Session HH03: V: Quantum Simulation and Algorithms

Automatic Quantum Circuit Generation for Finding Ground States

Quantum computing could advance basic science if we had software that automatically generates quantum circuits, circuits that compute the ground state of a given Hamiltonian. Our free and open-source software development [*] already does exactly that, but it not efficient yet. This talk will discuss the roadmap to make it efficient, and the roadblocks that we might encounter in the way. I will claim that tensor networks is the only known approach that can be both efficient and accurate. For this approach to work, we need to penalize or discard deep layered circuits, so that I will discuss the resulting impact to convergence. I will address also the need to use high performance (classical) computing, and the benefits of hybrid computing, where quantum circuit fitness can be evaluated on quantum hardware. Condensed matter, computational chemistry, high energy physics, all should benefit from this approach, as our generator would provide insightful, non-intuitive quantum circuits that could not have been designed manually.

(*) https://code.ornl.gov/gonzalo_3/evendim   

Simulating polaritonic ground states on noisy quantum devices

The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light-matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron-photon coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. We exploit various symmetries in qubit reduction methods, such as electron-photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H₂ molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron-photon correlation. We achieve chemical accuracy across a wide range of bond lengths, cavity frequencies, and coupling strengths. Our work serves as the foundation for further explorations of quantum computing applied toward polaritonic chemistry, such as computing excited state properties and predicting changes in reaction barriers during cavity-mediated proton transfer.   

Implementation of the Density-functional Theory on Quantum Computers

Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science.

A faithful implementation of the theory requires self-consistent calculations. However,

this effort involves repeatedly diagonalizing the Hamiltonian, for which a classical algorithm typically

requires a computational complexity that scales cubically with respect to the number of electrons.

This limits DFT’s applicability to large-scale problems with complex chemical environments and

microstructures. This article presents a quantum algorithm that has a linear scaling with respect to

the number of atoms, which is much smaller than the number of electrons. Our algorithm leverages

the quantum singular value transformation (QSVT) to generate a quantum circuit to encode the

density-matrix, and an estimation method for computing the output electron density. In addition,

we present a randomized block coordinate fixed-point method to accelerate the self-consistent field

calculations by reducing the number of components of the electron density that needs to be estimated.   

Quantum simulation of the nonlinear bosonic Kitaev chain in a parametric cavity

Multimode superconducting parametric cavities have been demonstrated as a versatile platform for analog quantum simulation. Cavity modes represent lattice sites in synthetic dimensions, and tunable interactions between these modes are created in-situ by parametrically driving a superconducting quantum interference device (SQUID), which terminates the cavity, with external flux pumps. Here we numerically study the nonlinear bosonic Kitaev chain model realized in a multimode cavity. The sites in the chain are coupled by external hopping and pairing drives, and further subjected to single-photon losses and Kerr nonlinearity. Above the threshold for the pairing strength, we show that apart from the usual bistable behavior in Kerr parametric oscillators, the system allows a dissipation-induced time crystal phase, in which the delayed temporal correlation functions exhibit sustained oscillations in the steady state.   

Analog variational quantum simulators with long-range interactions

Current experimental quantum devices do not meet the requirements for building fault-tolerant quantum computers, but they still can be used to address many-body problems as analogue quantum simulators. Some of these platforms, like superconducting circuits [1], trapped-ions [2], Rydberg atoms [3] or ultracold atoms [4], can be engineered to have long-range interactions between its components. However, the systems simulated are constrained by the type of interactions that can be engineered in the platform.

Variational methods have been suggested as a way to go beyond this limitation [5,6]. Among the different proposals, Variational Quantum Time Evolution algorithms (VarQTE) can perform either real or imaginary time evolution within the same framework [7]. In this work we propose to use this variational approach to fully harness the tunability of the long-range interactions in analogue quantum simulators. We demonstrate how some of the limitations of VarQTE can be solved using this tunable long-range, and benchmark this advantage against fixed range quantum simulators in both imaginary and real time evolution. Furthermore, we consider analogue quantum simulators made of qubits, bosons and fermions, using tensor network methods to highlight the role of the tunable long-range as the system size increases.

In summary, our work introduces a new set of tools that can be used to compute both ground states and dynamics of complex many-body Hamiltonians using simpler analogue quantum simulators.

