Session A51: Applications on Noisy Quantum Hardware I

Quantum simulation of conical intersections using trapped ions.

Conical intersections often control the reaction products of photochemical processes and occur when two electronic potential energy surfaces intersect [1]. Theory predicts that the conical intersection will result in a geometric phase for a wavepacket on the ground potential energy surface [2], and although conical intersections have been observed experimentally, the geometric phase has not been directly observed in a molecular system. In this presentation, I discuss results and methods from recent work [3] where we used a trapped atomic ion system to perform a quantum simulation of a conical intersection. The ion’s internal state served as the electronic state, and the motion of the atomic nuclei was encoded into the motion of the ions. The simulated electronic potential was constructed by applying state-dependent optical forces to the ion. We experimentally observed a clear manifestation of the geometric phase using adiabatic state preparation followed by motional state measurement. 

[1] Yarkony, David R. "Diabolical conical intersections." Reviews of Modern Physics 68.4 (1996): 985.

[2] Berry, Michael Victor. "Quantal phase factors accompanying adiabatic changes." Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 392.1802 (1984): 45-57.

[3] Whitlow, Jacob, Zhubing Jia, Ye Wang, Chao Fang, Jungsang Kim, and Kenneth R. Brown. "Quantum simulation of conical intersections using trapped ions." Nature Chemistry (2023): 1-6.   

High-fidelity analog quantum simulation with superconducting qubits

Analog quantum simulation is a promising path for achieving beyond-classical simulation applications, particularly due to its faster entanglement growth than digital circuits. The higher classical simulation complexity in analog simulation is rooted in the simultaneous interaction between all qubits and the potential inclusion of non-computational states in the Hilbert space; however, these same aspects also make analog calibration a daunting task. We here report on recent progress toward a transmon-based high-fidelity analog quantum simulator. Specifically, we present a new analog calibration framework achieving significant reduction in eigenfrequency error compared to past works. We then demonstrate time-domain control of the analog quantum simulator via cross-entropy benchmarking, and leverage hybrid digital-analog circuits to study the equilibrium and non-equilibrium properties of the 2D XY model. Our work paves the way for analog quantum simulation to become a competitive avenue toward beyond-classical applications.   

Experimental Realization of Topological Floquet Models in Circuit QED

Topological band structures are well known to produce symmetry-protected chiral edge states which transport particles unidirectionally. These same effects can be harnessed in the frequency domain using a spin-1/2 system subject to periodic drives [1]. Previously, the topological regime of such models was thought to be experimentally inaccessible due to a need for ultrastrong coupling; however, recent results have shown that the desired Hamiltonian is achievable in a rotating frame and can give rise to "boosting" of non-classical states of light in a cavity [2]. We show that the rotating magnetic field required for boosting can be achieved by combining an oscillatory flux bias with an amplitude modulated microwave drive in quadrature. Field amplitudes exceeding 100 MHz in both the X and Z axes have been achieved, surpassing the intrinsic qubit-cavity g of 30 MHz. The spatial profiles of the drive and boost cavities are used to design a low crosstalk chip with drive to boost isolation exceeding 40 dB. We present preliminary characterization of the cavity state boosting protocol.

[1]: I. Martin, G. Refael, and B. Halperin, Phys. Rev. X 7, 041008 (2017)

[2]: D. M. Long, P. J. D. Crowley, A. J. Kollár, and A. Chandran, Phys. Rev. Lett. 128, 183602 (2022).   

Practical Quantum Simulations from Error Mitigation and Qubit Subspace Techniques

The goal of this work is to outline a path to practical quantum simulations on the noisy intermediate scale quantum hardware available to us today. Qubit subspace techniques such as tapering and the contextual subspace methodology allow us to reduce the quantum resource required to simulate a problem Hamiltonian by projecting into a reduced subspace where various symmetries (physical or artificial) have been exploited. Having alleviated some burden on the quantum device by removing classical redundancy in the target system, we turn to techniques of quantum error mitigation to extract some usable signal from such inherently noisy platforms. In particular, we investigate strategies based on measurement error mitigation, symmetry verification, zero-noise extrapolation and dual-state purification with numerical benchmarking to identify an effective hybrid scheme. We then apply these findings to model systems on superconducting hardware to validate our simulation framework. This includes an accurate characterisation of the electron correlation potential energy curve of molecular nitrogen and ground state preparation of the spin-frustrated Kagome lattice, a proposed quantum spin liquid; the latter achieved first-place in the IBM Quantum Open Science Prize 2022/23.   

Observation of critical entanglement and quantum phase transitions on a quantum computer

The simulation of strongly-correlated quantum matter poses a significant challenge due to the curse of dimensionality and complex entanglement structures. This complexity is especially pronounced in the critical regime, where quantum fluctuations occur at all length scales and low-energy states are highly entangled. The (Trotterized) multiscale entanglement renormalization ansatz - a special type of tensor networks with narrow causal cones - makes it possible to study large many-body systems on noisy intermediate-scale quantum (NISQ) devices. Here we report on experimental results using ion-trap systems. In particular, we demonstrate a quantum phase transition with spontaneous symmetry breaking in the thermodynamic limit and we measure bipartite entanglement entropies, which scale according to an area law for gapped systems and according to a log-area law at the critical point. The experimental demonstration of the (Trotterized) multiscale entanglement renormalization ansatz approach with pre-optimized states is a pivotal step towards a full-fledged and practicable digital simulation of many-body systems on quantum computers.   

