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## Monday

### Programmable Quantum Simulators with Trapped Ions

Ion trap quantum computer and simulator systems have essentially perfect idle qubit/spin coherence properties with fully-connected and reconfigurable entanglement operations. The frontiers of this platform have thus expanded from the physics of qubits and gates to the engineering of optical control signals, the efficient compilation of quantum gates and Hamiltonians, the mitigation of errors in software, and demonstrations of algorithms and quantum simulations that touch many areas of science. I will present recent results in all of these fronts with state-of-the-art ion trap quantum computer systems and simulators, from both the Duke Quantum Center and IonQ, Inc. This includes high fidelity operations among many-qubits, a newly discovered scheme for single-step many body Hamiltonian operations, simulations of exotic phases of magnetism, and the outlook for further scaling of ion trap quantum computers based on a well-defined and modular architecture.

### Quantum gas microscopy of correlated systems with new ingredients: kinetic frustration and dipolar interactions

Quantum gas microscopy has revolutionized quantum simulation with ultracold atoms in optical lattices. So far, it has mostly been applied in the context of the “plain-vanilla” Hubbard model on the square lattice relevant to the high-temperature superconducting cuprates. In this talk, I will report on the microscopy of correlated systems with new ingredients: frustration and dipolar interactions. Our quantum simulations of triangular Hubbard systems have revealed the existence of a “high-temperature” magnetic polaron that emerges due to kinetic frustration in lightly doped systems. This is closely related to very recent observations of kinetic magnetism in Moiré materials and may provide microscopic insights into them. In another line of experiments, our quantum simulations with polar molecules pinned in an optical lattice have allowed us to explore tunable models of non-equilibrium quantum magnets.

### Quantum simulation on today’s quantum computers: Overcoming noise

Quantum simulation on present-day quantum processors rests on our ability to tackle the noise of the devices, thereby enabling access to new and useful regimes of quantum simulation. Here, we delve into the primary challenges associated with generic and many-body simulations on digital quantum computers, and present state-of-the-art approaches to overcome them. Specifically, we examine the application of Probabilistic Error Cancellation (PEC) with Sparse Pauli-Lindblad Models on Noisy Quantum Processors as a means to learn and mitigate noise. Moreover, we discuss recent findings and offer insights into the future prospects of quantum simulations involving 100 qubits or more and circuit depths exceeding 100.

### Solid State Atom-based Devices: an Experimental Platform for Quantum Simulation

Jonathan Wyrick(1), Fan Fei(1,2), Ehsan Khatami(4), Pradeep Namboodiri(1), Utsav(1), Joseph Fox(1,2), Garnett Bryant(1,3) and Richard Silver (1)

(1) Atom Scale Device Group, National Institute of Standards and Technology, Gaithersburg MD

(2) Department of Physics, University of Maryland, College Park, MD

(3) Joint Quantum Institute, University of Maryland, College Park, MD

(4) Department of Physics and Astronomy, San José State University, San José, CA

Dopant atoms imbedded in silicon and arranged with atomic precision in 3 dimensions enable construction of Hamiltonians for quantum simulation at the ultimate level of spatial detail: the atomic limit. For an atomically-defined simulation structure, the choice of dopant type, the number of dopants at a given site, and their configuration determine the physical characteristics of the local and long range electrostatic potential, tunnel coupling, and spin behavior. Nanometer scale highly doped STM patterned leads and gates can be aligned with atomic precision while e-beam fabricated electrodes, such as top-gates and ESR antennas, are placed with 10s to 100s of nanometer precision relative to the simulation structure, allowing for electrostatic tunability and coherent control/manipulation of the quantum states of the system.

At NIST, we are fabricating atomically-precise P devices in Si using scanning probe-based hydrogen depassivation lithography (HDL). We have built single atom transistors, few-donor/quantum dot devices, and arrayed few-donor devices, and have investigated these systems within the context of their application to analog quantum simulation. In particular, we have explored portions of the Hubbard model phase space using arrayed few-atom P clusters, whose properties such as magnetic ordering and Mott-like behavior are highly sensitive to the details of their atomic configurations. We use numerical calculations of an extended Fermi-Hubbard model (made possible by our choice of a small array size, 3×3) to simulate spin/charge occupation, the spatial distribution of the states of the many-body system, and magnetic correlations, for comparison and validation of the measurements made on the experimentally realized systems. In parallel we are developing more refined methods to interrogate these systems, such as spin manipulation and readout via RF reflectometry, using donor/quantum dot devices as targeted test structures. These efforts are aimed at establishing HDL fabricated dopant-in-Si devices as a useful, highly controlled platform for quantum simulation.