[1] X. Zhang et al., Science 379, 278-283 (2023).

[2] C. Kokail et al., Nature 569, 355–360 (2019).

[3] S. Ebadi et al., Nature 595, 227–232 (2021).

[4] J. Argüello-Luengo et al., Nature 574, 215–218 (2019).

[5] A. J. Daley et al., Nature 607, 667–676 (2022).

[6] C. Tabares et al., Phys. Rev. Lett. 131, 073602 (2023).

[7] X. Yuan et al., Quantum 3, 191 (2019).   

Quantum expectation value estimation by doubling the number of qubits

Estimating the expectation values of operators is crucial in many hybrid quantum-classical algorithms designed for near-term noisy devices. Its practical applications to quantum chemistry, however, are hampered by too many measurements required to suppress the statistical fluctuation. This is mainly because the expectation value of an operator, represented as a linear combination of multi-qubit Pauli operators (Pauli strings) on qubits, is estimated based on separate measurements of the individual Pauli strings, whose number grows with the system size. Here, to reduce the measurement cost, we utilize the fact that the expectation values of all the Pauli strings, albeit their absolute values alone, can be simultaneously ``measured'' by performing Bell basis measurements on two copies of the quantum state of interest. Taking molecular Hamiltonians for illustration, we numerically examine the efficiency of our method in terms of the measurement cost in comparison with the conventional methods adopted in near-term calculations.   

Potentials and Limitations of Analog Quantum Simulators in Variational Quantum Algorithms

The variational quantum algorithms have a potential to bring about useful applications of near-term quantum devices. While digital gate-based VQAs have been extensively investigated with well-known fundamental results such as barren plateaus, the analog paradigm remains relatively unexplored. In this work, we propose an experimental-friendly ansatz based on analog quench dynamics generated by native Hamiltonian of quantum hardware. By considering a disordered Ising spin chain as an example, we study three fundamental aspects of our ansatz including (i) universality and how (ii) expressivity and (iii) trainability scale with the number of qubits. We show that the ansatz is universal when allowing time within each quench to be parametrized. To study the other two aspects, we operate our ansatz in two different phases of matter namely thermalized and many-body localized (MBL) phases. While maximum expressivity can be achieved in both phases, it is exactly in this regime where the ansatz becomes untrainable with exponentially vanishing variance. Fortunately, since the number of quenches to achieve the maximum expressivity in MBL is much less than in the thermalized phase, this allows a novel strategy with trainability when our anzatz is initialized in MBL. Our results demonstrate the deep connection of quantum many-body phases with expressivity and trainability in analog VQAs.   

Preparation of MPS with log-depth quantum circuits

We consider the preparation of matrix-product states (MPS) via quantum circuits of local gates. We first prove that it is impossible to faithfully prepare translation-invariant normal MPS of length N with depth T = o(logN). We then introduce a circuit based on the renormalization-group transformation that can prepare this class with T = O(log N/ε) for error ε, and thus has optimal scaling. Our protocol naturally generalizes to inhomogeneous MPS. We also show that measurement and feedback lead to an exponential speed-up of the algorithm, to T = O(log log(N/ε)), and allows one to prepare all translationally-invariant MPS in the same depth.   

Rocky Raccoon: Automated quantum circuit optimization using graph-based deep reinforcement learning

Efficient compilation of quantum algorithms is crucial to the success of near-term and fault-tolerant quantum information processing devices. In general, circuit synthesis and gate decomposition results in quantum circuits with suboptimal gate count and circuit depth. Quantum circuit optimization aims to address this limitation by finding and applying strategies to simplify quantum circuits and reduce the amount of resources required to implement quantum algorithms. We propose a framework for quantum circuit optimization by formulating it as a Markov decision process, and use graph-based deep reinforcement learning to train an agent to optimize quantum circuits by applying local and simple rewrite rules. The agent in our framework is realized by a graph neural network which operates on a directed acyclic graph representation of a quantum circuit. The actions of the agent are formulated as simple rewrite rules applied to pairs of adjacent quantum gates. We'll discuss our ongoing work on benchmarking the framework and how the proposed agent may be used to discover complex circuit optimization strategies in an automated fashion by sequentially composing simple rewrite rules.