arXiv subjects

Guang Hao Low

Publications and source records attributed to Guang Hao Low.

At least 37 records · Page 2Linked to original sources

arXiv2024

End-to-End Quantum Simulation of a Chemical System

We demonstrate the first end-to-end integration of high-performance computing (HPC), reliable quantum computing, and AI in a case study on catalytic reactions producing chiral molecules. We present a hybrid computation workflow to determine the strongly correlated reaction configurations and estimate, for one such configuration, its active site's ground state energy. We combine 1) the use of HPC tools like AutoRXN and AutoCAS to systematically identify the strongly correlated chemistry within a large chemical space with 2) the use of logical qubits in the quantum computing stage to prepare the quantum ground state of the strongly correlated active site, demonstrating the advantage of logical qubits compared to physical qubits, and 3) the use of optimized quantum measurements of the logical qubits with so-called classical shadows to accurately predict various properties of the ground state including energies. The combination of HPC, reliable quantum computing, and AI in this demonstration serves as a proof of principle of how future hybrid chemistry applications will require integration of large-scale quantum computers with classical computing to be able to provide a measurable quantum advantage.

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arXiv2024

Classical shadows of fermions with particle number symmetry

We consider classical shadows of fermion wavefunctions with $η$ particles occupying $n$ modes. We prove that all $k$-Reduced Density Matrices (RDMs) may be simultaneously estimated to an average variance of $ε^{2}$ using at most $\binomη{k}\big(1-\frac{η-k}{n}\big)^{k}\frac{1+n}{1+n-k}/ε^{2}$ measurements in random single-particle bases that conserve particle number, and provide an estimator for any $k$-RDM with $\mathcal{O}(k^2η)$ classical complexity. Our sample complexity is a super-exponential improvement over the $\mathcal{O}(\binom{n}{k}\frac{\sqrt{k}}{ε^{2}})$ scaling of prior approaches as $n$ can be arbitrarily larger than $η$, which is common in natural problems. Our method, in the worst-case of half-filling, still provides a factor of $4^{k}$ advantage in sample complexity, and also estimates all $η$-reduced density matrices, applicable to estimating overlaps with all single Slater determinants, with at most $\mathcal{O}(\frac{1}{ε^{2}})$ samples, which is additionally independent of $η$.

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arXiv2024

Trading T gates for dirty qubits in state preparation and unitary synthesis

Efficient synthesis of arbitrary quantum states and unitaries from a universal fault-tolerant gate-set e.g. Clifford+T is a key subroutine in quantum computation. As large quantum algorithms feature many qubits that encode coherent quantum information but remain idle for parts of the computation, these should be used if it minimizes overall gate counts, especially that of the expensive T-gates. We present a quantum algorithm for preparing any dimension-$N$ pure quantum state specified by a list of $N$ classical numbers, that realizes a trade-off between space and T-gates. Our scheme uses $\mathcal{O}(\log{(N/ε)})$ clean qubits and a tunable number of $\sim(λ\log{(\frac{\log{N}}ε)})$ dirty qubits, to reduce the T-gate cost to $\mathcal{O}(\frac{N}λ+λ\log{\frac{N}ε}\log{\frac{\log{N}}ε})$. This trade-off is optimal up to logarithmic factors, proven through an unconditional gate counting lower bound, and is, in the best case, a quadratic improvement in T-count over prior ancillary-free approaches. We prove similar statements for unitary synthesis by reduction to state preparation. Underlying our constructions is a T-efficient circuit implementation of a quantum oracle for arbitrary classical data.

