Programmable Quantum Simulator Research Articles

Programmable adiabatic demagnetization for systems with trivial and topological excitations

We propose a simple, robust protocol to prepare a low-energy state of an arbitrary Hamiltonian on a quantum computer or programmable quantum simulator. The protocol is inspired by the adiabatic demagnetization technique, used to cool solid-state systems to extremely low temperatures. A fraction of the qubits (or spins) is used to model a spin bath that is coupled to the system. By an adiabatic ramp down of a simulated Zeeman field acting on the bath spins, energy and entropy are extracted from the system. The bath spins are then measured and reset to the polarized state, and the process is repeated until convergence to a low-energy steady state is achieved. We demonstrate the protocol via application to the quantum Ising model. We study the protocol's performance in the presence of noise and show how the information from the measurement of the bath spins can be used to monitor the cooling process. The performance of the algorithm depends on the nature of the excitations of the system; systems with non-local (topological) excitations are more difficult to cool than those with local excitations. We explore the possible mitigation of this problem by trapping topological excitations.

Programmable silicon-photonic quantum simulator based on a linear combination of unitaries

Simulating the dynamic evolution of physical and molecular systems in a quantum computer is of fundamental interest in many applications. The implementation of dynamics simulation requires efficient quantum algorithms. The Lie-Trotter-Suzuki approximation algorithm, also known as the Trotterization, is basic in Hamiltonian dynamics simulation. A multi-product algorithm that is a linear combination of multiple Trotterizations has been proposed to improve the approximation accuracy. However, implementing such multi-product Trotterization in quantum computers remains challenging due to the requirements of highly controllable and precise quantum entangling operations with high success probability. Here, we report a programmable integrated-photonic quantum simulator based on a linear combination of unitaries, which can be tailored for implementing the linearly combined multiple Trotterizations, and on the simulator we benchmark quantum simulation of Hamiltonian dynamics. We modify the multi-product algorithm by integrating it with oblivious amplitude amplification to simultaneously reach high simulation precision and high success probability. The quantum simulator is devised and fabricated on a large-scale silicon-photonic quantum chip, which allows the initialization, manipulation, and measurement of arbitrary four-qubit states and linearly combined unitary gates. As an example, the quantum simulator is reprogrammed to emulate the dynamics of an electron spin and nuclear spin coupled system. This work promises the practical dynamics simulations of real-world physical and molecular systems in future large-scale quantum computers.

Realization of higher-order topological lattices on a quantum computer

Programmable quantum simulators may one day outperform classical computers at certain tasks. But at present, the range of viable applications with noisy intermediate-scale quantum (NISQ) devices remains limited by gate errors and the number of high-quality qubits. Here, we develop an approach that places digital NISQ hardware as a versatile platform for simulating multi-dimensional condensed matter systems. Our method encodes a high-dimensional lattice in terms of many-body interactions on a reduced-dimension model, thereby taking full advantage of the exponentially large Hilbert space of the host quantum system. With circuit optimization and error mitigation techniques, we measured on IBM superconducting quantum processors the topological state dynamics and protected mid-gap spectra of higher-order topological lattices, in up to four dimensions, with high accuracy. Our projected resource requirements scale favorably with system size and lattice dimensionality compared to classical computation, suggesting a possible route to useful quantum advantage in the longer term.

Direct observation of geometric-phase interference in dynamics around a conical intersection.

Conical intersections are ubiquitous in chemistry and physics, often governing processes such as light harvesting, vision, photocatalysis and chemical reactivity. They act as funnels between electronic states of molecules, allowing rapid and efficient relaxation during chemical dynamics. In addition, when a reaction path encircles a conical intersection, the molecular wavefunction experiences a geometric phase, which can affect the outcome of the reaction through quantum-mechanical interference. Past experiments have measured indirect signatures of geometric phases in scattering patterns and spectroscopic observables, but there has been no direct observation of the underlying wavepacket interference. Here we experimentally observe geometric-phase interference in the dynamics of a wavepacket travelling around an engineered conical intersection in a programmable trapped-ion quantum simulator. To achieve this, we develop a technique to reconstruct the two-dimensional wavepacket densities of a trapped ion. Experiments agree with the theoretical model, demonstrating the ability of analogue quantum simulators-such as those realized using trapped ions-to accurately describe nuclear quantum effects.

