arXiv subjects

Modjtaba Shokrian Zini

Publications and source records attributed to Modjtaba Shokrian Zini.

At least 19 recordsLinked to original sources

arXiv2024

Better product formulas for quantum phase estimation

Quantum phase estimation requires simulating the evolution of the Hamiltonian, for which product formulas are attractive due to their smaller qubit cost and ease of implementation. However, the estimation of the error incurred by product formulas is usually pessimistic and task-agnostic, which poses problems for assessing their performance in practice for problems of interest. In this work, we study the error of product formulas for the specific task of quantum energy estimation. To this end, we employ the theory of Trotter error with a Magnus-based expansion of the effectively simulated Hamiltonian. The result is a generalization of previous energy estimation error analysis of gapped eigenstates to arbitrary order product formulas. As an application, we discover a 9-term second-order product formula with an energy estimation error that is quadratically better than Trotter-Suzuki. Furthermore, by leveraging recent work on low-energy dynamics of product formulas, we provide tighter bounds for energy estimation error in the low-energy subspace. We show that for Hamiltonians with some locality and positivity properties, the cost can achieve up to a quadratic asymptotic speedup in terms of the target error.

quant-ph↗

arXiv2024

Nonlinear Spectroscopy via Generalized Quantum Phase Estimation

Response theory has a successful history of connecting experimental observations with theoretical predictions. Of particular interest is the optical response of matter, from which spectroscopy experiments can be modelled. However, the calculation of response properties for quantum systems is often prohibitively expensive, especially for nonlinear spectroscopy, as it requires access to either the time evolution of the system or to excited states. In this work, we introduce a generalized quantum phase estimation framework designed for multi-variate phase estimation. This allows the treatment of general correlation functions enabling the recovery of response properties of arbitrary orders. The generalized quantum phase estimation circuit has an intuitive construction that is linked with a physical process of interest, and can directly sample frequencies from the distribution that would be obtained experimentally. In addition, we provide a single-ancilla modification of the new framework for early fault-tolerant quantum computers. Overall, our framework enables the efficient simulation of spectroscopy experiments beyond the linear regime, such as Raman spectroscopy, having that the circuit cost grows linearly with respect to the order of the target nonlinear response. This opens up an exciting new field of applications for quantum computers with potential technological impact.

quant-ph↗

arXiv2024

Simulating optically-active spin defects with a quantum computer

There is a pressing need for more accurate computational simulations of the opto-electronic properties of defects in materials to aid in the development of quantum sensing platforms. In this work, we explore how quantum computers could be effectively utilized for this purpose. Specifically, we develop fault-tolerant quantum algorithms to simulate optically active defect states and their radiative emission rates. We employ quantum defect embedding theory to translate the Hamiltonian of a defect-containing supercell into a smaller, effective Hamiltonian that accounts for dielectric screening effects. Our approach integrates block-encoding of the dipole operator with quantum phase estimation to selectively sample the optically active excited states that exhibit the largest dipole transition amplitudes. We also provide estimates of the quantum resources required to simulate a negatively-charged boron vacancy in a hexagonal boron nitride cluster. We conclude by offering a forward-looking perspective on the potential of quantum computers to enhance quantum sensor capabilities and identify specific scenarios where quantum computing can resolve problems traditionally challenging for classical computers.

quant-ph↗

arXiv2024

Simulating X-ray absorption spectroscopy of battery materials on a quantum computer

X-ray absorption spectroscopy is a crucial experimental technique for elucidating the mechanisms of structural degradation in battery materials. However, extracting information from the measured spectrum is challenging without high-quality simulations. In this work, we propose simulating near-edge X-ray absorption spectra as a promising application for quantum computing. It is attractive due to the ultralocal nature of X-ray absorption that significantly reduces the sizes of problems to be simulated, and because of the classical hardness of simulating spectra. We describe three quantum algorithms to compute the X-ray absorption spectrum and provide their asymptotic cost. One of these is a Monte-Carlo based time-domain algorithm, which is cost-friendly to early fault-tolerant quantum computers. We then apply the framework to an industrially relevant example, a CAS(22e,18o) active space for an O-Mn cluster in a Li-excess battery cathode, showing that practically useful simulations could be obtained with much fewer qubits and gates than ground-state energy estimation of the same material.

