arXiv subjects

Nic Ezzell

Publications and source records attributed to Nic Ezzell.

5 recordsLinked to original sources

arXiv2025

Advanced measurement techniques in quantum Monte Carlo: The permutation matrix representation approach

In a typical finite temperature quantum Monte Carlo (QMC) simulation, estimators for simple static observables such as specific heat and magnetization are known. With a great deal of system-specific manual labor, one can sometimes also derive more complicated non-local or even dynamic observable estimators. Within the permutation matrix representation (PMR) flavor of QMC, however, we show that one can derive formal estimators for arbitrary static observables. We also derive exact, explicit estimators for general imaginary-time correlation functions and non-trivial integrated susceptibilities thereof. We demonstrate the practical versatility of our method by estimating various non-local, random observables for the transverse-field Ising model on a square lattice.

cond-mat.stat-mech↗

arXiv2024

A universal black-box quantum Monte Carlo approach to quantum phase transitions

We derive exact, universal, closed-form quantum Monte Carlo estimators for finite-temperature energy susceptibility and fidelity susceptibility, applicable to essentially arbitrary Hamiltonians. Combined with recent advancements in Monte Carlo, our approach enables a black-box framework for studying quantum phase transitions--without requiring prior knowledge of an order parameter or the manual design of model-specific ergodic quantum Monte Carlo update rules. We demonstrate the utility of our method by applying a single implementation to the transverse-field Ising model, the XXZ model, and an ensemble of models related by random unitaries.

cond-mat.stat-mech↗

arXiv2023

Dynamical decoupling for superconducting qubits: a performance survey

Dynamical Decoupling (DD) is perhaps the simplest and least resource-intensive error suppression strategy for improving quantum computer performance. Here we report on a large-scale survey of the performance of 60 different DD sequences from 10 families, including basic as well as advanced sequences with high order error cancellation properties and built-in robustness. The survey is performed using three different superconducting-qubit IBMQ devices, with the goal of assessing the relative performance of the different sequences in the setting of arbitrary quantum state preservation. We find that the high-order universally robust (UR) and quadratic DD (QDD) sequences generally outperform all other sequences across devices and pulse interval settings. Surprisingly, we find that DD performance for basic sequences such as CPMG and XY4 can be made to nearly match that of UR and QDD by optimizing the pulse interval, with the optimal interval being substantially larger than the minimum interval possible on each device.

quant-ph↗

arXiv2023

Quantum Mixed State Compiling

The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm represents a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We consider two different ansätze for compiling the target state; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Additionally, we demonstrate on quantum hardware how our algorithm can be used to study hardware noise-induced states.

quant-ph↗

arXiv2022

The quantum low-rank approximation problem

We consider a quantum version of the famous low-rank approximation problem. Specifically, we consider the distance $D(ρ,σ)$ between two normalized quantum states, $ρ$ and $σ$, where the rank of $σ$ is constrained to be at most $R$. For both the trace distance and Hilbert-Schmidt distance, we analytically solve for the optimal state $σ$ that minimizes this distance. For the Hilbert-Schmidt distance, the unique optimal state is $σ= τ_R +N_R$, where $τ_R = Π_R ρΠ_R$ is given by projecting $ρ$ onto its $R$ principal components with projector $Π_R$, and $N_R$ is a normalization factor given by $N_R = \frac{1- \text{Tr}(τ_R)}{R}Π_R$. For the trace distance, this state is also optimal but not uniquely optimal, and we provide the full set of states that are optimal. We briefly discuss how our results have application for performing principal component analysis (PCA) via variational optimization on quantum computers.

quant-ph↗