### Assembling and probing synthetic quantum matter from microwave photons

Learning how to create and manipulate highly-entangled many-body systems is a central challenge of modern quantum science, with promising applications from quantum computation to many-body physics and quantum-enhanced metrology. Analog quantum simulators provide a rich playground for exploring the emergent collective phenomena in synthetic quantum systems, and how to harness these many-body effects for future quantum technologies.

In this talk, I will describe various approaches for assembling quantum matter from strongly interacting microwave photons. Our quantum circuit platform consists of an array of capacitively coupled transmon qubits acting as a Hubbard lattice for photons. I will highlight a novel approach to constructing low-entropy quantum fluids of light by employing particle-resolved assembly combined with adiabatic control of lattice disorder. Studying these fluids with site-resolved microscopy of entanglement and two-body correlations reveals how the photons delocalize and avoid one another, behaving as noninteracting fermions.

The precise time- and space-resolved control of the lattice potential landscape presents another unique capability in our platform for investigating out-of-equilibrium quantum dynamics. Using controlled perturbations in the lattice potential, we can spectroscopically probe quasiparticle excitations, prepare superpositions of many-body eigenstates and observe the propagation of sound modes of light in the lattice. Towards developing practical tools for quantum computers, I will show how we can leverage many-body dynamics in these fluids for preparing highly-entangled states useful for quantum information processing and metrology.

### Two Tales of Givens Rotations – assessing the potential for quantum advantage in quantum chemistry

We will give two specific contexts in quantum chemistry where Givens rotations are used. I will then connect these contexts to related near-term quantum algorithms. I will use this connection to assess the potential quantum advantage of several near-term quantum algorithms. If there is time left, I will briefly touch up on our recent results on quantum speed-up in real-time electron dynamics.

### Hardware-Efficient Quantum Simulation of Strongly Correlated Molecules and Materials with Reconfigurable Atom Arrays

Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors. As such, realizing practical quantum advantage for problems such as the accurate calculation of electronic properties is a key milestone, which has yet to be achieved. Herein, we introduce a programmable simulation framework for studying molecules and materials with strong correlations that can be approximated by model Hamiltonians. Specifically, we propose a method to simulate the dynamics of spin Hamiltonians in a hardware-efficient manner, using reconfigurable neutral atom arrays and multi-qubit entangling operations. We show that these tools enable Floquet engineering of many realistic systems, which include bi-quadratic and higher-order terms.Here, we present a suite of algorithms for extracting detailed spectral information from time-dynamics, through snapshot measurements and ancilla-assisted control, enabling the efficient evaluation of quantities relevant to quantum chemistry and materials science such as excitation energies and finite-temperature susceptibilities. Moreover, our approach can efficiently integrate state-of-the-art classical and quantum methods to prepare low-energy variational states and to initialize the dynamics. As an example, we show how this method can be used to compute chemically-relevant properties of polynuclear transition metal catalysts and 1D magnetic materials. Practical performance and extensions to larger systems in higher dimensions that should provide advantages over leading classical algorithms are discussed.

### Quantum simulation of spin diffusion in a Heisenberg chain

Understanding universal aspects of quantum dynamics is an exciting problem in statistical mechanics that has enjoyed renewed attention with the advent of modern-day quantum simulators. In particular, the spin dynamics of the 1D Heisenberg model have been conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution of the magnetization transferred across the chain’s center. The first two moments thereof show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.Furthermore, we present a scalable protocol for measuring full counting statistics in experiments or tensor-network simulations using an ancilla in the middle of the system, which acts as a turnstile with its phase keeping track of the time-integrated particle flux.

### Adaptive quantum simulation algorithms

Variational quantum eigensolvers (VQEs) constitute a class of hybrid quantum-classical simulation algorithms that are envisioned as possibly appropriate for noisy intermediate scale quantum processors. For VQEs to be useful, it is important to reduce the size of the ansatz and the number of required measurements. I will present our work addressing these issues with an ADAPT-VQE, adaptive, problem tailored approach to ansatz construction. I will also discuss recent work showing how the overhead can be lowered in ADAPT-VQE.

