Quantum Simulation Research Articles

Trotter error bounds and dynamic multi-product formulas for Hamiltonian simulation

Multi-product formulas (MPFs) are linear combinations of Trotter circuits offering high-quality simulation of Hamiltonian time evolution with fewer Trotter steps. Here we report two contributions aimed at making multi-product formulas more viable for near-term quantum simulations. First, we extend the theory of Trotter error with commutator scaling developed by Childs [A. M. Childs , ] to multi-product formulas. Our result implies that multi-product formulas can achieve a quadratic reduction of Trotter error in 1-norm (nuclear norm) on arbitrary time intervals compared with the regular product formulas without increasing the required circuit depth or qubit connectivity. The number of circuit repetitions grows only by a constant factor. Second, we introduce dynamic multi-product formulas with time-dependent coefficients chosen to minimize a certain efficiently computable proxy for the Trotter error. We use a minimax estimation method to make dynamic multi-product formulas robust to uncertainty from algorithmic errors, sampling, and hardware noise. We call this method the minimax MPF and we provide a rigorous bound on its error. Published by the American Physical Society 2024

Effective light-induced Hamiltonian for atoms with large nuclear spin

Ultracold fermionic atoms, having two valence electrons, exhibit a distinctive internal state structure, wherein the nuclear spin becomes decoupled from the electronic degrees of freedom in the ground electronic state. Consequently, the nuclear spin states are well isolated from the environment, rendering these atomic systems an opportune platform for quantum computation and quantum simulations. Coupling with off-resonance light is an essential tool to selectively and coherently manipulate the nuclear spin states. In this paper, we present a systematic derivation of the effective Hamiltonian for the nuclear spin states of ultracold fermionic atoms due to such an off-resonance light. We obtain compact expressions for the scalar, vector, and tensor light shifts taking into account both linear and quadratic contributions to the hyperfine splitting. The analysis has been carried out using the Green operator approach and solving the corresponding Dyson equation. Finally, we analyze different scenarios of light configurations which lead to the vector- and tensor-light shifts, as well as the pure spin-orbit coupling for the nuclear spin. Published by the American Physical Society 2024

Magnetic correlations of a doped and frustrated Hubbard model: Benchmarking the two-particle self-consistent theory against a quantum simulator

Magnetic correlations of a doped and frustrated Hubbard model: Benchmarking the two-particle self-consistent theory against a quantum simulator

Power-law-exponential interaction induced quantum spiral phases

We theoretically predict a kind of power-law-exponential (PLE) dipole-dipole interaction between quantum emitters in a 1D waveguide QED system. This unconventional long-range interaction is the combination of power-law growth and exponential decay couplings. Applying the PLE interaction to a spin model, we uncover the rich many-body phases. Most remarkably, we find that the PLE interaction can induce the ordered and critical spiral phases. These spiral phases emerge from the strong frustration generated by the power-law factor of the PLE interaction; hence they are absent for other types of long-range interaction, e.g., pure exponential and power-law decay interactions. Our work is also applicable for the higher-dimensional systems. It fundamentally broadens the realm of many-body physics and has significant applications in quantum simulation of strongly correlated matter. Published by the American Physical Society 2024

Efficient learning of continuous-variable quantum states

The characterization of continuous-variable quantum states is crucial for applications in quantum communication, sensing, simulation, and computing. However, a full characterization of multimode quantum states requires a number of experiments that grows exponentially with the number of modes. Here we propose an alternative approach where the goal is not to reconstruct the full quantum state, but rather to estimate its characteristic function at a given set of points. For multimode states with reflection symmetry, we show that the characteristic function at M points can be estimated using only O(logM) copies of the state, independently of the number of modes. When the characteristic function is known to be positive, as in the case of squeezed vacuum states, the estimation is achieved by an experimentally friendly setup using only beamsplitters and homodyne measurements. Published by the American Physical Society 2024

A quantum algorithm for the lattice-Boltzmann method advection-diffusion equation