Observing and braiding topological Majorana modes on programmable quantum simulators

Electrons are indivisible elementary particles, yet paradoxically a collection of them can act as a fraction of a single electron, exhibiting exotic and useful properties. One such collective excitation, known as a topological Majorana mode, is naturally stable against perturbations, such as unwanted local noise, and can thereby robustly store quantum information. As such, Majorana modes serve as the basic primitive of topological quantum computing, providing resilience to errors. However, their demonstration on quantum hardware has remained elusive. Here, we demonstrate a verifiable identification and braiding of topological Majorana modes using a superconducting quantum processor as a quantum simulator. By simulating fermions on a one-dimensional lattice subject to a periodic drive, we confirm the existence of Majorana modes localized at the edges, and distinguish them from other trivial modes. To simulate a basic logical operation of topological quantum computing known as braiding, we propose a non-adiabatic technique, whose implementation reveals correct braiding statistics in our experiments. This work could further be used to study topological models of matter using circuit-based simulations, and shows that long-sought quantum phenomena can be realized by anyone in cloud-run quantum simulations, whereby accelerating fundamental discoveries in quantum science and technology.

Continuous symmetry breaking in a two-dimensional Rydberg array.

Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions1-3. The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry leads to the emergence of gapless Goldstone modes controlling, for instance, the thermodynamic stability of the ordered phase4,5. Here, we realize a two-dimensional dipolar XY model that shows a continuous spin-rotational symmetry using a programmable Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of a long-range XY order, a feature prohibited in the absence of long-range dipolar interaction. Our exploration of the many-body physics of XY interactions complements recent works using the Rydberg-blockade mechanism to realize Ising-type interactions showing discrete spin rotation symmetry6-9.

Machine learning discovery of new phases in programmable quantum simulator snapshots

Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lead to the possibility of automatically discovering structures in experimental datasets that manual inspection may miss. Here, we introduce an interpretable unsupervised-supervised hybrid machine learning approach, the hybrid-correlation convolutional neural network (hybrid-CCNN), and apply it to experimental data generated using a programmable quantum simulator based on Rydberg atom arrays. Specifically, we apply hybrid-CCNN to discover and identify new quantum phases on square lattices with programmable interactions. The initial unsupervised dimensionality reduction and clustering stage first reveals five distinct quantum phase regions. In a second supervised stage, we refine these phase boundaries and seek insights into the phases by training multiple CCNN classifiers. A learned spatial weighting, introduced to the CCNNs in this work, enables discovery of spatial structure at scales beyond the filter size. The characteristic spatial weightings and snippets of correlations specifically recognized in each phase capture quantum fluctuations in the striated phase and identify a previously undetected boundary-ordered phase as well as motifs of more exotic ordered phases. These observations demonstrate that a combination of programmable quantum simulators with machine learning can be used as a powerful tool for detailed exploration of correlated quantum states of matter.

The randomized measurement toolbox

Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large quantum systems is the source of their power, but also makes them difficult to control precisely or characterize accurately using measured classical data. We review recently developed protocols for probing the properties of complex many-qubit systems using measurement schemes that are practical using today's quantum platforms. In all these protocols, a quantum state is repeatedly prepared and measured in a randomly chosen basis; then a classical computer processes the measurement outcomes to estimate the desired property. The randomization of the measurement procedure has distinct advantages; for example, a single data set can be employed multiple times to pursue a variety of applications, and imperfections in the measurements are mapped to a simplified noise model that can more easily be mitigated. We discuss a range of use cases that have already been realized in quantum devices, including Hamiltonian simulation tasks, probes of quantum chaos, measurements of nonlocal order parameters, and comparison of quantum states produced in distantly separated laboratories. By providing a workable method for translating a complex quantum state into a succinct classical representation that preserves a rich variety of relevant physical properties, the randomized measurement toolbox strengthens our ability to grasp and control the quantum world.

Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain

In recent years, programmable Rydberg-atom arrays have been widely used to simulate new quantum phases and phase transitions, generating great interest among theorists and experimentalists. Based on the large-scale density matrix renormalization group method, the ground-state phase diagram of one-dimensional Rydberg chains is investigated with fidelity susceptibility as an efficient diagnostic method. We find that the competition between Rydberg blockade and external detuning produces unconventional phases and phase transitions. As the Rydberg blockade radius increases, the phase transition between disordered and density-wave ordered phases changes from the standard Potts universality class to an unconventional chiral one. As the radius increases further (above Potts point but still close to the tip of the lobe), a very narrow intermediate floating-phase region begins to appear. A concise physical picture is also provided to illustrate the numerical results. Compared with previous studies, this work brings more evidence for commensurate-incommensurate quantum phase transitions in programmable quantum simulators from the perspective of quantum information, showing that fidelity susceptibility can be used to study such phase transitions.