### Purification-based quantum error mitigation of pair-correlated electron simulations

An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth. Here, we validate recently introduced “purification-based” error-mitigation strategies on physical simulation within the seniority-zero electron pairing subspace, which affords a computational stepping stone to a fully correlated model. We compare the performance of error mitigation based on doubling quantum resources in time (echo verification) or in space (virtual distillation), on up to $20$ qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques (e.g. post-selection). We study how the gain from error mitigation scales with the system size, and observe a polynomial suppression of error by echo verification and virtual distillation. Employing these error mitigation strategies enables the implementation of the largest variational algorithm for a correlated chemistry system to-date. Extrapolation of these results suggests significant hardware improvements will be required for classically intractable variational chemistry simulations.

## Tuesday

### Exploring quantum magnetism and spin squeezing with Rydberg atom arrays

Rydberg atoms in arrays of optical tweezers offer new perspectives for applications in

quantum simulation, quantum computation, and quantum metrology. In this talk, I will

describe our recent efforts to control dipolar interactions between Rydberg states to

engineer a 2D XY spin Hamiltonian. In this model, we adiabatically prepare low-

temperature states of both the XY ferro- and antiferromagnet. In the ferromagnetic

case, we observe the presence of long-range order enabled by long-range interactions

[1]. I will further show that by performing quantum quenches we can probe the

dispersion relation of the excitations in the system [2]. Finally, I will illustrate that by

carefully steering the out-of-equilibrium dynamics we can generate sizable spin

squeezing, which could be used for metrological applications [3].

References:

[1] Chen et al., Nature 616, 691 (2023).

[2] Chen et al., in preparation.

[3] Bornet et al., arXiv:2303.0053.

### Towards new frontiers of quantum science with dual-species atom arrays

In this talk, we will explore recent advancements in quantum science using Rydberg atom arrays and present future applications enabled by the use of a dual-species array based on a mixture of alkali and alkaline-earth atoms. Trapped arrays of interacting Rydberg atoms have become a leading platform for quantum information processing and quantum simulation due to their large system size and programmability. The use of two atomic species introduces the ability to store quantum information in one species and perform operations with the other, together with the possibility of selectively controlling inter and intra-species interactions for more flexible Hamiltonian engineering. These new features enable new and more efficient protocols for quantum error correction and collective quantum gates, and would allow access to a broader class of highly-entangled phases of matter. We will present our plans for a new experimental platform based on Yb and Rb atom arrays, which will take advantage of the different features of these two atomic species to create a flexible platform for quantum simulation and quantum information processing.

### A dual-species Rydberg array for quantum simulation and information processing

Neutral atoms have emerged as a powerful platform for quantum simulation and information processing. Optical tweezer arrays enable the trapping of hundreds of atomic qubits in programmable geometries, which can either be encoded in long-lived ground states, or excited into strongly interacting Rydberg levels. These techniques have led to key results in many-body physics including the discovery of many-body scars [1], and the observation of topological spin-liquid states [2] and continuous symmetry-breaking [3].

In the Bernien lab we are constructing a dual-species Rydberg array of rubidium and cesium atoms to build on these results [4]. Novel features offered by this architecture — including species-selective trapping, imaging, and control — result in capabilities such as mid-circuit measurements. I will first highlight recent work on ‘spectator qubits’ in which we combined such measurements with real-time feed-forward to mitigate correlated errors in a 2D array of up to 120 atomic qubits (Fig. 1) [5].

I will then present ongoing efforts to implement many-body Rydberg interactions. I will discuss opportunities arising from asymmetric inter- and intra-species interactions, such as simulations of many-body dynamics with additional effective dimensionality [6]. Finally, I will outline how the combination of Rydberg interactions with mid-circuit measurements will enable non-destructive stabilizer measurements, efficient preparation of long-range entangled states [7], and the exploration of measurement-induced phase transitions [8].

References:

[1] H. Bernien et al., Probing many-body dynamics on a 51-atom quantum simulator, Nature 551, 579-584 (2017)

[2] G. Semeghini et al., Probing topological spin liquids on a programmable quantum simulator, Science 364 1242-1247 (2021)

[3] C. Chen*, G. Bornet*, M. Bintz*, G. Emperauger* et al., Continuous symmetry breaking in a two-dimensional Rydberg array, Nature 616, 691-695 (2023)

[4] K. Singh et al., Dual-element two-dimensional atom array with continuous-mode operation, Phys. Rev. X 12 011040 (2022)

[5] K. Singh*, C. E. Bradley*, S. Anand* et al., Mid-circuit correction of correlated phase errors using an array of spectator qubits, Science (2023), DOI: 10.1126/science.ade533