quant-ph↗

arXiv2024

Ground State Preparation via Dynamical Cooling

Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which can be challenging for large, strongly-correlated systems. This issue has motivated the study of physically-inspired dynamical approaches such as thermodynamic cooling. In this work, we introduce a ground-state preparation algorithm based on the simulation of quantum dynamics. Our main insight is to transform the Hamiltonian by a shifted sign function via quantum signal processing, effectively mapping eigenvalues into positive and negative subspaces separated by a large gap. This automatically ensures that all states within each subspace conserve energy with respect to the transformed Hamiltonian. Subsequent time-evolution with a perturbed Hamiltonian induces transitions to lower-energy states while preventing unwanted jumps to higher energy states. The approach does not rely on a priori knowledge of energy gaps and requires no additional qubits to model a bath. Furthermore, it makes $\tilde{\mathcal{O}}(d^{\,3/2}/\epsilon)$ queries to the time-evolution operator of the system and $\tilde{\mathcal{O}}(d^{\,3/2})$ queries to a block-encoding of the perturbation, for $d$ cooling steps and an $\epsilon$-accurate energy resolution. Our results provide a framework for combining quantum signal processing and Hamiltonian simulation to design heuristic quantum algorithms for ground-state preparation.

quant-ph↗

arXiv2024

Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators

Hamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the implementation of exponentials of commutators, which has previously made it unappealing for quantum computing. The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle, at the expense of a lack of provable global numeric error bounds. In this work, we establish one such error bound for CFQM-based time-dependent quantum Hamiltonian simulation by carefully estimating the error of each step involved in their definition. This allows us to compare its cost with the alternatives, and show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude. As a result, we find that CFQMs may be particularly useful to simulate time-dependent Hamiltonians on early fault-tolerant quantum computers.

quant-ph↗

arXiv2024

Better bounds for low-energy product formulas

Product formulas are one of the main approaches for quantum simulation of the Hamiltonian dynamics of a quantum system. Their implementation cost is computed based on error bounds which are often pessimistic, resulting in overestimating the total runtime. In this work, we rigorously consider the error induced by product formulas when the state undergoing time evolution lies in the low-energy sector with respect to the Hamiltonian of the system. We show that in such a setting, the usual error bounds based on the operator norm of nested commutators can be replaced by those restricted to suitably chosen low-energy subspaces, yielding tighter error bounds. Furthermore, under some locality and positivity assumptions, we show that the simulation of generic product formulas acting on low-energy states can be done asymptotically more efficiently when compared with previous results.

quant-ph↗

arXiv2023

Improved Bayesian Regret Bounds for Thompson Sampling in Reinforcement Learning

In this paper, we prove the first Bayesian regret bounds for Thompson Sampling in reinforcement learning in a multitude of settings. We simplify the learning problem using a discrete set of surrogate environments, and present a refined analysis of the information ratio using posterior consistency. This leads to an upper bound of order $\widetilde{O}(H\sqrt{d_{l_1}T})$ in the time inhomogeneous reinforcement learning problem where $H$ is the episode length and $d_{l_1}$ is the Kolmogorov $l_1-$dimension of the space of environments. We then find concrete bounds of $d_{l_1}$ in a variety of settings, such as tabular, linear and finite mixtures, and discuss how how our results are either the first of their kind or improve the state-of-the-art.

stat.ML↗

arXiv2023

Initial state preparation for quantum chemistry on quantum computers

Quantum algorithms for ground-state energy estimation of chemical systems require a high-quality initial state. However, initial state preparation is commonly either neglected entirely, or assumed to be solved by a simple product state like Hartree-Fock. Even if a nontrivial state is prepared, strong correlations render ground state overlap inadequate for quality assessment. In this work, we address the initial state preparation problem with an end-to-end algorithm that prepares and quantifies the quality of initial states, accomplishing the latter with a new metric -- the energy distribution. To be able to prepare more complicated initial states, we introduce an implementation technique for states in the form of a sum of Slater determinants that exhibits significantly better scaling than all prior approaches. We also propose low-precision quantum phase estimation (QPE) for further state quality refinement. The complete algorithm is capable of generating high-quality states for energy estimation, and is shown in select cases to lower the overall estimation cost by several orders of magnitude when compared with the best single product state ansatz. More broadly, the energy distribution picture suggests that the goal of QPE should be reinterpreted as generating improvements compared to the energy of the initial state and other classical estimates, which can still be achieved even if QPE does not project directly onto the ground state. Finally, we show how the energy distribution can help in identifying potential quantum advantage.