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arXiv2024

An efficient quantum algorithm for generation of ab initio n-th order susceptibilities for non-linear spectroscopies

We develop and analyze a fault-tolerant quantum algorithm for computing $n$-th order response properties necessary for analysis of non-linear spectroscopies of molecular and condensed phase systems. We use a semi-classical description in which the electronic degrees of freedom are treated quantum mechanically and the light is treated as a classical field. The algorithm we present can be viewed as an implementation of standard perturbation theory techniques, focused on {\it ab initio} calculation of $n$-th order response functions. We provide cost estimates in terms of the number of queries to the block encoding of the unperturbed Hamiltonian, as well as the block encodings of the perturbing dipole operators. Using the technique of eigenstate filtering, we provide an algorithm to extract excitation energies to resolution $γ$, and the corresponding linear response amplitude to accuracy $ε$ using ${O}\left(N^{6}η^2{γ^{-1}ε^{-1}}\log(1/ε)\right)$ queries to the block encoding of the unperturbed Hamiltonian $H_0$, in double factorized representation. Thus, our approach saturates the Heisenberg $O(γ^{-1})$ limit for energy estimation and allows for the approximation of relevant transition dipole moments. These quantities, combined with sum-over-states formulation of polarizabilities, can be used to compute the $n$-th order susceptibilities and response functions for non-linear spectroscopies under limited assumptions using $\widetilde{O}\left({N^{5n+1}η^{n+1}}/{γ^nε}\right)$ queries to the block encoding of $H_0$.

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arXiv2024

Capturing many-body correlation effects with quantum and classical computing

Theoretical descriptions of excited states of molecular systems in high-energy regimes are crucial for supporting and driving many experimental efforts at light source facilities. However, capturing their complicated correlation effects requires formalisms that provide a hierarchical infrastructure of approximations. These approximations lead to an increased overhead in classical computing methods, and therefore, decisions regarding the ranking of approximations and the quality of results must be made on purely numerical grounds. The emergence of quantum computing methods has the potential to change this situation. In this study, we demonstrate the efficiency of Quantum Phase Estimator (QPE) in identifying core-level states relevant to x-ray photoelectron spectroscopy. We compare and validate the QPE predictions with exact diagonalization and real-time equation-of-motion coupled cluster formulations, which are some of the most accurate methods for states dominated by collective correlation effects.

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arXiv2023

Efficient quantum algorithm for nonlinear reaction-diffusion equations and energy estimation

Nonlinear differential equations exhibit rich phenomena in many fields but are notoriously challenging to solve. Recently, Liu et al. [1] demonstrated the first efficient quantum algorithm for dissipative quadratic differential equations under the condition $R < 1$, where $R$ measures the ratio of nonlinearity to dissipation using the $\ell_2$ norm. Here we develop an efficient quantum algorithm based on [1] for reaction-diffusion equations, a class of nonlinear partial differential equations (PDEs). To achieve this, we improve upon the Carleman linearization approach introduced in [1] to obtain a faster convergence rate under the condition $R_D < 1$, where $R_D$ measures the ratio of nonlinearity to dissipation using the $\ell_{\infty}$ norm. Since $R_D$ is independent of the number of spatial grid points $n$ while $R$ increases with $n$, the criterion $R_D<1$ is significantly milder than $R<1$ for high-dimensional systems and can stay convergent under grid refinement for approximating PDEs. As applications of our quantum algorithm we consider the Fisher-KPP and Allen-Cahn equations, which have interpretations in classical physics. In particular, we show how to estimate the mean square kinetic energy in the solution by postprocessing the quantum state that encodes it to extract derivative information.