[6] L. Homeier et al., Quantum simulation of Z2 lattice gauge theories with dynamical matter from two-body interactions in (2+1)D, arXiv:2205.08541 (2022)

[7] R. Verresen et al., Efficiently preparing Schrödinger’s cat, fractons and non-Abelian topological order in quantum devices, arXiv:2112.03061 (2022)

[8] M. Ippoliti et al., Entanglement phase transitions in measurement-only dynamics, Phys. Rev. X 11, 011030 (2021)

### Benchmarking highly-entangled states on a large-scale analog quantum simulator

Quantum devices have reached a competitive stage where classical computers struggle to accurately represent the highly-entangled quantum states targeted in experiments. Here, we utilize a high-fidelity, Rydberg quantum simulator to perform fidelity benchmarking in the high entanglement regime where exact classical simulation becomes impractical. Our approach involves a learning-based extrapolation protocol for benchmarking a 60-atom system, along with the introduction of a new, highly-efficient approximate classical algorithm. Additionally, we develop an efficient estimator for mixed-state entanglement, demonstrating the competitiveness of our quantum simulator with state-of-the-art digital quantum devices. We also evaluate the cost of approximate classical simulation, which enables us to quantify the boundary between quantum and classical systems. Our results provide a new paradigm for evaluating the performance of both analog and digital quantum devices in the beyond-classically-exact regime.

### Generating highly entangled many-body states on a superconducting processor

Entanglement and its propagation are central to understanding quantum systems. Notably,

within closed interacting many-body systems, entanglement is believed to yield emergent

thermodynamic behavior, yet a universal understanding remains challenging. Quantum

hardware platforms provide a means to study the formation and scaling of entanglement. Here, we use a controllable 4-by-4 array of superconducting qubits to emulate a two-dimensional hard-core Bose-Hubbard lattice. Rather than preparing a definite state, we generate superposition states by simultaneously driving all lattice sites. We extract correlation lengths and entanglement energy for states prepared across the many-body energy spectrum of the lattice, observing volume-law entanglement scaling for states at the center of the spectrum and a crossover to the onset of area-law scaling near its edges. Lastly, we discuss extensions of this state preparation protocol that leverage the dynamic capability of superconducting processors by tracking the propagation of entanglement following a mid-experiment quantum quench.

### High threshold codes for neutral atom qubits with biased erasure errors

The requirements for fault-tolerant quantum error correction can be simplified by leveraging structure in the noise of the underlying hardware. In this work, we identify a new type of

structured noise motivated by neutral atom qubits, biased erasure errors, which arises when qubit errors are dominated by detectable leakage from only one of the computational states of the qubit. We study the performance of this model using gate-level simulations of the XZZX surface code. Using the predicted erasure fraction and bias of metastable 171Yb qubits, we find a threshold of 8.2%, which is 1.9 times higher than the threshold for unbiased erasures, and 7.5 times higher than the threshold for depolarizing errors. Surprisingly, the improved threshold is achieved without bias-preserving controlled-not gates, and instead results from the lower noise entropy in this model. We also introduce an XZZX cluster state construction for measurement-based error correction, hybrid-fusion, that is optimized for this noise model. By combining fusion operations and deterministic entangling gates, this construction preserves the intrinsic symmetry of the XZZX code, leading to a higher threshold of 10.3% and enabling the use of rectangular codes with fewer qubits.

### Analogue quantum simulation with Coulomb-confined quantum dots in silicon

Recent demonstrations of few semiconductor quantum dot systems for analogue quantum simulation of the Fermi-Hubbard model due to the inherent ability of quantum dots show tremendous promise for exploring highly interacting electron systems. Phosphorus-doped silicon quantum dots created from the Coulombic potential of the donors have large electron-electron interactions and large kinetic energy terms compared to the temperature of the system. Additionally, these Coulomb-confined quantum dots require significantly lower control structures and can be fabricated with sub-nanometre precision using a scanning tunneling microscope (STM). In this talk, I will describe the features of Coulomb-confined quantum dots in silicon that make them promising for large-scale quantum simulation and present our recent demonstration of the interacting Su-Schrieffer-Heeger (SSH) model using Si:P quantum dots. Finally, by leveraging the low-gate density and sub-nanometre fabrication accuracy I will show how these Coulomb-confined quantum dots can be used for large-scale quantum simulation of the extended Fermi-Hubbard model.