Randomizing multi-product formulas for Hamiltonian simulation

Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of quantum simulation algorithms are deterministic, a recent surge of ideas has shown that randomization can greatly benefit algorithmic performance. In this work, we introduce a scheme for quantum simulation that unites the advantages of randomized compiling on the one hand and higher-order multi-product formulas, as they are used for example in linear-combination-of-unitaries (LCU) algorithms or quantum error mitigation, on the other hand. In doing so, we propose a framework of randomized sampling that is expected to be useful for programmable quantum simulators and present two new multi-product formula algorithms tailored to it. Our framework reduces the circuit depth by circumventing the need for oblivious amplitude amplification required by the implementation of multi-product formulas using standard LCU methods, rendering it especially useful for early quantum computers used to estimate the dynamics of quantum systems instead of performing full-fledged quantum phase estimation. Our algorithms achieve a simulation error that shrinks exponentially with the circuit depth. To corroborate their functioning, we prove rigorous performance bounds as well as the concentration of the randomized sampling procedure. We demonstrate the functioning of the approach for several physically meaningful examples of Hamiltonians, including fermionic systems and the Sachdev–Ye–Kitaev model, for which the method provides a favorable scaling in the effort.

Two-Dimensional Programmable Tweezer Arrays of Fermions.

We prepare high-filling two-component arrays of tens of fermionic ^{6}Li atoms in optical tweezers, with the atoms in the ground motional state of each tweezer. Using a stroboscopic technique, we configure the arrays in various two-dimensional geometries with negligible Floquet heating. A full spin- and density-resolved readout of individual sites allows us to postselect near-zero entropy initial states for fermionic quantum simulation. We prepare a correlated state in a two-by-two tunnel-coupled Hubbard plaquette, demonstrating all the building blocks for realizing a programmable fermionic quantum simulator.

Dynamical Preparation of Quantum Spin Liquids in Rydberg Atom Arrays.

We theoretically analyze recent experiments [Semeghini etal., Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasiadiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase-the resonating valence bond state of hard dimers-in a time that scales linearly with the number of atoms. Moreover, we provide a two-parameter variational manifold of tensor network states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the nonequilibrium state, establishing the emergence of topological order.

Quantifying information scrambling via classical shadow tomography on programmable quantum simulators

We develop techniques to probe the dynamics of quantum information, and implement them experimentally on an IBM superconducting quantum processor. Our protocols adapt shadow tomography for the study of time evolution channels rather than of quantum states, and rely only on single-qubit operations and measurements. We identify two unambiguous signatures of quantum information scrambling, neither of which can be mimicked by dissipative processes, and relate these to many-body teleportation. By realizing quantum chaotic dynamics in experiment, we measure both signatures, and support our results with numerical simulations of the quantum system. We additionally investigate operator growth under this dynamics, and observe behaviour characteristic of quantum chaos. As our methods require only a single quantum state at a time, they can be readily applied on a wide variety of quantum simulators.

Dynamical topological phase realized in a trapped-ion quantum simulator.

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in almost isolated systems. Here achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work indicates that these capabilities can enable dynamical phases and critical phenomena that show topologically robust methods to create, protect and manipulate quantum entanglement that self-correct against large classes of errors. However, so far, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders1-5. In this work, we demonstrate an emergent dynamical symmetry-protected topological phase6, in a quasiperiodically driven array of ten 171Yb+ hyperfine qubits in Quantinuum's System Model H1 trapped-ion quantum processor7. This phase shows edge qubits that are dynamically protected from control errors, cross-talk and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. This property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders8,9 that would enable error-resilient manipulation of quantum information.

Bulk and boundary quantum phase transitions in a square Rydberg atom array

Motivated by recent experimental realizations of exotic phases of matter on programmable quantum simulators, we carry out a comprehensive theoretical study of quantum phase transitions in a Rydberg atom array on a square lattice, with both open and periodic boundary conditions. In the bulk, we identify several first-order and continuous phase transitions by performing large-scale quantum Monte Carlo simulations and develop an analytical understanding of the nature of these transitions using the framework of Landau-Ginzburg-Wilson theory. Remarkably, we find that under open boundary conditions, the boundary itself undergoes a second-order quantum phase transition, independent of the bulk. These results explain recent experimental observations and provide important insights into both the adiabatic state preparation of novel quantum phases and quantum optimization using Rydberg atom array platforms.

