arXiv subjects

Bryan Gard

Publications and source records attributed to Bryan Gard.

9 recordsLinked to original sources

arXiv2025

Hadamard Random Forest: Reconstructing real-valued quantum states with exponential reduction in measurement settings

Quantum tomography is a crucial tool for characterizing quantum states and devices and estimating nonlinear properties of the systems. Performing full quantum state tomography on an $N_\mathrm{q}$ qubit system requires an exponentially increasing overhead with $O(3^{N_\mathrm{q}})$ distinct Pauli measurement settings to resolve all complex phases and reconstruct the density matrix. However, many potential quantum computing applications, such as linear system solves, require only real-valued amplitudes. We introduce a readout method for real-valued quantum states that reduces measurement settings required for state vector reconstruction to $O(N_\mathrm{q})$; the post-processing cost remains exponential $\Omega(2^{N_\mathrm{q}})$. This approach offers a substantial speedup over conventional tomography. We experimentally validate our method up to 10 qubits on the latest available IBM quantum processor and demonstrate that it accurately extracts key properties such as entanglement and magic. Our method also outperforms the standard SWAP test for state overlap estimation. This calculation resembles a numerical integration in certain cases and can be applied to extract nonlinear properties, which are important in application fields. We further implement the method to readout the solution from a quantum linear solver.

quant-ph↗

arXiv2024

Incompressible Navier-Stokes solve on noisy quantum hardware via a hybrid quantum-classical scheme

Partial differential equation solvers are required to solve the Navier-Stokes equations for fluid flow. Recently, algorithms have been proposed to simulate fluid dynamics on quantum computers. Fault-tolerant quantum devices might enable exponential speedups over algorithms on classical computers. However, current and foreseeable quantum hardware introduce noise into computations, requiring algorithms that make judicious use of quantum resources: shallower circuit depths and fewer qubits. Under these restrictions, variational algorithms are more appropriate and robust. This work presents a hybrid quantum-classical algorithm for the incompressible Navier--Stokes equations. A classical device performs nonlinear computations, and a quantum one uses a variational solver for the pressure Poisson equation. A lid-driven cavity problem benchmarks the method. We verify the algorithm via noise-free simulation and test it on noisy IBM superconducting quantum hardware. Results show that high-fidelity results can be achieved via this approach, even on current quantum devices. Multigrid preconditioning of the Poisson problem helps avoid local minima and reduces resource requirements for the quantum device. A quantum state readout technique called HTree is used for the first time on a physical problem. Htree is appropriate for real-valued problems and achieves linear complexity in the qubit count, making the Navier-Stokes solve further tractable on current quantum devices. We compare the quantum resources required for near-term and fault-tolerant solvers to determine quantum hardware requirements for fluid simulations with complexity improvements.

physics.flu-dyn↗

arXiv2023

ADAPT-QAOA with a classically inspired initial state

Quantum computing may provide advantage in solving classical optimization problems. One promising algorithm is the quantum approximate optimization algorithm (QAOA). There have been many proposals for improving this algorithm, such as using an initial state informed by classical approximation solutions. A variation of QAOA called ADAPT-QAOA constructs the ansatz dynamically and can speed up convergence. However, it faces the challenge of frequently converging to excited states which correspond to local minima in the energy landscape, limiting its performance. In this work, we propose to start ADAPT-QAOA with an initial state inspired by a classical approximation algorithm. Through numerical simulations we show that this new algorithm can reach the same accuracy with fewer layers than the standard QAOA and the original ADAPT-QAOA. It also appears to be less prone to the problem of converging to excited states.

quant-ph↗

arXiv2023

Fully quantum algorithm for lattice Boltzmann methods with application to partial differential equations

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. This method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical PDEs: the diffusion and Burgers' equations on different quantum simulators. We find good agreement between quantum simulations and classical solutions for the presented algorithm.

physics.comp-ph↗

arXiv2022

Modelling noise in global Molmer-Sorensen interactions applied to quantum approximate optimization

Many-qubit M{\o}lmer-S{\o}rensen (MS) interactions applied to trapped ions offer unique capabilities for quantum information processing, with applications including quantum simulation and the quantum approximate optimization algorithm (QAOA). Here, we develop a physical model to describe many-qubit MS interactions under four sources of experimental noise: vibrational mode frequency fluctuations, laser power fluctuations, thermal initial vibrational states, and state preparation and measurement errors. The model parameterizes these errors from simple experimental measurements, without free parameters. We validate the model in comparison with experiments that implement sequences of MS interactions on two $^{171}$Yb$^+$ ions. The model shows reasonable agreement after several MS interactions as quantified by the reduced chi-squared statistic $\chi^2_\mathrm{red} \approx 2$. As an application we examine MaxCut QAOA experiments on three and six ions. The experimental performance is quantified by approximation ratios that are $91\%$ and $83\%$ of the optimal theoretical values. Our model predicts $0.93^{+0.03}_{-0.02}$ and $0.95^{+0.04}_{-0.03}$, respectively, with disagreement in the latter value attributable to secondary noise sources beyond those considered in our analysis. With realistic experimental improvements to reduce measurement error and radial trap frequency variations the model achieves approximation ratios that are 99$\%$ of the optimal. Incorporating these improvements into future experiments is expected to reveal new aspects of noise for future modeling and experimental improvements.