### Exciton transport in a 2×4 Ge quantum dot ladder device

Analog fermionic quantum simulators can give insight into complicated many-body quantum phenomena beyond the capabilities of classical computers. Among the available platforms, semiconductor quantum dot systems excel for their in-situ tunability, thermal energies lower than any other relevant energy scale and the naturally occurring long-range Coulomb interaction. The latter is particularly relevant for several exotic states of matter, from Wigner crystals to excitonic insulators. Here, we present the control of a 2×4 quantum dot device embedded in a Ge/SiGe heterostructure. Individual gates for the control of tunnel couplings and site occupations allow us to tune the device into the single charge regime and explore exciton formation and transport enabled by the long-range Coulomb interaction. We demonstrate control of the tunnel couplings between all the dots and tune the device into two separate 1D channels: a drive channel and a drag channel. While the tunneling between the channels is suppressed, we still retain a sizable Coulomb interaction which favors exciton formation. Through charge sensing, we are able to detect the position of all the charges at any point in time and quantify the Coulomb interaction strength. We then purposefully transfer single charges in the drive channel and, in the right conditions, observe that a charge of opposite sign is carried along in the drag channel. This signature of exciton transport opens the possibility for the exploration of exciton condensation and could give insight into the mechanisms governing their formation. Moreover, our experiment positions quantum dot systems as a unique candidate for the simulation of complex phases of matter governed by the long-range Coulomb interaction.

### Hybrid quantum dots for quantum simulation of Kondo lattice models

Simplified effective Hamiltonians are key to understanding the behavior of quantum many-body systems, however, even relatively simple models often defy computational treatment on the fastest classical supercomputers. This has prompted the development of several quantum simulation platforms, each with a distinctive set of advantages. The use of ultracold atom arrays to model electrons in a bulk crystal has seen tremendous progress, but explorations of quantum phase transitions has been limited by the difficulty in cooling down to a many-body ground state. Few-site semiconductor quantum dot arrays implement a lattice of “artificial atoms” in a reservoir of mobile electrons, and have provided controllable realizations of diverse ground state phenomena. However, intersite inhomogeneity presents a major roadblock to scaling and tuning larger arrays. A new paradigm for quantum simulation is based on quantum dots formed from a hybrid metal-semiconductor island. The quasi-continuous level spectrum of the metallic component screens out differences between similarly patterned islands – enabling an array of sites to behave essentially identically, while the semiconductor retains tunability of intersite coupling through electrostatic gating, providing a scalable platform for simulating strong interactions. Recent work on a pair of hybrid metal-GaAs dots investigated a novel non-Fermi liquid critical point based on Kondo interactions mediated by the charge of the metallic island[1]. The islands had to be a few microns wide, given how ohmic contacts are made to GaAs. The surface Fermi level pinning in InAs provides a pathway for designing submicron hybrid dots with larger charging energy, enabling investigations of critical scaling over a broader temperature range. We have demonstrated the essential building blocks in an InAs quantum well – clean quantum point contacts[2], highly transparent transmission (>99%) of 1D modes into submicron metal islands, and tunable hybrid metal-InAs dots – for building sizable arrays to gain insights into the Kondo lattice coherence in heavy-fermion materials.

1. Pouse, W. et al. Nat. Phys. (2023)

2. Hsueh, C.L., Sriram, P. et al. Phys. Rev. B 105, 195303 (2022)

## Wednesday

### Even Newer Approaches to Quantum Simulation of Systems

In keeping with the tradition of always giving a talk on “New Approaches to Quantum Simulation” that I have kept for the last five years, I’ll be talking about even newer approaches to quantum simulation. In particular, here I will talk about recent developments of methods that hybridize existing approaches to quantum simulations such as QDrift, Qubitization and Trotter formulas, We will show that these methods can, in certain cases, improve the scaling of existing quantum algorithms. Next, I will talk about ways that constant factors can be improved by hybridizing compilation methods with quantum simulation to break up a Hamiltonian into a sum of fragments that can be inexpensively simulated through the greedy introduction of artificial terms into the Hamiltonian. Then I will discuss recent approaches that borrow ideas from error mitigation to show how low order Trotter formulas can be extrapolated to give error scaling that rivals that of linear combinations of unitaries methods for energy estimation. Lastly, I will discuss how quantum forces can be computed in simulation and show how quantum and classical dynamics can be hybridized to improve the performance polynomially with respect to the best known approaches for molecular dynamics by incorporating the classical simulation within the quantum computer. Finally, I will conclude by discussing the prospective methods that I may talk about in my similarly titled talk at next years conference.

