Session W50: Quantum Simulation of Many-Body Physics

Engineering the Kitaev spin liquid in a quantum dot system

The Kitaev model on a honeycomb lattice may provide a robust topological quantum memory platform, but finding a material that realizes the unique spin liquid phase remains a considerable challenge. We demonstrate that an effective Kitaev Hamiltonian can arise from a half-filled Fermi-Hubbard Hamiltonian where each site can experience a magnetic field in a different direction. As such, we provide a method for realizing the Kitaev spin liquid on a single hexagonal plaquette made up of twelve quantum dots. Despite the small system size, there are clear signatures of the Kitaev spin-liquid ground state, and there is a range of parameters where these signatures are predicted, allowing a potential platform where Kitaev spin-liquid physics can be explored experimentally in quantum dot plaquettes.   

Quantum approximate spectral decomposition

The linearity of quantum mechanics allows us to analyze dynamics via the spectral decomposition of the Hamiltonian. In many-body systems, however, the Hilbert space dimension is exponentially large in the number of degrees of freedom, and at finite energy densities the level separations are exponentially small. As a consequence, even fault-tolerant quantum computers cannot efficiently construct highly-excited eigenstates. This raises the question of whether the spectral decomposition remains a useful tool for the analysis of many-body dynamics. I will introduce a generalization of the spectral decomposition which allows for the approximate reconstruction of the dynamics of both observables and entanglement up to polynomial times, and present an algorithm allowing for its efficient extraction on quantum computers.   

Linking Pump-Probe Experiments and Quantum Simulations: A Linear Response Framework.

Response functions are a fundamental aspect of physics; they represent the link between experimental observations and the underlying quantum many-body state. However, this link is often under-appreciated, as the Lehmann formalism for obtaining response functions in linear response has no direct link to experiment. A previously proposed linear response framework for obtaining response functions on quantum computers restored this link by making the experiment an inextricable part of the quantum simulation. This method is frequency- and momentum-selective, ancilla-free, and encompassing a larger pool of operators that can be directly measured. Another powerful, prospective application of this method entails directly simulating a pump-probe experiment where the system is driven out of equilibrium by an ultrafast laser pulse and probed afterwards to measure its non-equilibrium Green's functions. Using this, and putting the functional derivative approach into action, we investigate the phenomenon of confinement within condensed-matter physics, which involves the emergence of a startling attractive potential between the quasi-particles of a spin-system that alters the dynamics and the spreading of correlations. We study this non-trivial occurrence in long-range Ising models as a compelling example by measuring both their longitudinal and transverse non-equal time correlation functions.   

Bosonic Quantum Simulation with a Superconducting Transmon Lattice

Quantum simulation with superconducting qubits has largely focused on models of two-level systems such as the hard-core Bose-Hubbard model. However, this choice massively truncates the size of the accessible Hilbert space – reducing the complexity of computation and preventing quantum information from being stored in the higher levels of the system. In this talk, we will discuss the feasibility of performing multi-level analog quantum simulation of the Bose-Hubbard model using superconducting transmon qudits. This approach offers several advantages, including efficient emulation of time evolution, reduced leakage from the computational subspace, and a wider range of Hamiltonian parameter values represented by the model. However, with these improvements comes increased complexity in readout and tomography protocols. We will give an overview of the design and control of transmon-based Bose-Hubbard emulators. We consider contributions to decoherence and decay of these higher excited states and discuss their impact on many-body behavior. Finally, we will give an outlook for future experiments as we move towards meaningful quantum advantage on noisy intermediate-scale quantum hardware.   

Utilizing transmon qudits for quantum simulation of the Fermi-Hubbard model

The Fermi-Hubbard model is instrumental in shedding light on the complexities of many strongly correlated phenomena in condensed matter physics. Although exact solutions for the Fermi-Hubbard model are attainable in specific settings, quantum simulations offer the possible exploration of this model within more complex scenarios. In this work, we introduce a novel approach to simulating the Fermi-Hubbard model utilizing transmon qudits. Leveraging on the inherent properties of qudits, we develop an effective map between the fermionic degrees of the Fermi-Hubbard model, to a single four-level system (i.e., a ququart), thus reducing the complexity of encoding and simulating the many-body systems. While our approach is generic and hardware agnostic, we showcase the power of this method by utilizing superconducting transmons and their native gates as our qudits. Our results reveal the advantages of qudits in quantum simulations, providing valuable insights into the underlying physics of strongly correlated systems and establishing a new paradigm for the study of quantum many-body systems using higher-dimensional computational subspaces.   

Quantum algorithm for solving the XXX-Heisenberg model describing spin dynamics in a trinuclear copper complex

Daria D. Nakritskaia^1,2, Sergey A. Varganov¹, Yuri Alexeev<sup>2

1</sup> Department of Chemistry, University of Nevada, Reno, 1664 N. Virginia Street, Reno, NV 89557-0216, USA

² Argonne National Laboratory, 9700 South Cass Avenue, Building 240, Argonne, IL, 60439, USA

 

Efficient dynamics simulation of spin systems on a classical computer is limited by the exponential growth of Hilbert space with the number of interacting spins. . The scalability of the problem reduces from exponential to linear when implemented on a quantum computer, which allows to expand the model size, with the limitation being only the number of qubits. The Heisenberg model is one of the simplest models that describes the behavior of spin systems and has been previously implemented on the quantum hardware for an XY model[SV1] . To make such quantum simulations more resilient to noise, the depth of quantum circuit can be reduced using the Yang-Baxter equation (YBE), which has been done before for the one-dimensional XY-Heisenberg model. We investigate spin dynamics in a Cu₃(saltatris(2-hydroxybenzylidene)triaminoguanidine)(pyridine)₆ complex, focusing on the three spin-1/2 Cu(II) ions.  We obtain the antiferromagnetic exchange constant from the electronic structure calculations and map it on the XXX-Heisenberg model. We solve the XXX-Heisenberg Hamiltonian in time-dependent magnetic field using 1) traditional classical algorithm, 2) the YBE quantum algorithm on a quantum simulator and 3) the YBE algorithm on a multi-qubit quantum device. 