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arXiv2023

On the complexity of implementing Trotter steps

Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian term number, comparing unfavorably to algorithms using more advanced techniques. We develop methods to perform faster Trotter steps with complexity sublinear in the number of terms. We achieve this for a class of Hamiltonians whose interaction strength decays with distance according to power law. Our methods include one based on a recursive block encoding and one based on an average-cost simulation, overcoming the normalization-factor barrier of these advanced quantum simulation techniques. We also realize faster Trotter steps when certain blocks of Hamiltonian coefficients have low rank. Combining with a tighter error analysis, we show that it suffices to use $\left(η^{1/3}n^{1/3}+\frac{n^{2/3}}{η^{2/3}}\right)n^{1+o(1)}$ gates to simulate uniform electron gas with $n$ spin orbitals and $η$ electrons in second quantization in real space, asymptotically improving over the best previous work. We obtain an analogous result when the external potential of nuclei is introduced under the Born-Oppenheimer approximation. We prove a circuit lower bound when the Hamiltonian coefficients take a continuum range of values, showing that generic $n$-qubit $2$-local Hamiltonians with commuting terms require at least $Ω(n^2)$ gates to evolve with accuracy $ε=Ω(1/poly(n))$ for time $t=Ω(ε)$. Our proof is based on a gate-efficient reduction from the approximate synthesis of diagonal unitaries within the Hamming weight-$2$ subspace, which may be of independent interest. Our result thus suggests the use of Hamiltonian structural properties as both necessary and sufficient to implement Trotter steps with lower gate complexity.

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arXiv2022

Assessing requirements to scale to practical quantum advantage

While quantum computers promise to solve some scientifically and commercially valuable problems thought intractable for classical machines, delivering on this promise will require a large-scale quantum machine. Understanding the impact of architecture design choices for a scaled quantum stack for specific applications, prior to full realization of the quantum system, is an important open challenge. To this end, we develop a framework for quantum resource estimation, abstracting the layers of the stack, to estimate resources required across these layers for large-scale quantum applications. Using a tool that implements this framework, we assess three scaled quantum applications and find that hundreds of thousands to millions of physical qubits are needed to achieve practical quantum advantage. We identify three qubit parameters, namely size, speed, and controllability, that are critical at scale to rendering these applications practical. A goal of our work is to accelerate progress towards practical quantum advantage by enabling the broader community to explore design choices across the stack, from algorithms to qubits.

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arXiv2022

Periodic Plane-Wave Electronic Structure Calculations on Quantum Computers

A procedure for defining virtual spaces, and the periodic one-electron and two-electron integrals, for plane-wave second quantized Hamiltonians has been developed and demonstrated using full configuration interaction (FCI) simulations and variational quantum eigensolver (VQE) circuits on Quantinuum's ion trap quantum computers accessed through Microsoft's Azure Quantum service. This work is an extension to periodic systems of a new class of algorithms in which the virtual spaces were generated by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. In this extension, the integration of the first Brillouin zone is automatically incorporated into the two-electron integrals. With these procedures we have been able to derive virtual spaces, containing only a few orbitals, that were able to capture a significant amount of correlation. The focus in this manuscript is on comparing the simulations of small molecules calculated with plane-wave basis sets with large periodic unit cells at the $Γ$-point, including images, to results for plane-wave basis sets with aperiodic unit cells. The results for this approach were promising as we were able to obtain good agreement between periodic and aperiodic results for an LiH molecule. Simulations performed on the Quantinuum H1-1 quantum computer were able to produce surprisingly good energies, reproducing the FCI values for the 1 COVO Hamiltonian to within 11 milliHartree (6.9 kcal/mol), when corrected for noise.

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arXiv2021

Halving the cost of quantum multiplexed rotations

We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls applying $n$ single-qubit arbitrary phase rotations from $4n b+\mathcal{O}(\sqrt{cn b})$ to $2n b+\mathcal{O}(\sqrt{cn b})$, and reduce the number of qubits needed by up to a factor of two. This generic quantum circuit primitive is found in many quantum algorithms, and our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations. We achieve this by extending recent ideas on stochastic compilation of quantum circuits to classical data and discuss space-time trade-offs and concentration of measure in its implementation.

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arXiv2021

Robust Calibration of a Universal Single-Qubit Gate-Set via Robust Phase Estimation

An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the systematic errors in gates and then using controls to correct the implementation. Quantum process tomography is a standard technique for estimating these errors, but is both time consuming, (when one only wants to learn a few key parameters), and is usually inaccurate without resources like perfect state preparation and measurement, which might not be available. With the goal of efficiently and accurately estimating specific errors using minimal resources, we develop a parameter estimation technique, which can gauge key systematic parameters (specifically, amplitude and off-resonance errors) in a universal single-qubit gate-set with provable robustness and efficiency. In particular, our estimates achieve the optimal efficiency, Heisenberg scaling, and do so without entanglement and entirely within a single-qubit Hilbert space. Our main theorem making this possible is a robust version of the phase estimation procedure of Higgins et al. [B. L. Higgins, New J. Phys. 11, 073023 (2009)].

