arXiv subjects

Eleanor Rieffel

Publications and source records attributed to Eleanor Rieffel.

At least 19 recordsLinked to original sources

arXiv2026

Imposing Constraints on Driver Hamiltonians and Mixing Operators: From Theory to Practical Implementation

Driver Hamiltonians and Mixing Operators that satisfy constraints is an important part of ansatz construction for many quantum algorithms. In this manuscript, we give general algebraic expressions for finding Hamiltonian terms and analogously unitary primitives, that satisfy constraint embeddings and use these to give complexity characterizations of the related problems. We prove that knowing if operators exist that enforce classical constraints is NP-Complete in the general case, but give algorithmic procedures with worse-case polynomial runtime to find any operators with a constant locality bound; a useful result since many constraints imposed admit local operators to enforce them in practice. We then give algorithmic procedures to turn these algebraic primitives into Hamiltonian drivers and unitary mixers that can be used for Constrained Quantum Annealing (CQA) and Quantum Alternating Operator Ansatz (QAOA) constructions by tackling practical problems related to finding an appropriate set of reduced generators and defining corresponding drivers and mixers accordingly. We consider a new QAOA approach based on the maximally disjoint subset as well as higher order constraint satisfaction terms for 1-in-3 SAT, which dramatically outperform the X-mixer.

quant-ph↗

arXiv2026

Partitioned Iterative Quantum Scheduling of Satellites for Urgent Disaster Response: Case study of Wildfire

The standard in Earth-observation tasks today is having near real-time access to surface images in response to changing conditions. For instance, as urban environments interface more with wildlands and wildfires become less predictable, their tracking with satellite resources becomes essential. This requires the coordination of increasingly large constellations of satellites, giving rise to challenging computational problems. With wildfire detection and tracking as a backdrop, we investigate the power of special purpose and novel computing paradigms to tackle the ensuing satellite scheduling problems, making a compelling case for quantum algorithms. We bring quantum scheduling algorithms closer to implementation by examining both the emerging iterative quantum algorithm framework, which comes with analytic guarantees compared to some classical algorithms, and distributed quantum computing methods whose relevance is on the rise as utility-scale problems begin to get solved with quantum computers. Drawing strength from several computing fronts, we develop a distributed/parallelization scheme in conjunction with the quantum algorithm design and apply these techniques to real-world datasets for wildfire detection. While our quantum subprocesses are currently too small to see significant quantum advantage, our results validate the utility of these techniques, and continue forging the path toward distributed quantum computing.

quant-ph↗

arXiv2026

Qudit Designs and Where to Find Them

Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing exponential separations between classical and quantum query complexity. While unitary designs originating from a group structure, such as the Clifford group, have proven to be incredibly useful for qubit systems, unfortunately, this is no longer true for qudits. In fact, the classification of finite-group representations rules out the existence of unitary 2-designs for arbitrary qudit dimensions. This severely limits the applicability of standard quantum information primitives when it comes to qudit systems. We overcome these limitations with a three-fold contribution. First, we introduce a general technique to construct families of weighted state t-designs in arbitrary qudit dimensions. These weighted state-designs generalize classical shadow tomography protocol from qubits to qudits. Second, we introduce a Clifford character RB that allows us to benchmark the qudit Clifford group in any dimension, including non-prime-power dimensions. And third, we establish bounds on the quantum circuit complexity of generating approximate unitary-designs from native gates in existing quantum hardware such as high-spin and cavity-QED qudits. Our work further highlights the analogy between spin and optical coherent states by proving that spin-GKP codewords form a state 2-design while spin coherent states do not; in direct analogy with the optical case. This work is structured as a pedagogical and self-contained introduction to unitary designs and their applications to qudit systems.

quant-ph↗

arXiv2026

Scattering Processes from Quantum Simulation Algorithms for Scalar Field Theories

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a finite volume approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as $O(λN^7 |Ω|^3/(M^{5/2} ε^{3/2}))$ where $λ$ is the coupling strength, $N$ is the occupation cutoff, $|Ω|$ is the volume of the spatial lattice, $M$ is the mass of the particles and $ε$ is the uncertainty in the energy calculation used for the $S$-matrix determination. Qubitization in the field basis scales as $O(|Ω|^2 (k^2 Λ+kM^2)/ε)$ where $k$ is the cutoff in the field and $Λ$ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of $4\times 10^6$ physical qubits and $10^{12}$ $T$-gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns. This places the simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results.