Data-enhanced variational Monte Carlo simulations for Rydberg atom arrays

Rydberg atom arrays are programmable quantum simulators capable of preparing interacting qubit systems in a variety of quantum states. Due to long experimental preparation times, obtaining projective measurement data can be relatively slow for large arrays, which poses a challenge for state reconstruction methods such as tomography. Today, novel ground-state wave-function Ans\"atze like recurrent neural networks (RNNs) can be efficiently trained not only from projective measurement data, but also through Hamiltonian-guided variational Monte Carlo (VMC). In this paper, we demonstrate how pretraining modern RNNs on even small amounts of data significantly reduces the convergence time for a subsequent variational optimization of the wave function. This suggests that essentially any amount of measurements obtained from a state prepared in an experimental quantum simulator could provide significant values for neural-network-based VMC strategies.

Controlling Rydberg Excitations Using Ion-Core Transitions in Alkaline-Earth Atom-Tweezer Arrays

Scalable local control over gate operations is an outstanding challenge in the field of quantum computing and programmable quantum simulation with Rydberg-atom arrays. One approach is to use a global field to excite atoms to the Rydberg state and tune individual atoms in and out of resonance via local light shifts. In this work, we point out that photon-scattering errors from light shifts can be significantly reduced if the light shift is applied to the Rydberg state instead of the ground state, which can be realized in Rydberg states of alkaline-earth atoms using optical transitions in the ion core. As a proof of concept, we experimentally demonstrate global control of Rydberg excitations in an Yb optical-tweezer array via light shifts induced by a laser tuned near the Yb+6s→6p1/2 transition. We also perform detailed spectroscopy of the induced light shift and scattering rates of the 6sns3S1 Rydberg states and reveal the existence of satellite lines where losses from autoionization are strongly suppressed. This work can be readily extended to implement local gate operations in Rydberg-atom arrays.Received 18 October 2021Revised 27 January 2022Accepted 24 March 2022DOI:https://doi.org/10.1103/PRXQuantum.3.020326Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum information architectures & platformsPhysical SystemsRydberg atoms & moleculesTechniquesAtom & ion coolingOptical tweezersAtomic, Molecular & OpticalQuantum Information

Floquet integrability and long-range entanglement generation in the one-dimensional quantum Potts model

We develop a Floquet protocol for long-range entanglement generation in the one-dimensional quantum Potts model, which generalizes the transverse-filed Ising model by allowing each spin to have $n>2$ states. We focus on the case of $n=3$, so that the model describes a chain of qutrits. The suggested protocol creates qutrit Bell-like pairs with nonlocal long-range entanglement that spans over the entire chain. We then conjecture that the proposed Floquet protocol is integrable and explicitly construct a few first nontrivial conserved quantities that commute with the stroboscopic evolution operator. Our analysis of the Floquet integrability relies on the deep connection between the quantum Potts model and a much broader class of models described by the Temperley-Lieb algebra. We work at the purely algebraic level and our results on Floquet integrability are valid for any representation of the Temperley-Lieb algebra. We expect that our findings can be probed with present experimental facilities using Rydberg programmable quantum simulators and can find various applications in quantum technologies.

Photonic quantum simulations of coupled PT -symmetric Hamiltonians

Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum systems has ignited efforts to simulate and investigate many-particle quantum systems across exceptional points. Here we use a programmable integrated photonic chip to simulate a model comprised of twin pairs of $PT$-symmetric Hamiltonians, with each the time reverse of its twin. We simulate quantum dynamics across exceptional points including two- and three-particle interference, and a particle-trembling behaviour that arises due to interference between subsystems undergoing time-reversed evolutions. These results show how programmable quantum simulators can be used to investigate foundational questions in quantum mechanics.

Quantum register of fermion pairs.

Quantum control of motion is central for modern atomic clocks1 and interferometers2. It enables protocols to process and distribute quantum information3,4, and allows the probing of entanglement in correlated states of matter5. However, the motional coherence of individual particles can be fragile to maintain, as external degrees of freedom couple strongly to the environment. Systems in nature with robust motional coherence instead often involve pairs of particles, from the electrons in helium, to atom pairs6, molecules7 and Cooper pairs. Here we demonstrate long-lived motional coherence and entanglement of pairs of fermionic atoms in an optical lattice array. The common and relative motion of each pair realize a robust qubit, protected by exchange symmetry. The energy difference between the two motional states is set by the atomic recoil energy, is dependent on only the mass and the lattice wavelength, and is insensitive to the noise of the confining potential. We observe quantum coherence beyond ten seconds. Modulation of the interactions between the atoms provides universal control of the motional qubit. The methods presented here will enable coherently programmable quantum simulators of many-fermion systems8, precision metrology based on atom pairs and molecules9,10 and, by implementing further advances11-13, digital quantum computation using fermion pairs14.