We present a versatile and efficient quantum algorithm based on the Lattice Boltzmann method (LBM) approximate solution of the linear advection-diffusion equation (ADE). We emphasize that the LBM approximation modifies the diffusion term of the underlying exact ADE and leads to a modified equation (mADE). Due to its versatility in terms of operator splitting, the proposed quantum LBM algorithm for the mADE provides a building block for future quantum algorithms to solve the linearized Navier-Stokes equation on quantum computers. We split the algorithm into four operations: initialization, collision, streaming, and calculation of the macroscopic quantities. We propose general quantum building blocks for each operator, which adapt intrinsically from the general three-dimensional case to smaller dimensions and apply to arbitrary lattice-velocity sets. Based on (sub-linear) amplitude data encoding, we propose improved initialization and collision operations with reduced complexity and efficient sampling-based simulation. Quantum streaming algorithms are based on previous developments. The proposed quantum algorithm allows for the computation of successive time steps, requiring full state measurement and reinitialization after every time step. It is validated by comparison with a digital implementation and based on analytical solutions in one and two dimensions. Furthermore, we demonstrate the versatility of the quantum algorithm for two cases with non-uniform advection velocities in two and three dimensions. Various velocity sets are considered to further highlight the flexibility of the algorithm. We benchmark our optimized quantum algorithm against previous methods employed in sampling-based quantum simulators. We demonstrate sampling efficiency, with sampling accelerated convergence requiring fewer shots.

Exactly solvable model of light-scattering errors in quantum simulations with metastable trapped-ion qubits

Exactly solvable model of light-scattering errors in quantum simulations with metastable trapped-ion qubits

Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large-N_{c} Expansion.

Quantum simulations of the dynamics of QCD have been limited by the complexities of mapping the continuous gauge fields onto quantum computers. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom, we show how the Hilbert space and interactions can be expanded in inverse powers of N_{c}. At leading order in this expansion, the Hamiltonian simplifies dramatically, both in the required size of the Hilbert space as well as the type of interactions involved. Adding a truncation of the resulting Hilbert space in terms of local energy states we give explicit constructions that allow simple representations of SU(3) gauge fields on qubits and qutrits. This formulation allows a simulation of the real time dynamics of a SU(3) lattice gauge theory on a 5×5 and 8×8 lattice on ibm_torino with a CNOT depth of 113.

Observation of Pairwise Level Degeneracies and the Quantum Regime of the Arrhenius Law in a Double-Well Parametric Oscillator

By applying a microwave drive to a specially designed Josephson circuit, we have realized a double-well model system: a Kerr oscillator submitted to a squeezing force. We have observed, for the first time, the spectroscopic fingerprint of a quantum double-well Hamiltonian when its barrier height is increased: a pairwise level kissing (coalescence) corresponding to the exponential reduction of tunnel splitting in the excited states as they sink under the barrier. The discrete levels in the wells also manifest themselves in the activation time across the barrier which, instead of increasing smoothly as a function of the barrier height, presents steps each time a pair of excited states is captured by the wells. This experiment illustrates the quantum regime of Arrhenius’s law, whose observation is made possible here by the unprecedented combination of low dissipation, time-resolved state control, 98.5% quantum nondemolition single shot measurement fidelity, and complete microwave control over all Hamiltonian parameters in the quantum regime. Direct applications to quantum computation and simulation are discussed. Published by the American Physical Society 2024

Quantum-assisted rendezvous on graphs: explicit algorithms and quantum computer simulations

Abstract We study quantum advantage in one-step rendezvous games on simple graphs analytically, numerically, and using noisy intermediate-scale quantum (NISQ) processors. Our protocols realise the recently discovered (Mironowicz 2023 New J. Phys. 25 013023) optimal bounds for small cycle graphs and cubic graphs. In the case of cycle graphs, we generalise the protocols to arbitrary graph size. The NISQ processor experiments realise the expected quantum advantage with high accuracy for rendezvous on the complete graph K 3. In contrast, for the graph 2 K 4 , formed by two disconnected 4-vertex complete graphs, the performance of the NISQ hardware is sub-classical, consistent with the deeper circuit and known qubit decoherence and gate error rates.

Two-axis twisting using Floquet-engineered XYZ spin models with polar molecules.

Polar molecules confined in an optical lattice are a versatile platform to explore spin-motion dynamics based on strong, long-range dipolar interactions1,2. The precise tunability3 of Ising and spin-exchange interactions with both microwave and d.c. electric fields makes the molecular system particularly suitable for engineering complex many-body dynamics4-6. Here we used Floquet engineering7 to realize new quantum many-body systems of polar molecules. Using a spin encoded in the two lowest rotational states of ultracold 40K87Rb molecules, we mutually validated XXZ spin models tuned by a Floquet microwave pulse sequence against those tuned by a d.c. electric field through observations of Ramsey contrast dynamics. This validation sets the stage for the realization of Hamiltonians inaccessible with static fields. In particular, we observed two-axis twisting8 mean-field dynamics, generated by a Floquet-engineered XYZ model using itinerant molecules in two-dimensional layers. In the future, Floquet-engineered Hamiltonians could generate entangled states for molecule-based precision measurement9 or could take advantage of the rich molecular structure for quantum simulation of multi-level systems10,11.