### Randomized quantum algorithms

I will overview a series of results on how randomization can help with compilation of circuits and design of quantum algorithms. This review will include the qDRIFT algorithm that enables quantum simulation and phase estimation with a complexity that is independent of the number of the number of terms in a Hamiltonian. Then I will discuss more recent work where randomization is applied to expectation value estimation problems such as eigenvalue thresholding. I will close with some recent experimental results using randomized algorithms.

### Exponential quantum speedup in simulating coupled classical oscillators

We present a quantum algorithm for simulating the classical dynamics of 2^n coupled oscillators (e.g., 2^n masses coupled by springs). Our approach leverages a mapping between the Schrödinger equation and Newton’s equation for harmonic potentials such that the amplitudes of the evolved quantum state encode the momenta and displacements of the classical oscillators. When individual masses and spring constants can be efficiently queried, and when the initial state can be efficiently prepared, the complexity of our quantum algorithm is polynomial in n, almost linear in the evolution time, and sublinear in the sparsity. As an example application, we apply our quantum algorithm to efficiently estimate the kinetic energy of an oscillator at any time. We show that any classical algorithm solving this same problem is inefficient and must make 2^{Ω(n)} queries to the oracle and, when the oracles are instantiated by efficient quantum circuits, the problem is BQP-complete. Thus, our approach solves a potentially practical application with an exponential speedup over classical computers. Finally, we show that under similar conditions our approach can efficiently simulate more general classical harmonic systems with 2^n modes. Paper available at https://arxiv.org/abs/2303.13012.

### Simulating one-dimensional quantum chromodynamics on a quantum computer: Real-time evolutions of tetra- and pentaquarks

Quantum chromodynamics – the theory of quarks and gluons – has been known for decades, but it is yet to be fully understood. A recent example is the prediction and experimental discovery of tetraquarks, that opened a new research field. Crucially, numerous unsolved questions of the standard model can exclusively be addressed by nonperturbative calculations. Quantum computers can solve problems for which well established QCD methods are inapplicable, such as real-time evolution. We take a key step in exploring this possibility by performing a real-time evolution of tetraquark and pentaquark physics in one-dimensional SU(3) gauge theory on a superconducting quantum computer. Our experiment represents a first quantum computation involving quarks with three colour degrees of freedom, i.e. with the gauge group of QCD.

### Accelerating variational quantum Monte Carlo using the variational quantum eigensolver

Variational Monte Carlo (VMC) methods are used to sample classically from distributions corresponding to quantum states which have an efficient classical description. VMC methods are based on performing a number of steps of a Markov chain starting with samples from a simple initial distribution. In this talk I will discuss recent work where we propose replacing this initial distribution with samples produced using a quantum computer, for example using the variational quantum eigensolver (VQE).

We show that, based on the use of initial distributions generated by numerical simulations and by experiments on quantum hardware, convergence to the target distribution can be accelerated compared with classical samples; the energy can be reduced compared with the energy of the state produced by VQE; and VQE states produced by small quantum computers can be used to accelerate large instances of VMC. Quantum-enhanced VMC makes minimal requirements of the quantum computer and offers the prospect of accelerating classical methods using noisy samples from near-term quantum computers which are not yet able to accurately represent ground states of complex quantum systems.

This talk is based on the paper arXiv:2307.07719, which is joint work with Stasja Stanisic.

### Doping a frustrated Fermi-Hubbard magnet

The electronic and magnetic properties of quantum materials crucially depend on their crystalline structure. In contrast to their counterparts in cubic and square lattices, strongly correlated systems hosted by geometrically frustrated lattices can feature a plethora of novel ordered states and intriguing magnetic phases such as quantum spin liquids. Promising candidate materials for such phases can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmatic model capturing the interplay between strong correlations and magnetic frustration. However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model.

In this talk, we show how recent experimental progress in Fermi gas microscopy can shed light on the magnetic states of a Hubbard model with controllable frustration and doping, by implementing anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling, we first probe signatures of a transition from a collinear Néel antiferromagnet to a short-range 120◦ spiral phase upon introducing frustration. Away from half-filling in triangular-like geometries, antiferromagnetic correlations tend to be stabilized by hole dopants but get further suppressed by particle dopants and even invert at a particle doping above 20%, hinting at a ferromagnetic instability. Measuring higher-order spin correlations can further shed light on the possible kinetic origin of magnetism in triangular lattices. This work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices, and realizing t − t′ square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials.

