Session Z09: Quantum Advantage Over Classical Systems

Developping a Rydberg Cesium quantum simulator

The quest for a quantum advantage in noisy physical devices is a grand challenge in the current era of quantum information science.  We are developing an experiment to explore the boundaries of robustness and computational complexity in a Rydberg quantum simulator using cesium.  Typified by long coherence times and weak coupling to laboratory noise, neutral atoms make an excellent platform to investigate entanglement growth in the presence of noise.  We will present our most recent experimental progress.   

Fast quantum many-body state preparation using non-Gaussian variational ansatz and quantum optimal control

We show how to exploit a variational ansatz based on non-Gaussian wavefunctions for fast non-adiabatic preparation of quantum many-body states using quantum optimal control. We demonstrate this on the example of spin-boson model, where we determine the optimal time variation of the Hamiltonian parameters to prepare (near) critical ground states in times, which clearly outperform optimized adiabatic protocols. To this end we use the time dependent variational principle and polaron-like ansatz states, which correspond to generalized many-body squeezed cat states of the bosonic modes coupled to the spin.   

Author not Attending

Simulation of bosonic systems with dense coupling graphs can be hard for classical computers and include interesting problems such as boson sampling, spin-boson Hamiltonians with long range interactions as well as light-matter interactions cite{H,O}. For general bosonic systems, the response functions can be used to extract information about the dynamics as well as identifying the critical points. For example, in quantum optics, measuring $g^{(1)}$ and $g^{(2)}$ are the standard toolbox used to quantify the classical and quantum correlations between photons. However, the utility of quantum simulations of bosonic systems can be limited by the exponential resources needed to characterize the dynamics of the infinite dimensional Fock space corresponding to the interacting collective phonons in the chain of ions. Here, we present efficient protocols to probe $g^{(1)}$ and $g^{(2)}$ of phonons which require polynomial number of local operations for a given number of collective phonons involved in the quantum simulation. 

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ibitem{H}Young, S., Häffner, H. & Sarovar, M. Quantum simulation of weak-field light-matter interactions. {em Phys. Rev. Res.}. extbf{5}, 013027 (2023,1), https://link.aps.org/doi/10.1103/PhysRevResearch.5.013027

ibitem{O} Or Katz and Christopher Monroe.

ewblock Programmable quantum simulations of bosonic systems with trapped ions, 2022;

ewblock arXiv:2207.13653.   

Quantum computational advantage with Gaussian boson sampling

Quantum computers promise to perform certain tasks that are believed to be intractable to classical computers. Boson sampling is such a task and is considered a strong candidate to demonstrate the quantum computational advantage. Rather than being a single-shot event, the establishment of quantum computational advantage will be the result of a long-term competition between the quantum devices and the classical algorithms. We report Gaussian boson sampling (GBS) experiment which registered up to 113 photon-click events out of a on a 144-mode fully connected photonic circuit. Exploring the idea of stimulated emission of squeezed photons, a new high-brightness and scalable quantum light source is developed which has simultaneously near-unity purity and efficiency. The obtained samples are efficiently validated, ruling out the known classical mockup hypotheses. We measure and reveal the high-order correlations in the GBS samples, which are evidence of robustness against certain classical simulation schemes. This work yields a Hilbert space dimension up to ∼10^43, and a sampling rate ∼10^24 faster than using brute-force simulation on classical supercomputers, and an overwhelming advantage over the best known exact classical sampling algorithms.

In another aspect, Gaussian boson sampling (GBS) is not only a feasible protocol for demonstrating quantum computational advantage, but also mathematically associated with certain graph-related and quantum chemistry problems. In particular, it is proposed that the generated samples from the GBS could be harnessed to enhance the classical stochastic algorithms in searching some graph features. We investigate the open question of whether the GBS enhancement over the classical stochastic algorithms persists – and how it scales – with an increasing system size on Jiuzhang in the computationally interesting regime. We experimentally observe the presence of GBS enhancement with large photon-click number and a robustness of the enhancement under certain noise. Our work is a step toward testing real-world problems using the existing noisy intermediate-scale quantum computers.   

Quantum Simulation of Strongly Correlated Molecules with Rydberg Atom Arrays

Of the potential applications for near-term programmable quantum simulators, one of the most promising isstudying quantum chemistry and materials problems. In this work, we develop a simulation framework, combining classical computational chemistry techniques with quantum simulation, for studying low-energy properties of certain molecules and materials with strong spin correlations. For such systems, classical electronic structure algorithms can efficiently compute effective spin Hamiltonians that capture the low-energy physics. However, eigenstates of these models are often strongly correlated and require methods which can capture large quantum fluctuations. As such, we propose to use Rydberg atom arrays to encode and simulate such effective Hamiltonians and develop a hardware efficient Hamiltonian simulation based on dynamical reconfiguration and multi-qubit Rydberg gates. The framework also includes algorithms for the extraction of detailed spectral information from time dynamics, including observables relevant for chemistry, through snapshot measurements and ancilla-assisted control. As a proof of concept, we ultimately apply the developed methodology to simulate and analyze organometallic catalysts, single-molecular magnets, and propose near-term simulations of 2D magnetic materials.   