Probing spin hydrodynamics on a superconducting quantum simulator

Characterizing the nature of hydrodynamical transport properties in quantum dynamics provides valuable insights into the fundamental understanding of exotic non-equilibrium phases of matter. Experimentally simulating infinite-temperature transport on large-scale complex quantum systems is of considerable interest. Here, using a controllable and coherent superconducting quantum simulator, we experimentally realize the analog quantum circuit, which can efficiently prepare the Haar-random states, and probe spin transport at infinite temperature. We observe diffusive spin transport during the unitary evolution of the ladder-type quantum simulator with ergodic dynamics. Moreover, we explore the transport properties of the systems subjected to strong disorder or a tilted potential, revealing signatures of anomalous subdiffusion in accompany with the breakdown of thermalization. Our work demonstrates a scalable method of probing infinite-temperature spin transport on analog quantum simulators, which paves the way to study other intriguing out-of-equilibrium phenomena from the perspective of transport.

Quantum-Accelerated Flight Selection: Probing Grover's Algorithm and Quantum Device Efficiency

Current flight search platforms primarily consider four essential factors when planning a trip: departure/arrival dates, as well as the origin and destination locations. However, when additional parameters are added to this search, the problem shifts from a simple to a complex search, as the engine must sift through a massive dataset of flights, including information on airlines, flight routes, fees, and more. To address this challenge and improve flight search efficiency amidst data-intensive and resource-demanding environments, this paper proposes the use of Grover's search algorithm. This algorithm is demonstrated as the optimal solution for searches with increased constraints. The paper highlights the practical application of Grover's search algorithm across three datasets of assorted sizes, as well as various quantum hardware and simulators available in the NISQ era. Furthermore, this paper provides an in-depth understanding of the complexity of quantum circuit design, including the key phases of state encoding and amplitude amplification. The effectiveness of these approaches is evaluated through analysis of execution times and quantum measurement results. The aim is to showcase the potential of quantum computing in revolutionizing real-world search tasks, particularly in the realm of flight selection.

Direct observation of a few-photon phase shift induced by a single quantum emitter in a waveguide

Realizing a sensitive photon-number-dependent phase shift on a light beam is required both in classical and quantum photonics. It may lead to new applications for classical and quantum photonics machine learning or pave the way for realizing photon-photon gate operations. Nonlinear phase-shifts require efficient light-matter interaction, and recently quantum dots coupled to nanophotonic devices have enabled near-deterministic single-photon coupling. We experimentally realize an optical phase shift of 0.19π ± 0.03 radians ( ≈ 34 degrees) using a weak coherent state interacting with a single quantum dot in a planar nanophotonic waveguide. The phase shift is probed by interferometric measurements of the light scattered from the quantum dot in the waveguide. The process is nonlinear in power, the saturation at the single-photon level and compatible with scalable photonic integrated circuitry. The work may open new prospects for realizing high-efficiency optical switching or be applied for proof-of-concept quantum machine learning or quantum simulation demonstrations.

Quantum neural network approach to Markovian dissipative dynamics of many-body open quantum systems.

Numerous variational methods have been proposed for solving quantum many-body systems, but they often face exponentially increasing computational complexity as the Hilbert space dimension grows. To address this, we introduce a novel approach using quantum neural networks to simulate the dissipative dynamics of many-body open quantum systems. This method combines neural-network quantum state representation with the time-dependent variational principle, both implemented via quantum algorithms. This results in accurate open quantum dynamics described by the Lindblad quantum master equation, exemplified by the spin-boson and transverse field Ising models. Our approach avoids the computational expense of classical algorithms and demonstrates the potential advantages of quantum computing for many-body simulations. To reduce measurement errors, we introduce a projection reset procedure, which could benefit other quantum simulations. In addition, our approach can be extended to simulate non-Markovian quantum dynamics.

Quantum-Annealing-Inspired Algorithms for Track Reconstruction at High-Energy Colliders

Charged particle reconstruction or track reconstruction is one of the most crucial components of pattern recognition in high-energy collider physics. It is known to entail enormous consumption of computing resources, especially when the particle multiplicity is high, which will be the conditions at future colliders, such as the High Luminosity Large Hadron Collider and Super Proton–Proton Collider. Track reconstruction can be formulated as a quadratic unconstrained binary optimization (QUBO) problem, for which various quantum algorithms have been investigated and evaluated with both a quantum simulator and hardware. Simulated bifurcation algorithms are a set of quantum-annealing-inspired algorithms, known to be serious competitors to other Ising machines. In this study, we show that simulated bifurcation algorithms can be employed to solve the particle tracking problem. The simulated bifurcation algorithms run on classical computers and are suitable for parallel processing and usage of graphical processing units, and they can handle significantly large amounts of data at high speed. These algorithms exhibit reconstruction efficiency and purity comparable to or sometimes improved over those of simulated annealing, but the running time can be reduced by as much as four orders of magnitude. These results suggest that QUBO models together with quantum-annealing-inspired algorithms are valuable for current and future particle tracking problems.