quant-ph↗

arXiv2023

Quantum simulation of battery materials using ionic pseudopotentials

Ionic pseudopotentials are widely used in classical simulations of materials to model the effective potential due to the nucleus and the core electrons. Modeling fewer electrons explicitly results in a reduction in the number of plane waves needed to accurately represent the states of a system. In this work, we introduce a quantum algorithm that uses pseudopotentials to reduce the cost of simulating periodic materials on a quantum computer. We use a qubitization-based quantum phase estimation algorithm that employs a first-quantization representation of the Hamiltonian in a plane-wave basis. We address the challenge of incorporating the complexity of pseudopotentials into quantum simulations by developing highly-optimized compilation strategies for the qubitization of the Hamiltonian. This includes a linear combination of unitaries decomposition that leverages the form of separable pseudopotentials. Our strategies make use of quantum read-only memory subroutines as a more efficient alternative to quantum arithmetic. We estimate the computational cost of applying our algorithm to simulating lithium-excess cathode materials for batteries, where more accurate simulations are needed to inform strategies for gaining reversible access to the excess capacity they offer. We estimate the number of qubits and Toffoli gates required to perform sufficiently accurate simulations with our algorithm for three materials: lithium manganese oxide, lithium nickel-manganese oxide, and lithium manganese oxyfluoride. Our optimized compilation strategies result in a pseudopotential-based quantum algorithm with a total Toffoli cost four orders of magnitude lower than the previous state of the art for a fixed target accuracy.

quant-ph↗

arXiv2023

Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer

There is a pressing need to develop new rechargeable battery technologies that can offer higher energy storage, faster charging, and lower costs. Despite the success of existing methods for the simulation of battery materials, they can sometimes fall short of delivering accurate and reliable results. Quantum computing has been discussed as an avenue to overcome these issues, but only limited work has been done to outline how they may impact battery simulations. In this work, we provide a detailed answer to the following question: how can a quantum computer be used to simulate key properties of a lithium-ion battery? Based on recently-introduced first-quantization techniques, we lay out an end-to-end quantum algorithm for calculating equilibrium cell voltages, ionic mobility, and thermal stability. These can be obtained from ground-state energies of materials, which is the core calculation executed by the quantum computer using qubitization-based quantum phase estimation. The algorithm includes explicit methods for preparing approximate ground states of periodic materials in first quantization. We bring these insights together to perform the first estimation of the resources required to implement a quantum algorithm for simulating a realistic cathode material, dilithium iron silicate.

quant-ph↗

arXiv2022

The Smallest Interacting Universe

The co-emergence of locality between the Hamiltonian and initial state of the universe is studied in a simple toy model. We hypothesize a fundamental loss functional for the combined Hamiltonian and quantum state and minimize it by gradient descent. This minimization yields a tensor product structure simultaneously respected by both the Hamiltonian and the state, suggesting that locality can emerge by a process analogous to spontaneous symmetry breaking. We discuss the relevance of this program to the arrow of time problem. In our toy model, we interpret the emergence of a tensor factorization as the appearance of individual degrees of freedom within a previously undifferentiated (raw) Hilbert space. Earlier work [5, 6] looked at the emergence of locality in Hamiltonians only, and found strong numerical confirmation of that raw Hilbert spaces of $\dim = n$ are unstable and prefer to settle on tensor factorization when $n=pq$ is not prime, and in [6] even primes were seen to "factor" after first shedding a small summand, e.g. $7=1+2\cdot 3$. This was found in the context of a rather general potential functional $F$ on the space of metrics $\{g_{ij}\}$ on $\mathfrak{su}(n)$, the Lie algebra of symmetries. This emergence of qunits through operator-level spontaneous symmetry breaking (SSB) may help us understand why the world seems to consist of myriad interacting degrees of freedom. But understanding why the universe has an initial Hamiltonian $H_0$ with a many-body structure is of limited conceptual value unless the initial state, $|ψ_0\rangle$, is also structured by this tensor decomposition. Here we adapt $F$ to become a functional on $\{g,|ψ_0\rangle\}=(\text{metrics})\times (\text{initial states})$, and find SSB now produces a conspiracy between $g$ and $|ψ_0\rangle$, where they simultaneously attain low entropy by settling on the same qubit decomposition.