Multi-task learning with quantum reservoir computing

With the rapid development of experimental technology, a large degree of controllability has been available in a broad spectrum of noise-intermediate-scale quantum (NISQ) devices. To take full advantage of the computational power of those NISQ devices, we study the potential quantum advantage of quantum reservoir computing and the learning power of specially designed quantum reservoirs. Here we construct the classical and quantum reservoirs and contrast their computational capacities to demonstrate the potential quantum advantage. Furthermore, we study the learning power of the designed quantum reservoir. We find the designed quantum reservoir can simultaneously learn different tasks: a synthetic oscillatory network of transcriptional regulators, chaotic motifs in gene regulatory networks, and fractional-order Chua's circuit with a memristor. Except for those artificial systems, we also investigate the real-world problem, the exchange rate prediction. The quantum reservoir has acquired outstanding performance on the above tasks.   

a hybrid quantum algorithm for time-independent quantum scattering problems

We propose a hybrid quantum-classical algorithm for solving molecular quantum scattering problems, which are central to atmospheric chemistry, combustion, and astrochemistry. The algorithm is based on the S-matrix version of the Kohn variational principle proposed by Zhang, Chu, and Miller [J. Chem. Phys. 88, 6233 (1988)], in which the quantum scattering problem is mapped onto a symmetric matrix inversion problem. The latter is solved on a noisy intermediate-scale quantum processor using the variational quantum linear solver (VQLS) algorithm [Bravo-Prieto et al, arXiv:1909.05820]. Applications to one and two-dimensional scattering problems are presented to validate the approach.   

Experimentally quantifying the boundary between classical and quantum advantage

Which is the better representation of some ideal quantum evolution, a classical computer using an approximate simulation algorithm, or a noisy quantum simulator? We experimentally test this question by producing maximum-entanglement entropy states with as many as 60 atoms using a Rydberg atom array with state-of-the-art fidelity, and compare against similarly state-of-the-art classical simulation algorithms. In this high-entanglement regime, neither the classical nor quantum device has perfect fidelity, but the classical algorithm's limited accuracy can be precisely controlled by varying the degree of classical resources employed. This allows us to define the equivalent classical cost to perform evolution with the same fidelity as the quantum experiment. We show that with incremental experimental improvements, the classical cost required to "beat" the quantum device increases by orders-of-magnitude, and even in the present day we find the quantum experiment can outperform the classical computer in finite sampling from these high-entanglement states. Our results include advances in classically simulating quantum evolution, benchmarking quantum devices in the naively beyond-classical regime, and quantitatively understanding the boundary between classical and quantum advantage.   

Deterministic and Entanglement-Efficient Preparation of Amplitude-Encoded Quantum Registers

Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector b is encoded in the amplitudes of a quantum state |b>.  However, efficiently preparing |b>is known to be a difficult problem because an arbitrary state of Q qubits generally requires approximately 2^Q entangling gates, which results in significant decoherence on today’s Noisy-Intermediate Scale Quantum (NISQ) computers. We present a deterministic (non-variational) algorithm that allows one to flexibly reduce the quantum resources required for state preparation in an entanglement-efficient manner. Although this comes at the expense of reduced theoretical fidelity, actual fidelities on current NISQ computers might actually be higher due to reduced decoherence. We show this to be true for various cases of interest such as the normal and log-normal distributions. For low entanglement states, our algorithm can prepare states with more than an order of magnitude fewer entangling gates as compared to isometric decomposition.   

Atomic boson sampling and quantum supremacy

We consider quantum statistical physics of many-body equilibrium fluctuations in an interacting Bose-Einstein-condensed (BEC) gas. We find a universal analytic formula for a characteristic function (Fourier transform) of a joint probability distribution for the atom occupation numbers in a BEC gas and discuss #P-hardness of computing this distribution. The latter is done by means of the new theorem that we recently revealed and proved - the Hafnian master theorem generalizing the classical permanent master theorem of MacMahon. We suggest an atomic boson sampling in the many-body interacting systems as an alternative to a widely studied Gaussian boson sampling of photons for demonstrating quantum supremacy of the many-body systems over classical simulators. We outline a multi-qubit BEC trap, formed by a set of the single-qubit potential wells, as a convenient model for studying atomic boson sampling.