arXiv subjects
Publications and source records attributed to Nathan Wiebe.
Quantum computers promise to impact industrial applications, for which quantum chemical calculations are required, by virtue of their high accuracy. This perspective explores the challenges and opportunities of applying quantum computers to drug design, discusses where they could transform industrial research and elaborates on what is needed to reach this goal.
The potential energy surface (PES) of molecules with respect to their nuclear positions is a primary tool in understanding chemical reactions from first principles. However, obtaining this information is complicated by the fact that sampling a large number of ground states over a high-dimensional PES can require a vast number of state preparations. In this work, we propose using a generative quantum machine learning model to prepare quantum states at arbitrary points on the PES. The model is trained using quantum data consisting of ground-state wavefunctions associated with different classical nuclear coordinates. Our approach uses a classical neural network to convert the nuclear coordinates of a molecule into quantum parameters of a variational quantum circuit. The model is trained using a fidelity loss function to optimize the neural network parameters. We show that gradient evaluation is efficient and numerically demonstrate our method's ability to prepare wavefunctions on the PES of hydrogen chains, water, and beryllium hydride. In all cases, we find that a small number of training points are needed to achieve very high overlap with the groundstates in practice. From a theoretical perspective, we further prove limitations on these protocols by showing that if we were able to learn across an avoided crossing using a small number of samples, then we would be able to violate Grover's lower bound. Additionally, we prove lower bounds on the amount of quantum data needed to learn a locally optimal neural network function using arguments from quantum Fisher information. This work further identifies that quantum chemistry can be an important use case for quantum machine learning.
This paper discusses quantum algorithms for the generator coordinate method (GCM) that can be used to benchmark molecular systems. The GCM formalism defined by exponential operators with exponents defined through generators of the Fermionic U(N) Lie algebra (Thouless theorem) offers a possibility of probing large sub-spaces using low-depth quantum circuits. In the present studies, we illustrate the performance of the quantum algorithm for constructing a discretized form of the Hill-Wheeler equation for ground and excited state energies. We also generalize the standard GCM formulation to multi-product extension that when collective paths are properly probed, can systematically introduce higher rank effects and provide elementary mechanisms for symmetry purification when generator states break the spatial or spin symmetries. The GCM quantum algorithms also can be viewed as an alternative to existing variational quantum eigensolvers, where multi-step classical optimization algorithms are replaced by a single-step procedure for solving the Hill-Wheeler eigenvalue problem.
Many proposals to scale quantum technology rely on modular or distributed designs where individual quantum processors, called nodes, are linked together to form one large multinode quantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, a limiting factor of these machines will be internode gates, which may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require a range of techniques, including improvements in entanglement generation, the use of entanglement distillation, and optimized software and compilers, and it remains unclear how improvements to these components interact to affect overall system performance, what performance from each is required, or even how to quantify the performance of each. In this paper, we employ a `co-design' inspired approach to quantify overall MNQC performance in terms of hardware models of internode links, entanglement distillation, and local architecture. In the case of superconducting MNQCs with microwave-to-optical links, we uncover a tradeoff between entanglement generation and distillation that threatens to degrade performance. We show how to navigate this tradeoff, lay out how compilers should optimize between local and internode gates, and discuss when noisy quantum links have an advantage over purely classical links. Using these results, we introduce a roadmap for the realization of early MNQCs which illustrates potential improvements to the hardware and software of MNQCs and outlines criteria for evaluating the landscape, from progress in entanglement generation and quantum memory to dedicated algorithms such as distributed quantum phase estimation. While we focus on superconducting devices with optical interconnects, our approach is general across MNQC implementations.