Individually tunable tunnelling coefficients in optical lattices using local periodic driving

Abstract Ultracold atoms in optical lattices have emerged as powerful quantum simulators of translationally invariant systems with many applications in e.g. strongly-correlated and topological systems. However, the ability to locally tune all Hamiltonian parameters remains an outstanding goal that would enable the simulation of a wider range of quantum phenomena. Motivated by recent advances in quantum gas microscopes and optical tweezers, we here show theoretically how local control over individual tunnelling links in an optical lattice can be achieved by incorporating local time-periodic potentials. We propose to periodically modulate the on-site energy of individual lattice sites and employ Floquet theory to demonstrate how this provides full individual control over the tunnelling amplitudes in one dimension. We provide various example configurations realising interesting topological models such as extended Su–Schrieffer–Heeger models that would be challenging to realise by other means. Extending to two dimensions, we demonstrate that local periodic driving in a Lieb lattice engineers a two-dimensional (2D) network with fully controllable tunnelling magnitudes. In a three-site plaquette, we show full simultaneous control over the relative tunnelling amplitudes and the gauge-invariant flux piercing the plaquette, providing a clear stepping stone to building a fully programmable 2D tight-binding model. We also explicitly demonstrate how utilise our technique to generate a magnetic field gradient in 2D. This local modulation scheme is applicable to many different lattice geometries.

Noise-Aware Variational Eigensolvers: A Dissipative Route for Lattice Gauge Theories

We propose a novel variational ansatz for the ground-state preparation of the Z2 lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve >99% precision in energy in both the confined and deconfined phase of the Z2 LGT. We benchmark our proposal against the unitary Hamiltonian variational ansatz showing a reduction in the required number of variational layers to achieve a target precision. After performing a finite-size scaling analysis, we show that our dissipative variational ansatz can predict accurate critical exponents without requiring a number of layers that scales with the system size, which is the standard situation for unitary ansätze. Furthermore, we investigate the performance of this variational eigensolver subject to circuit-level noise, determining variational error thresholds that fix the error rate below which it would be beneficial to increase the number of layers. In light of these quantities and for typical gate errors p in current quantum processors, we provide a detailed assessment of the prospects of our scheme to explore the Z2 LGT on near-term devices. Published by the American Physical Society 2024

Energetic cost as a consequence of parallel transporting speed limit

Time-optimal unitary operating quantum systems and energy-efficient quantum gates are vital in quantum engineering. Here, we establish the connection between the energetic cost and the quantum speed limit for parallel evolving of a quantum system. Our results show that the energetic cost is the consequence of parallel transporting speed limit, which opens up the critical role of parallel transport of the quantum state for the quantum technologies such as the quantum simulation, the quantum information processing. Our investigations present a route to construct the energetic-efficient quantum gate. In addition, our theoretical framework provides an alternative method for calculating quantum speed limit. Two typical relevant systems are employed to illustrate our results: the spin-1/2 particle in the rotating magnetic field and the entanglement swap gate.

Authenticated hierarchical quantum state sharing based on non-maximally entangled states

Hierarchical quantum state sharing (HQSTS) provides a way for the quantum state from one party to another among multiple parties asymmetrically. In the process, it is necessary to ensure the legitimacy and authenticity of participants to defend against attacks caused by neglecting authentication. Hence, we propose a three-phase probabilistic HQSTS protocol with identity authentication. Firstly, the legitimacy of participants is verified in the identity authentication phase, which effectively prevents impersonation and deception. Secondly, the sender Alice sends the target quantum state to three agents asymmetrically, which implies that there is a hierarchy of agents regarding their ability to recover the secret state. The high authority agent can recover the state without the cooperation of all agents, while the low authority agent has to recover the state with the cooperation of all agents. Thirdly, based on the non-maximally entangled cluster states, the sharing of the arbitrary three-qubit states is realized, which increases the amount of information transmitted. Using the Qiskit framework, the quantum circuit and simulation results for a particular case are given to verify the feasibility and correctness of our protocol. Moreover, the security of the protocol is analyzed from the perspective of both internal and external attacks.