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arXiv2021

Prospects of Quantum Computing for Molecular Sciences

Molecular science is governed by the dynamics of electrons, atomic nuclei, and their interaction with electromagnetic fields. A reliable physicochemical understanding of these processes is crucial for the design and synthesis of chemicals and materials of economic value. Although some problems in this field are adequately addressed by classical mechanics, many require an explicit quantum mechanical description. Such quantum problems represented by exponentially large wave function should naturally benefit from quantum computation on a number of logical qubits that scales only linearly with system size. In this perspective, we focus on the potential of quantum computing for solving relevant problems in the molecular sciences -- molecular physics, chemistry, biochemistry, and materials science.

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arXiv2021

Quantum computing enhanced computational catalysis

The quantum computation of electronic energies can break the curse of dimensionality that plagues many-particle quantum mechanics. It is for this reason that a universal quantum computer has the potential to fundamentally change computational chemistry and materials science, areas in which strong electron correlations present severe hurdles for traditional electronic structure methods. Here, we present a state-of-the-art analysis of accurate energy measurements on a quantum computer for computational catalysis, using improved quantum algorithms with more than an order of magnitude improvement over the best previous algorithms. As a prototypical example of local catalytic chemical reactivity we consider the case of a ruthenium catalyst that can bind, activate, and transform carbon dioxide to the high-value chemical methanol. We aim at accurate resource estimates for the quantum computing steps required for assessing the electronic energy of key intermediates and transition states of its catalytic cycle. In particular, we present new quantum algorithms for double-factorized representations of the four-index integrals that can significantly reduce the computational cost over previous algorithms, and we discuss the challenges of increasing active space sizes to accurately deal with dynamical correlations. We address the requirements for future quantum hardware in order to make a universal quantum computer a successful and reliable tool for quantum computing enhanced computational materials science and chemistry, and identify open questions for further research.

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arXiv2020

Quantum algorithm for simulating real time evolution of lattice Hamiltonians

We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in its vicinity). This class of Hamiltonians is very general and is believed to capture fundamental interactions of physics. Our algorithm simulates the time evolution of such a Hamiltonian on $n$ qubits for time $T$ up to error $ε$ using $\mathcal O( nT \mathrm{polylog} (nT/ε))$ gates with depth $\mathcal O(T \mathrm{polylog} (nT/ε))$. Our algorithm is the first simulation algorithm that achieves gate cost quasilinear in $nT$ and polylogarithmic in $1/ε$. Our algorithm also readily generalizes to time-dependent Hamiltonians and yields an algorithm with similar gate count for any piecewise slowly varying time-dependent bounded local Hamiltonian. We also prove a matching lower bound on the gate count of such a simulation, showing that any quantum algorithm that can simulate a piecewise constant bounded local Hamiltonian in one dimension to constant error requires $\tilde Ω(nT)$ gates in the worst case. The lower bound holds even if we only require the output state to be correct on local measurements. To our best knowledge, this is the first nontrivial lower bound on the gate complexity of the simulation problem. Our algorithm is based on a decomposition of the time-evolution unitary into a product of small unitaries using Lieb-Robinson bounds. In the appendix, we prove a Lieb-Robinson bound tailored to Hamiltonians with small commutators between local terms, giving zero Lieb-Robinson velocity in the limit of commuting Hamiltonians. This improves the performance of our algorithm when the Hamiltonian is close to commuting.