The practical benefits of hybrid quantum information processing hardware that contains continuous-variable objects (bosonic modes such as mechanical or electromagnetic oscillators) in addition to traditional (discrete-variable) qubits have recently been demonstrated by experiments with bosonic codes that reach the break-even point for quantum error correction and by efficient Gaussian boson sampling simulation of the Franck-Condon spectra of triatomic molecules that is well beyond the capabilities of current qubit-only hardware. The goal of this Co-design Center for Quantum Advantage (C2QA) project is to develop an instruction set architecture (ISA) for hybrid qubit/bosonic mode systems that contains an inventory of the fundamental operations and measurements that are possible in such hardware. The corresponding abstract machine model (AMM) would also contain a description of the appropriate error models associated with the gates, measurements and time evolution of the hardware. This information has been implemented as an extension of Qiskit. Qiskit is an opensource software development toolkit (SDK) for simulating the quantum state of a quantum circuit on a system with Python 3.7+ and for running the same circuits on prototype hardware within the IBM Quantum Lab. We introduce the Bosonic Qiskit software to enable the simulation of hybrid qubit/bosonic systems using the existing Qiskit software development kit. This implementation can be used for simulating new hybrid systems, verifying proposed physical systems, and modeling systems larger than can currently be constructed. We also cover tutorials and example use cases included within the software to study Jaynes- Cummings models, bosonic Hubbard models, plotting Wigner functions and animations, and calculating maximum likelihood estimations using Wigner functions.
Protein design is a technique to engineer proteins by modifying their sequence to obtain novel functionalities. In this method, amino acids in the sequence are permutated to find the low energy states satisfying the configuration. However, exploring all possible combinations of amino acids is generally impossible to achieve on conventional computers due to the exponential growth of possibilities with the number of designable sites. Thus, sampling methods are currently used as a conventional approach to address the protein design problems. Recently, quantum computation methods have shown the potential to solve similar types of problems. In the present work, we use the general idea of Grover's algorithm, a pure quantum computation method, to design circuits at the gate-based level and address the protein design problem. In our quantum algorithms, we use custom pair-wise energy tables consisting of eight different amino acids. Also, the distance reciprocals between designable sites are included in calculating energies in the circuits. Due to the noisy state of current quantum computers, we mainly use quantum computer simulators for this study. However, a very simple version of our circuits is implemented on real quantum devices to examine their capabilities to run these algorithms. Our results show that using $\mathcal{O}(\sqrt N)$ iterations, the circuits find the correct results among all $N$ possibilities, providing the expected quadratic speed up of Grover's algorithm over classical methods.
Quantum simulations of Lattice Gauge Theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors in order to retain a local Hamiltonian. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss' law constraint to correct one-qubit errors for a $\mathbb{Z}_2$ or truncated U(1) LGT in 1+1 and 2+1 dimensions with a link flux cutoff of $1$. Unlike existing work on detecting violations of Gauss' law, our circuits are fault tolerant and the overall error correction scheme outperforms a naïve application of the $[5,1,3]$ code. The constructions outlined can be extended to LGT systems with larger cutoffs and may be of use in understanding how to hybridize error correction and quantum simulation for LGTs in higher space-time dimensions and with different symmetry groups.
We prove an entanglement area law for a class of 1D quantum systems involving infinite-dimensional local Hilbert spaces. This class of quantum systems include bosonic models such as the Hubbard-Holstein model, and both U(1) and SU(2) lattice gauge theories in one spatial dimension. Our proof relies on new results concerning the robustness of the ground state and spectral gap to the truncation of Hilbert space, applied within the approximate ground state projector (AGSP) framework from previous work. In establishing this area law, we develop a system-size independent bound on the expectation value of local observables for Hamiltonians without translation symmetry, which may be of separate interest. Our result provides theoretical justification for using tensor network methods to study the ground state properties of quantum systems with infinite local degrees of freedom.
Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error $\varepsilon$ as $\mathcal{O}(1/\varepsilon)$. In this paper, we address the task of estimating the expectation values of $M$ different observables, each to within additive error $\varepsilon$, with the same $1/\varepsilon$ dependence. We describe an approach that leverages Gilyén et al.'s quantum gradient estimation algorithm to achieve $\mathcal{O}(\sqrt{M}/\varepsilon)$ scaling up to logarithmic factors, regardless of the commutation properties of the $M$ observables. We prove that this scaling is worst-case optimal in the high-precision regime if the state preparation is treated as a black box, even when the operators are mutually commuting. We highlight the flexibility of our approach by presenting several generalizations, including a strategy for accelerating the estimation of a collection of dynamic correlation functions.
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic advantages for some Hamiltonians, but incurs prohibitive constant factors and is incompatible with methods like qubitization. We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations over known algorithms. These approaches show asymptotic improvements over the individual methods that comprise them and further make interaction picture simulation methods practical in the near term. Physical applications of these hybridized methods yield a gate complexity scaling as $\log^2 Λ$ in the electric cutoff $Λ$ for the Schwinger Model and independent of the electron density for collective neutrino oscillations, outperforming the scaling for all current algorithms with these parameters. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $λ$ used to impose an energy cost on time-evolution into an unphysical subspace.
In recent years there has been substantial development in algorithms for quantum phase estimation. In this work we provide a new approach to online Bayesian phase estimation that achieves Heisenberg limited scaling that requires exponentially less classical processing time with the desired error tolerance than existing Bayesian methods. This practically means that we can perform an update in microseconds on a CPU as opposed to milliseconds for existing particle filter methods. Our approach assumes that the prior distribution is Gaussian and exploits the fact, when optimal experiments are chosen, the mean of the prior distribution is given by the position of a random walker whose moves are dictated by the measurement outcomes. We then argue from arguments based on the Fisher information that our algorithm provides a near-optimal analysis of the data. This work shows that online Bayesian inference is practical, efficient and ready for deployment in modern FPGA driven adaptive experiments.
The Fermi-Hubbard model (FHM) on a two dimensional square lattice has long been an important testbed and target for simulating fermionic Hamiltonians on quantum hardware. We present an alternative for quantum simulation of FHMs based on an adiabatic protocol that could be an attractive target for next generations of quantum annealers. Our results rely on a recently introduced low-weight encoding that allows the FHM to be expressed in terms of Pauli operators with locality of at most three. We theoretically and numerically determine promising quantum annealing setups for both interacting 2D spinless and spinful systems, that enable to reach near the ground state solution with high fidelity for systems as big as $6\times 6$ (spinless) and $4\times 3$ (spinful). Moreover, we demonstrate the scaling properties of the minimal gap and analyze robustness of the protocol against control noise. Additionally, we identify and discuss basic experimental requirements to construct near term annealing hardware tailored to simulate these problems. Finally, we perform a detailed resource estimation for the introduced adiabatic protocol, and discuss pros and cons of this approach relative to gate-based approaches for near-term platforms.
In this work we present the Scaled QUantum IDentifier (SQUID), an open-source framework for exploring hybrid Quantum-Classical algorithms for classification problems. The classical infrastructure is based on PyTorch and we provide a standardized design to implement a variety of quantum models with the capability of back-propagation for efficient training. We present the structure of our framework and provide examples of using SQUID in a standard binary classification problem from the popular MNIST dataset. In particular, we highlight the implications for scalability for gradient-based optimization of quantum models on the choice of output for variational quantum models.
It is for the first time that Quantum Simulation for High Energy Physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in Quantum Information Sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This community whitepaper is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.
In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated in polynomial time under reasonable assumptions while properly treating all four components of the wavefunction of the fermionic field. In particular, we provide a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. We find that the number of $T$-gates needed to perform such simulations on a $3D$ lattice of $n_s$ sites scales at worst as $O(n_s^3/ε)^{1+o(1)}$ in the thermodynamic limit for position basis simulations and $O(n_s^{4+2/3}/ε)^{1+o(1)}$ in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of $\widetilde{O}(n_s^{2+2/3}/ε)$ for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of $\widetilde{O}(n_s^{5+2/3}/ε)$. We further provide concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than $10^{13}$ non-Clifford operations and also provide a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED which can provide a reasonable initial guess for the ground state. Finally, we estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.