hep-th↗

arXiv2021

Mixed-state TQFTs

In this short note, we propose a generalization of Atiyah type TQFTs from pure states to mixed states in the sense that the Hilbert space of pure states associated to a space manifold is replaced by a quantum coherent space related to density matrices. Atiyah type TQFT is a symmetric monoidal functor from the Bord category of manifolds to the category Vec of finite dimensional vector spaces. In this paper, we define mixed-state TQFTs by replacing the target category Vec by QCS--the category of quantum coherent spaces, then a mixed-state TQFT is simply a symmetric monoidal functor from Bord to QCS. We also discuss how to construct interesting examples from subsystem quantum error correction codes beyond the trivial ones--all Atiyah type TQFTs.

math.QA↗

arXiv2021

The Universe from a Single Particle II

We continue to explore, in the context of a toy model, the hypothesis that the interacting universe we see around us could result from single particle (undergraduate) quantum mechanics via a novel spontaneous symmetry breaking (SSB) acting at the level of probability distributions on Hamiltonians (rather than on states as is familiar from both Ginzburg-Landau superconductivity and the Higgs mechanism). In an earlier paper [7] we saw qubit structure emerge spontaneously on $\mathbb{C}^4$ and $\mathbb{C}^8$, and in this work we see $\mathbb{C}^6$ spontaneously decomposing as $\mathbb{C}^2\otimes \mathbb{C}^3$ and very curiously $\mathbb{C}^5$ (and $\mathbb{C}^7$) splitting off one (one or three) directions and then factoring. This evidence provides additional support for the broad hypothesis: Nature will seek out tensor decompositions where none are present. We consider how this finding may form a basis for the origins of interaction and ask if it can be related to established foundational discussions such as string theory.

hep-th↗

arXiv2021

Symmetry Protected Quantum Computation

We consider a model of quantum computation using qubits where it is possible to measure whether a given pair are in a singlet (total spin $0$) or triplet (total spin $1$) state. The physical motivation is that we can do these measurements in a way that is protected against revealing other information so long as all terms in the Hamiltonian are $SU(2)$-invariant. We conjecture that this model is equivalent to BQP. Towards this goal, we show: (1) this model is capable of universal quantum computation with polylogarithmic overhead if it is supplemented by single qubit $X$ and $Z$ gates. (2) Without any additional gates, it is at least as powerful as the weak model of "permutational quantum computation" of Jordan [14, 18]. (3) With postselection, the model is equivalent to PostBQP.

quant-ph↗

arXiv2021

The Universe from a Single Particle

We explore the emergence of many-body physics from quantum mechanics via spontaneous symmetry breaking. To this end, we study potentials which are functionals on the space of Hamiltonians enjoying an unstable critical point corresponding to a random quantum mechanical system (the Gaussian unitary ensemble), but also less symmetrical local minima corresponding to interacting systems at the level of operators.

hep-th↗

arXiv2020

A Highly Symmetric Hamilton Decomposition for Hypercubes

A Hamilton decomposition of a graph is a partitioning of its edge set into disjoint spanning cycles. The existence of such decompositions is known for all hypercubes of even dimension $2n$. We give a decomposition for the case $n = 2^a3^b$ that is highly symmetric in the sense that every cycle can be derived from every other cycle just by permuting the axes. We conjecture that a similar decomposition exists for every n.

math.CO↗

arXiv2020

Coagent Networks Revisited

Coagent networks formalize the concept of arbitrary networks of stochastic agents that collaborate to take actions in a reinforcement learning environment. Prominent examples of coagent networks in action include approaches to hierarchical reinforcement learning (HRL), such as those using options, which attempt to address the exploration exploitation trade-off by introducing abstract actions at different levels by sequencing multiple stochastic networks within the HRL agents. We first provide a unifying perspective on the many diverse examples that fall under coagent networks. We do so by formalizing the rules of execution in a coagent network, enabled by the novel and intuitive idea of execution paths in a coagent network. Motivated by parameter sharing in the hierarchical option-critic architecture, we revisit the coagent network theory and achieve a much shorter proof of the policy gradient theorem using our idea of execution paths, without any assumption on how parameters are shared among coagents. We then generalize our setting and proof to include the scenario where coagents act asynchronously. This new perspective and theorem also lead to more mathematically accurate and performant algorithms than those in the existing literature. Lastly, by running nonstationary RL experiments, we survey the performance and properties of different generalizations of option-critic models.

cs.LG↗