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arXiv2020

Towards quantum computing for high-energy excited states in molecular systems: quantum phase estimations of core-level states

This paper explores the utility of the quantum phase estimation (QPE) in calculating high-energy excited states characterized by promotions of electrons occupying inner energy shells. These states have been intensively studied over the last few decades especially in supporting the experimental effort at light sources. Results obtained with the QPE are compared with various high-accuracy many-body techniques developed to describe core-level states. The feasibility of the quantum phase estimator in identifying classes of challenging shake-up states characterized by the presence of higher-order excitation effects is also discussed.

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arXiv2020

A Variational Quantum Algorithm for Preparing Quantum Gibbs States

Preparation of Gibbs distributions is an important task for quantum computation. It is a necessary first step in some types of quantum simulations and further is essential for quantum algorithms such as quantum Boltzmann training. Despite this, most methods for preparing thermal states are impractical to implement on near-term quantum computers because of the memory overheads required. Here we present a variational approach to preparing Gibbs states that is based on minimizing the free energy of a quantum system. The key insight that makes this practical is the use of Fourier series approximations to the logarithm that allows the entropy component of the free-energy to be estimated through a sequence of simpler measurements that can be combined together using classical post processing. We further show that this approach is efficient for generating high-temperature Gibbs states, within constant error, if the initial guess for the variational parameters for the programmable quantum circuit are sufficiently close to a global optima. Finally, we examine the procedure numerically and show the viability of our approach for five-qubit Hamiltonians using Trotterized adiabatic state preparation as an ansatz.

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arXiv2019

Well-conditioned multiproduct Hamiltonian simulation

Product formula approximations of the time-evolution operator on quantum computers are of great interest due to their simplicity, and good scaling with system size by exploiting commutativity between Hamiltonian terms. However, product formulas exhibit poor scaling with the time $t$ and error $ε$ of simulation as the gate cost of a single step scales exponentially with the order $m$ of accuracy. We introduce well-conditioned multiproduct formulas, which are a linear combination of product formulas, where a single step has polynomial cost $\mathcal{O}(m^2\log{(m)})$ and succeeds with probability $Ω(1/\operatorname{log}^2{(m)})$. Our multiproduct formulas imply a simple and generic simulation algorithm that simultaneously exploits commutativity in arbitrary systems and has a worst-case cost $\mathcal{O}(t\log^{2}{(t/ε)})$ which is optimal up to poly-logarithmic factors. In contrast, prior Trotter and post-Trotter Hamiltonian simulation algorithms realize only one of these two desirable features. A key technical result of independent interest is our solution to a conditioning problem in previous multiproduct formulas that amplified numerical errors by $e^{Ω(m)}$ in the classical setting, and led to a vanishing success probability $e^{-Ω(m)}$ in the quantum setting.

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arXiv2019

Quantum simulations of excited states with active-space downfolded Hamiltonians

Many-body techniques based on the double unitary coupled cluster ansatz (DUCC) can be used to downfold electronic Hamiltonians into low-dimensional active spaces. It can be shown that the resulting dimensionality reduced Hamiltonians are amenable for quantum computing. Recent studies performed for several benchmark systems using quantum phase estimation (QPE) algorithms demonstrated that these formulations can recover a significant portion of ground-state dynamical correlation effects that stem from the electron excitations outside of the active space. These results have also been confirmed in studies of ground-state potential energy surfaces using quantum simulators. In this letter, we study the effectiveness of the DUCC formalism in describing excited states. We also emphasize the role of the QPE formalism and its stochastic nature in discovering/identifying excited states or excited-state processes in situations when the knowledge about the true configurational structure of a sought after excited state is limited or postulated (due to the specific physics driving excited-state processes of interest). In this context, we can view the QPE algorithm as an engine for verifying various hypotheses for excited-state processes and providing statistically meaningful results that correspond to the electronic state(s) with the largest overlap with a postulated configurational structure. We illustrate these ideas on examples of strongly correlated molecular systems, characterized by small energy gaps and high density of quasi-degenerate states around the Fermi level.

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