Quantum Computed Green's Functions using a Cumulant Expansion of the Lanczos Method

In this work, we present a quantum computational method to calculate the many-body Green's function matrix in a spin orbital basis. We apply our approach to finite-sized fermionic Hubbard models and related impurity models within Dynamical Mean Field Theory, and demonstrate the calculation of Green's functions on Quantinuum's H1-1 trapped-ion quantum computer. Our approach involves a cumulant expansion of the Lanczos method, using Hamiltonian moments as measurable expectation values. This bypasses the need for a large overhead in the number of measurements due to repeated applications of the variational quantum eigensolver (VQE), and instead measures the expectation value of the moments with one set of measurement circuits. From the measured moments, the tridiagonalised Hamiltonian matrix can be computed, which in turn yields the Green's function via continued fractions. While we use a variational algorithm to prepare the ground state in this work, we note that the modularity of our implementation allows for other (non-variational) approaches to be used for the ground state.   

Simulating Parity Magnetic Effects with Superconducting Qubits

A highly tunable diamond energy diagram is constructed with four coupled superconducting qubits. We parametrically modulate their tunable couplers, mapping the momentum space to parameter space and realizing 4D Dirac-like Hamiltonian with fourfold degenerate points. Then we apply an additional pump microwave field to manipulate the energy of tensor monopoles, providing an effective magnetic and pseudo-electric field. By using non-adiabatic response methods we obtain the fractional second Chern number. Combining these elements we obtain the topological current of parity magnetic effect. Our experiments pave the way to explore the higher-dimensional topological states of matter and deepen our understanding of the topological effects.   

Scattering in 1+1D Scalar Field Theory on a Quantum Computer

The scattering of wavepackets in one-dimensional interacting scalar field theory is simulated on a quantum computer. To initialize the "asymptotic states" for the scattering, the vacuum of the theory is prepared with a variational algorithm. Localized wavepackets with equal but opposite momenta are then created on opposite ends of the lattice. The system is then time-evolved to study the dynamics of scattering events and their products. Quantum resource requirements and impacts of digitization and discretization on the quality of the results are discussed, as well as challenges and implications of this work.   

Digital quantum simulation of thermal observables using a global quench

Thermal state preparation is essential for quantum simulation since it describes the natural equilibrium states of matter. We discuss the thermalization protocol based on a global quench that induces all-to-all random interaction within a few-qubit system. The interaction constants are drawn from complex Gaussian distribution. Running the protocol multiple times and averaging the results over realizations of the interaction constants leads to thermal observables. We implement our protocol on the IBM quantum computer for a four-qubit system. Using circuit recompilation, we restore the thermal observables predicted by the exact dynamics evaluated on a classical computer. We show thermal occupation probabilities for the sixteen states with temperature controlled by the variance of the interaction constants and duration of the quench protocol.   

Nonlocal quantum games using deformed topologically ordered states

We introduce a nonlocal quantum game for which toric code ground states are a resource. Players who share a fixed-point state beforehand win with unit probability, whereas the optimal classical strategy only wins three quarters of the time. Unlike previous examples, the fixed-point strategy continues to surpass the optimal classical strategy away from the fixed point, leading to robust quantum advantage throughout an appreciable fraction of the toric code phase. We demonstrate this robustness experimentally on the Quantinuum H1-1 quantum computer by playing the game with a continuous family of randomly deformed toric code states created by applying weak measurements to every qubit.   

Quantum simulation of scalar field theories in qudit systems

We discuss the implementation of quantum algorithms for lattice Φ4 theory on circuit quantum electrodynamics (cQED) system. The field is represented on qudits in a discretized field amplitude basis. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates. Considering the set of universal gates formed by the single-qudit phase gate and the displacement gate, we address initial state preparation and single-qudit gate synthesis with variational methods.   

Probing correlated phase of quantum matter in driven-dissipative superconducting circuit lattice

Superconducting (SC) circuits have recently emerged as one of the leading platforms for quantum computation and simulation. Utilizing the high flexibility of the circuit QED toolbox, engineered baths offer a new powerful tool for the driven-dissipative control of quantum states and quantum processes. In this work, we create bath-coupled SC circuit analog quantum simulators to explore many-body physics in open quantum systems. We implement a hardware-efficient way to engineer dynamically tunable local particle baths by controlling the sideband coupling between the SC lattice and readout resonators, and apply them to prepare many-body states in a circuit Bose-Hubbard lattice. We present a new method for measuring current and current statistics in a strongly interacting lattice to characterize correlated lattice phases in open quantum systems. We will also discuss future plans for creating non-local correlated baths and their applications.