## Thursday

### Exploring new scientific frontiers with programmable quantum systems

We will provide an overview of the ongoing work towards realization of programmable quantum simulators. As a specific example, we will discuss the recent advances involving programmable, coherent manipulation of quantum systems based on neutral atom arrays excited into Rydberg states, allowing the control over several hundred qubits in two dimensions. Recent developments involving both analog and digital quantum simulations and quantum information processing will be described. In particular, the realization of novel quantum processing architecture based on dynamically reconfigurable entanglement and the steps towards quantum error correction will be discussed. Finally, we will discuss opportunities for realization of useful, large-scale quantum processors.

### Proofs of Quantumness

### Linear combination of Hamiltonian simulation for non-unitary dynamics with optimal state preparation cost

We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters. This talk is based on the paper [arXiv:2303.01029].

### Improved Accuracy for Trotter Simulations Using Polynomial Extrapolation

Quantum metrology allow for measuring properties of a quantum system at an optimal scaling known as the Heisenberg limit. However, when the quantum states of interest are prepared using approximate time evolution on a digital quantum computer, the accrued errors will typically deviate from this fundamental limit. In this work, we show how algorithmic errors due to Trotterized time evolution can be mitigated through the use of standard polynomial interpolation techniques. This can be seen as an extrapolation to zero step size, akin to the zero-noise polynomial extrapolation techniques recently developed for mitigating hardware errors. We perform a rigorous error analysis of the interpolation approach for estimating eigenvalues and time-evolved expectation values and show that the Heisenberg limit is achieved up to polylogarithmic factors. Unfortunately, these accuracy gains come at the price of a quadratically worse scaling in simulation time in the case of expectation values, which may be improved with better analysis. Our work suggests that accuracies approaching those of state-of-the-art simulation algorithms may be achieved using Trotter and classical resources alone, for a number of relevant algorithmic tasks.

### Hamiltonian simulation by compensating Trotter error with linear combination of unitary operations

Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltonian simulation methods. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates after the Kth-order Trotter formula, we realize a better time scaling than 2Kth-order Trotter. Our first algorithm exponentially improves the accuracy scaling of the Kth-order Trotter formula. In the second algorithm, we consider the detailed structure of Hamiltonians and construct LCU for Trotter errors with commutator scaling. Consequently, for lattice Hamiltonians, the algorithm enjoys almost linear system-size dependence and quadratically improves the accuracy of the Kth-order Trotter.

### Matchgate Shadows for Fermionic Quantum Simulation

“Classical shadows” are estimators of an unknown quantum state, constructed from suitably distributed random measurements on copies of that state. In this submission, we analyze classical shadows obtained using random matchgate circuits, which correspond to fermionic Gaussian unitaries. We prove that the first three moments of the Haar distribution over the continuous group of matchgate circuits are equal to those of the discrete uniform distribution over only the matchgate circuits that are also Clifford unitaries; thus, the latter forms a “matchgate 3-design.” This implies that the classical shadows resulting from the two ensembles are functionally equivalent. We show how one can use these matchgate shadows to efficiently estimate inner products between an arbitrary quantum state and fermionic Gaussian states, as well as the expectation values of local fermionic operators and various other quantities, thus surpassing the capabilities of prior work. As a concrete application, this enables us to apply wavefunction constraints that control the fermion sign problem in the quantum-classical auxiliary-field quantum Monte Carlo algorithm (QC-AFQMC), without the exponential post-processing cost incurred by the original approach.

## Friday

### Discovering novel quantum dynamics with superconducting qubits

In recent years superconducting qubits have become one of the leading platforms for quantum computation and simulation. In 2019 and by using a 53 qubit processor, the google team demonstrated that a quantum processor could perform certain computational tasks exponentially faster than a classical computer [1]. Going beyond this milestone, we seek to utilize these Noisy Intermediate Scale Quantum (NISQ) processors to study computationally intractable nonequilibrium quantum dynamics. I will present some of our recent works in studying integrability breaking [2] and universality classes of infinite temperature dynamics in the 1D Heisenberg chain [3]. The aim of the talk is to provide a sense of what NISQ discoveries to anticipate and a time scale for them.

[1] Nature 574, 505–510 (2019)

[2] Nature 612, 240-245 (2022)

[3] Arxiv.org/abs/2306.0933

### Probing critical states of matter on digital quantum computers

I will describe Quantinuum’s trapped ion QCCD quantum computers, with a particular focus on the key technical challenges and solutions for realizing mid-circuit measurement and reuse of qubits. In addition to the importance these capabilities play in quantum error correction, they also afford remarkable efficiencies in simulating many-body physics, enabling explorations of physics at length scales well beyond the limits that would be naively guessed from the size of present-day quantum computers. I will discuss recent work utilizing quantum implementations of hierarchical tensor networks to represent critical ground states of spin chains on Quantinuum’s H1 series quantum computers, demonstrating that current quantum computing hardware is already capable of extracting accurate estimates of critical properties of infinite systems.