While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular properties can be expressed an energy derivative, including molecular forces, which are essential for applications such as molecular dynamics simulations. Here, we introduce new quantum algorithms for computing molecular energy derivatives with significantly lower complexity than prior methods. Under cost models appropriate for noisy-intermediate scale quantum devices we demonstrate how low rank factorizations and other tomography schemes can be optimized for energy derivative calculations. We perform numerics revealing that our techniques reduce the number of circuit repetitions required by many orders of magnitude for even modest systems. In the context of fault-tolerant algorithms, we develop new methods of estimating energy derivatives with Heisenberg limited scaling incorporating state-of-the-art techniques for block encoding fermionic operators. Our results suggest that the calculation of forces on a single nucleus may be of similar cost to estimating energies of chemical systems, but that further developments are needed for quantum computers to meaningfully assist with molecular dynamics simulations.
We describe quantum circuits with only $\widetilde{\cal O}(N)$ Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of $N$ arbitrary (e.g., molecular) orbitals. With ${\cal O}(λ/ ε)$ repetitions of these circuits one can use phase estimation to sample in the molecular eigenbasis, where $λ$ is the 1-norm of Hamiltonian coefficients and $ε$ is the target precision. This is the lowest complexity that has been shown for quantum computations of chemistry within an arbitrary basis. Furthermore, up to logarithmic factors, this matches the scaling of the most efficient prior block encodings that can only work with orthogonal basis functions diagonalizing the Coloumb operator (e.g., the plane wave dual basis). Our key insight is to factorize the Hamiltonian using a method known as tensor hypercontraction (THC) and then to transform the Coulomb operator into an isospectral diagonal form with a non-orthogonal basis defined by the THC factors. We then use qubitization to simulate the non-orthogonal THC Hamiltonian, in a fashion that avoids most complications of the non-orthogonal basis. We also reanalyze and reduce the cost of several of the best prior algorithms for these simulations in order to facilitate a clear comparison to the present work. In addition to having lower asymptotic scaling spacetime volume, compilation of our algorithm for challenging finite-sized molecules such as FeMoCo reveals that our method requires the least fault-tolerant resources of any known approach. By laying out and optimizing the surface code resources required of our approach we show that FeMoCo can be simulated using about four million physical qubits and under four days of runtime, assuming $1\,μ$s cycle times and physical gate error rates no worse than $0.1\%$.
Accurate models of real quantum systems are important for investigating their behaviour, yet are difficult to distill empirically. Here, we report an algorithm -- the Quantum Model Learning Agent (QMLA) -- to reverse engineer Hamiltonian descriptions of a target system. We test the performance of QMLA on a number of simulated experiments, demonstrating several mechanisms for the design of candidate Hamiltonian models and simultaneously entertaining numerous hypotheses about the nature of the physical interactions governing the system under study. QMLA is shown to identify the true model in the majority of instances, when provided with limited a priori information, and control of the experimental setup. Our protocol can explore Ising, Heisenberg and Hubbard families of models in parallel, reliably identifying the family which best describes the system dynamics. We demonstrate QMLA operating on large model spaces by incorporating a genetic algorithm to formulate new hypothetical models. The selection of models whose features propagate to the next generation is based upon an objective function inspired by the Elo rating scheme, typically used to rate competitors in games such as chess and football. In all instances, our protocol finds models that exhibit $F_1$-score $\geq 0.88$ when compared with the true model, and it precisely identifies the true model in 72% of cases, whilst exploring a space of over $250,000$ potential models. By testing which interactions actually occur in the target system, QMLA is a viable tool for both the exploration of fundamental physics and the characterisation and calibration of quantum devices.