Photon-photon Interactions in Quasi-1D Lattices of Coplanar Waveguides

The field of circuit QED has emerged as a rich platform for both quantum computation and quantum simulation. Lattices of coplanar waveguide (CPW) resonators realize artificial photonic materials in the tight-binding limit [1] capable of realizing non-Euclidean geometries [2] and unconventional unit cells [3]. Combined with strong qubit-photon interactions, these systems can be used to study dynamical phase transitions, many-body phenomena, spin models in driven-dissipative systems, and interacting photons. In this talk, we present data from a quasi-1D coplanar waveguide lattice device with unconventional linear and flat bands, and 3 flux tunable qubits. By probing the device, we can directly map out the band structures that emerge from the lowest two photonic modes of the CPW resonator and examine qubit mediated interactions between lattice modes.

 

[1] D. Underwood et al., Phys. Rev. A 86, 023837 (2012)

[2] A. J. Kollár et al., Nature 571, 45 (2019)

[3] A. J. Kollár et al., Comm. Math. Phys. 376,1909 (2019)   

Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were 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, P(M), of the magnetization transferred across the chain's center. The first two moments of P(M) 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.   

Quantum circuits for toric code and X-cube fracton model

We propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground state of the toric code in $lceil 2L+2+log_{2}(d)+frac{L}{2d} ceil$ time steps. Our algorithm reformulates the problem into a purely geometric one, facilitating its extension to attain the ground state of certain 3D topological phases, such as the 3D toric model in $3L+8$ steps and the X-cube fracton model in $12L+11$ steps. Furthermore, we introduce a gluing method involving measurements, enabling our technique to attain the ground state of the 2D toric code on an arbitrary planar lattice and paving the way to more intricate 3D topological phases.   

Isolated Majorana mode in a quantum computer from a duality twist

Investigating the interplay of dualities, generalized symmetries, and topological defects beyond theoretical models is an important challenge in condensed matter physics and quantum materials. A simple model exhibiting this physics is the transverse-field Ising model, which can host a noninvert- ible topological defect that performs the Kramers-Wannier duality transformation. When acting on one point in space, this duality defect imposes the duality twisted boundary condition and binds a single Majorana zero mode. This Majorana zero mode is unusual as it lacks localized partners and has an infinite lifetime, even in finite systems. Using Floquet driving of a closed Ising chain with a duality defect, we generate this Majorana zero mode in a digital quantum computer. We detect the mode by measuring its associated persistent autocorrelation function using an efficient sampling protocol and a compound strategy for error mitigation. We also show that the Majorana zero mode resides at the domain wall between two regions related by a Kramers-Wannier duality. Finally, we highlight the robustness of the isolated Majorana zero mode to integrability and symmetry-breaking perturbations. Our findings offer an approach to investigating exotic topological defects in digitized quantum devices.   

Digital simulations of equilibrium symmetry-protected topological phases

Symmetry plays a fundamental role in the characterization of quantum phases of matter. Recently, the emergence of symmetry-protected topological (SPT) phases has shed light on a new realm of short-range entangled states. In our study, we demonstrate the equilibrium symmetry-protected topological (SPT) phase transitions through digital simulations executed on a quantum computer. Utilizing the quantum imaginary-time evolution (QITE) method, we prepare the ground states of the Ising spin with cluster interactions across different phases. Through our noisy simulations, we capture the edge state in nontrivial SPT phases and depict the phase transitions from ferromagnetic (FM) to SPT phases. We further probe the entanglement properties of the SPT phase.  Our work offers insights into the digital simulation of the complex nature of quantum phase transitions on the current quantum processor.   

Gauged cooling of topological excitations and emergent fermions on quantum simulators

Simulated cooling is a robust method for preparing low-energy states of many-body Hamiltonians on near-term quantum simulators. In such schemes, a subset of the simulator's spins (or qubits) are treated as a ``bath,'' which extracts energy and entropy from the system of interest. However, such protocols are inefficient when applied to systems whose excitations are highly non-local in terms of the microscopic degrees of freedom, such as topological phases of matter; such excitations are difficult to extract by a local coupling to a bath. We explore a route to overcome this obstacle by encoding of the system's degrees of freedom into those of the quantum simulator in a non-local manner. To illustrate the approach, we show how to efficiently cool the ferromagnetic phase of the quantum Ising model, whose excitations are domain walls, via a 

``gauged cooling'' protocol in which the Ising spins are coupled to a $Z_2$ gauge field that simultaneously acts as a reservoir for removing excitations. 

We show that our protocol can prepare the ground states of the ferromagnetic and paramagnetic phases equally efficiently. 

The gauged cooling protocol naturally extends to (interacting) fermionic systems, where it is equivalent to cooling by coupling to a fermionic bath via single-fermion hopping.    

The fast multipole method on a quantum computer

The fast multipole method (FMM) is a classical algorithm for approximating pairwise interactions between n particles in O(n) time, improving on the O(n^2) complexity required by direct computation. The ability to implement FMM on a quantum computer with O(n) gate complexity would lead to asymptotically faster algorithms for quantum chemistry. However, translating classical algorithms to quantum circuits without incurring polynomial overhead is not in general straightforward. In this talk, I will show how FMM can nevertheless be adapted to a quantum computer using O(n) gates, by exploiting the underlying structure of the algorithm.