15 J. Watson: ***The Uncomputability of Phase Diagrams*

Determining the phase diagram of a material is a question of central importance to condensed matter physics. We prove that the general task of determining the quantum phase diagram of a many-body Hamiltonian is uncomputable, by explicitly constructing a one-parameter family of Hamiltonians for which this is the case. This result builds off recent results proving undecidability of the spectral gap problem by Cubitt, Perez-Garcia and Wolf, as well as Bausch et al.. However, in all previous constructions, the Hamiltonian was necessarily a discontinuous function of its parameters, making it difficult to derive rigorous implications for phase diagrams or related condensed matter questions. Prior to our results, it was unclear whether this was possible. We develop new Hamiltonian constructions together with stronger spectral bounds, that allow us to exploit the Solovay-Kitaev algorithm and phase estimation error analysis to overcome this obstacle. As well as implying uncomputablity of phase diagrams, our result also proves that undecidability can hold for a positive measure set of a Hamiltonian's parameter space. This brings the spectral gap undecidability results a step closer to standard condensed matter problems, where one typically studies phase diagrams of many-body models as a function of one or more continuously varying real parameters, such as magnetic field strength or pressure.

**15:00 - 15:45 S. Bravyi: **Shallow quantum circuits: from quantum advantage to classical simulation

I will discuss a restricted class of quantum computations that can be realized by constant-depth quantum circuits composed of nearest-neighbor gates on a 2D or 3D grid of qubits. The main question is whether such quantum circuits can be more powerful than classical algorithms in some sense. On the positive side, we propose a computational problem which is provably hard for constant-depth classical circuits. However, the problem can be solved by noisy constant-depth quantum circuits in 3D, provided that the noise rate is below a constant threshold value. On the negative side, we show that constant-depth quantum circuits in 2D or 3D are not as powerful as may have been expected. I will describe classical simulation algorithms that approximate output probabilities or expected values of Pauli operators for such circuits. The simulation cost is O(n) in the 2D case and exponential in n^{1/3} in the 3D case. Here n is the number of qubits.

Based on: arXiv:1904.01502, arXiv:1909.11485

**15:45 - 16:15 E. Torrontegui: ***Ultra-fast two qubit ion gate using sequences of resonant pulses*

We propose a new protocol to implement ultra-fast two qubit phase gates with trapped ions using spin-dependent kicks induced by resonant transitions. The arrival times of a discrete pulse train sequence are optimized such the gate is implemented in times faster than the trapping oscillation period T < 2π/ω. Such gates allow to increase the number of gate operations that can be completed within the coherence time of the ion-qubits favoring the development of scalable quantum computers.

**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** *Modulating quantum dynamics for quantum information processing *

Dynamical decoupling (DD) methods are currently applied to Nanoscale NMR problems. I this talk I will review our current work in DD protocols applied to quantum sensing problems, and show that the same techniques are useful when incorporated to quantum information processing methods for high-fidelity quantum computing tasks.

**12:45 - 13:15 D. Porras**: *Topological amplification in driven-dissipative lattices*

A proper characterization of non-trivial topological phases in dissipative systems is highly non-trivial. However, quantum simulator setups offer us exciting possibilities to implement quantum many-body phases which should show the emergence of topological non-trivial phenomena. This is the case of superconducting circuits, trapped ion crystals or ultra-cold atom setups, where couplings between sites can be controlled to break time-reversal symmetry and induce effective gauge fields. In this work we present a definition of topological invariants for driven dissipative lattices that relies on a formal mapping between a non-Hermitian coupling matrix and an effective band Hamiltonian. In a nutshell, our work allows to extend the formalism of topological band theory to dissipative bosonic lattices. Our formalism shows a link between directional amplification and non-trivial topological phenomena, leading to the concept of "topological amplifier". We present a proposal to implement our ideas with superconducting circuits.

D. Porras and S. Fernández-Lorenzo, Phys. Rev. Lett. 122, 143901 (2019)

**15:00 - 15:45 J. Home**

**15:45 - 16:15 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.

**16:45 - 17:15 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.