quant-ph↗

arXiv2021

Warm-Started QAOA with Custom Mixers Provably Converges and Computationally Beats Goemans-Williamson's Max-Cut at Low Circuit Depths

We generalize the Quantum Approximate Optimization Algorithm (QAOA) of Farhi et al. (2014) to allow for arbitrary separable initial states with corresponding mixers such that the starting state is the most excited state of the mixing Hamiltonian. We demonstrate this version of QAOA, which we call QAOA-warmest, by simulating Max-Cut on weighted graphs. We initialize the starting state as a warm-start using $2$ and $3$-dimensional approximations obtained using randomized projections of solutions to Max-Cut's semi-definite program, and define a warm-start dependent custom mixer. We show that these warm-starts initialize the QAOA circuit with constant-factor approximations of $0.658$ for $2$-dimensional and $0.585$ for $3$-dimensional warm-starts for graphs with non-negative edge weights, improving upon previously known trivial (i.e., $0.5$ for standard initialization) worst-case bounds at $p=0$. These factors in fact lower bound the approximation achieved for Max-Cut at higher circuit depths, since we also show that QAOA-warmest with any separable initial state converges to Max-Cut under the adiabatic limit as $p\rightarrow \infty$. However, the choice of warm-starts significantly impacts the rate of convergence to Max-Cut, and we show empirically that our warm-starts achieve a faster convergence compared to existing approaches. Additionally, our numerical simulations show higher quality cuts compared to standard QAOA, the classical Goemans-Williamson algorithm, and a warm-started QAOA without custom mixers for an instance library of $1148$ graphs (upto $11$ nodes) and depth $p=8$. We further show that QAOA-warmest outperforms the standard QAOA of Farhi et al. in experiments on current IBM-Q and Quantinuum hardware.

quant-ph↗

arXiv2020

Generating Target Graph Couplings for QAOA from Native Quantum Hardware Couplings

We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped ion quantum hardware to find approximate solutions to Max-Cut. We present a mathematical description of the problem and provide approximately optimal algorithmic constructions that generate arbitrary unweighted coupling graphs with $n$ nodes in $O(n)$ global entangling operations and weighted graphs with $m$ edges in $O(m)$ operations. These upper bounds are not tight in general, and we formulate a mixed-integer program to solve the graph coupling problem to optimality. We perform numeric experiments on small graphs with $n\le8$ and show that optimal sequences, which use fewer operations, can be found using mixed-integer programs. Noisy simulations of Max-Cut QAOA show that our implementation is less susceptible to noise than the standard gate-based compilation.

quant-ph↗

arXiv2016

Enhanced Thermal Object Imaging by Photon Addition or Subtraction

Long-baseline interferometry (LBI) is used to reconstruct the image of faint thermal objects. The image quality, for a given exposure time, is in general limited by a low signal-to-noise ratio (SNR). We show theoretically that a significant increase of the SNR, in a LBI, is possible by adding or subtracting photons to the thermal beam. At low photon counts, photon addition-subtraction technology strongly enhances the image quality. We have experimentally realized a nondeterministic physical protocol for photon subtraction. Our theoretical predictions are supported by experimental results.

physics.optics↗

arXiv2016

Advances in quantum metrology: Continuous variables in phase space

This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe quantum states of light and optical interferometry. We discuss the advantages of Wigner functions and their use to describe many quantum states of light. Throughout our metrology discussions, we will also discuss various quantum limits and use quantum Fisher information to show optimal bounds. When applicable, we also discuss the use of quantum Gaussian information and how it relates to our Wigner function treatment. The remainder of our discussion focuses on investigating the effects of photon addition and subtraction to various states of light and analyze the nondeterministic nature of this process. We use examples of $m$ photon additions to a coherent state as well as discuss the properties of an $m$ photon subtracted thermal state. We also provide an argument that this process must always be a nondeterministic one, or the ability to violate quantum limits becomes apparent. We show that using phase measurement as one's metric is much more restrictive, which limits the usefulness of photon addition and subtraction. When we consider SNR however, we show improved SNR statistics, at the cost of increased measurement time. In this case of SNR, we also quantify the efficiency of the photon addition and subtraction process.

quant-ph↗