### Quantum Computation with globally driven Rydberg atom arrays

Individually trapped neutral atoms offer a promising platform for the controlled, bottom-up engineering of quantum many-body systems. These atoms can be manipulated readily in large numbers and interact strongly when excited to Rydberg states. In this talk I will discuss a novel approach to use this platform for quantum computation. Our model does not require any local addressing or dynamical rearrangement. Instead the quantum algorithm is completely specified by the static atomic positions and executed by driving the array with a global, resonant laser field in a Rydberg blockade regime.

### Quantum algorithms for the ground state energy

Estimating the ground state energy of a quantum Hamiltonian is a fundamental task in quantum chemistry and condensed matter physics. Quantum algorithms offer a promising path towards getting highly precise estimates for quantum systems beyond the capability of classical algorithms. As quantum computers become more robust to noise with the improvement of quantum error correction capability, we may need different algorithms for this task at different stages of this development. I will first talk about quantum algorithms for this task that are designed for early fault-tolerant quantum computers, where besides the runtime we also want to minimize the number of qubits and the circuit depth. For quantum computers with sufficient error correcting power, I will present a near-optimal algorithm that optimizes the total runtime.

### Hardware-efficient quantum simulation of non-abelian lattice gauge theories

Simulating the real-time dynamics of non-abelian lattice gauge theories (LGTs) is an outstanding challenge, where quantum simulators can provide a practical advantage over classical methods. In this talk, I will present our recent results concerning co-designed hardware as well as new quantum algorithms towards achieving this goal. Specifically, I review a qudit architecture based on Rydberg atoms for implementing pure LGTs [1], and introduce an extension to a hybrid fermion-qudit processor, where the fermionic statistics of dynamical matter is accounted for at the hardware level [2]. On the software level, I briefly discuss a q-deformed formulation of LGTs as an alternative truncation of the infinite-dimensional local Hilbert space of non-abelian gauge fields, which provides the basis for efficient classical and quantum spin network algorithms [3].

[1] González-Cuadra, Zache, Carrasco, Kraus & Zoller, Phys. Rev. Lett. 129, 160501 (2022)

[2] Zache, González-Cuadra & Zoller, arXiv:2303.08683 (2023)

[3] Zache, González-Cuadra & Zoller, arXiv:2304.02527 (2023)

### Hamiltonian Learning of classical and quantum field theories

Synthetic quantum systems, such as those based on bosonic and fermionic trapped quantum gases, offer an excellent opportunity to study the complexities of quantum many-body physics. Recently, a set of efficient tools called “Hamiltonian learning (HL)” has been developed to uncover the underlying microscopic interactions in these systems from experiment and verify the performance of engineered quantum devices used for quantum simulation. While HL is well developed for discrete lattice-based many-body systems, its application to continuous quantum systems faces a challenge due to the absence of a lattice scale. However, by utilizing the spatial scale introduced by measurement resolution, effective field theories can emerge as suitable descriptions. In this talk, I will present a protocol that capitalizes on the locality of effective field theories to extract their Hamiltonians from experimental data. Our approach involves constraining the Hamiltonian through relationships among correlation functions, which we derive from a field theory ansatz. The effectiveness of our method is demonstrated in theoretical studies of both classical and (free) quantum fields. Furthermore, I showcase its application in a ultracold quantum gas experiment in the classical-statistical regime. The present work paves the way for quantitatively certifying emergent field theories in quantum simulators.

### Flat-band Localization and Interaction-Induced Delocalization of Photons

Lattices with dispersionless, or flat, energy bands have attracted significant interest in part due to the strong dependence of particle dynamics on interactions. Using superconducting transmon qubits, we design a plaquette of a lattice whose band structure consists entirely of flatbands under the addition of a synthetic magnetic field of pi. We first observe compact localization in the dynamics of a single particle, the hallmark of all-bands-flat physics. Next, we initialize two photons bound by interactions on the same site and observe an interaction-enabled delocalized walk across the plaquette. These results mark the first experimental observation of a quantum walk that becomes delocalized due to interactions and establish superconducting circuits as a platform for studies of flat-band-lattice dynamics with strong interactions.