quant-ph↗

arXiv2025

Dynamical Logical Qubits in the Bacon-Shor Code

The Bacon-Shor code is a quantum error correcting subsystem code composed of weight 2 check operators that admits a single logical qubit, and has distance $d$ on a $d \times d$ square lattice. We show that when viewed as a Floquet code, by choosing an appropriate measurement schedule of the check operators, it can additionally host several dynamical logical qubits. Specifically, we identify a period 4 measurement schedule of the check operators that preserves logical information between the instantaneous stabilizer groups. Such a schedule measures not only the usual stabilizers of the Bacon-Shor code, but also additional stabilizers that protect the dynamical logical qubits against errors. We show that the code distance of these Floquet-Bacon-Shor codes scales as $Θ(d/\sqrt{k})$ on an $n = d \times d$ lattice with $k$ dynamical logical qubits, along with the logical qubit of the parent subsystem code. Unlike the usual Bacon-Shor code, the Floquet-Bacon-Shor code family introduced here can therefore saturate the subsystem bound $kd = O(n)$. Moreover, several errors are shown to be self-corrected purely by the measurement schedule itself. This work provides insights into the design space for dynamical codes and expands the known approaches for constructing Floquet codes.

quant-ph↗

arXiv2024

How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits

In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits. Nevertheless, there are significant outstanding challenges in quantum hardware, fabrication, software architecture, and algorithms on the path towards a full-stack scalable quantum computing technology. Here, we provide a comprehensive review of these scaling challenges. We show how to facilitate scaling by adopting existing semiconductor technology to build much higher-quality qubits, employing systems engineering approaches, and performing distributed heterogeneous quantum-classical computing. We provide a detailed resource and sensitivity analysis for quantum applications on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. We provide comprehensive resource estimates for several utility-scale applications including quantum chemistry calculations, catalyst design, NMR spectroscopy, and Fermi-Hubbard simulation. We show that orders of magnitude enhancement in performance could be obtained by a combination of hardware improvements and tight quantum-HPC integration. Furthermore, we introduce high-performance architectures for quantum-probabilistic computing with custom-designed accelerators to tackle today's industry-scale classical optimization, machine learning, and quantum simulation tasks in a cost-effective manner.

quant-ph↗

arXiv2023

Scrambling and operator entanglement in local non-Hermitian quantum systems

The breakdown of Lieb-Robinson bounds in local, non-Hermitian quantum systems opens up the possibility for a rich landscape of quantum many-body phenomenology. We elucidate this by studying information scrambling and quantum chaos in non-Hermitian variants of paradigmatic local quantum spin-chain models. We utilize a mixture of exact diagonalization and tensor network techniques for our numerical results and focus on three dynamical quantities: (i) out-of-time-ordered correlators (OTOCs), (ii) operator entanglement of the dynamics, and (iii) entanglement growth following a quench from product initial states. We show that while OTOCs fail to capture information scrambling in a simple, local, non-Hermitian transverse-field Ising model, the closely related operator entanglement is a robust measure of dynamical properties of interest. Moreover, we show that the short-time growth of operator entanglement can generically detect ``entanglement phase transitions'' in these systems while its long-time average is shown to be a reliable indicator of quantum chaos and entanglement phases. This allows us to extend operator entanglement based diagnostics from previous works on closed and open quantum systems, to the new arena of monitored quantum dynamics. Finally, we remark on the efficacy of these dynamical quantities in detecting integrability/chaos in the presence of continuous monitoring.

quant-ph↗

arXiv2023

Anomaly Detection in Aeronautics Data with Quantum-compatible Discrete Deep Generative Model

Deep generative learning cannot only be used for generating new data with statistical characteristics derived from input data but also for anomaly detection, by separating nominal and anomalous instances based on their reconstruction quality. In this paper, we explore the performance of three unsupervised deep generative models -- variational autoencoders (VAEs) with Gaussian, Bernoulli, and Boltzmann priors -- in detecting anomalies in flight-operations data of commercial flights consisting of multivariate time series. We devised two VAE models with discrete latent variables (DVAEs), one with a factorized Bernoulli prior and one with a restricted Boltzmann machine (RBM) as prior, because of the demand for discrete-variable models in machine-learning applications and because the integration of quantum devices based on two-level quantum systems requires such models. The DVAE with RBM prior, using a relatively simple -- and classically or quantum-mechanically enhanceable -- sampling technique for the evolution of the RBM's negative phase, performed better than the Bernoulli DVAE and on par with the Gaussian model, which has a continuous latent space. Our studies demonstrate the competitiveness of a discrete deep generative model with its Gaussian counterpart on anomaly-detection tasks. Moreover, the DVAE model with RBM prior can be easily integrated with quantum sampling by outsourcing its generative process to measurements of quantum states obtained from a quantum annealer or gate-model device.

cs.LG↗

arXiv2022

Advantage of pausing: parameter setting for quantum annealers

Prior work showed the efficacy of pausing midanneal: such a pause improved the probability of success by orders of magnitude in a class of native problem instances and improved the time to solution in a class of embedded problem instances. A physics-based picture provides qualitative suggestions for where pausing midanneal is effective, for the interplay between annealing schedule parameters and other annealing properties and parameters such as embedding size and strength of the ferromagnetic coupling $|J_F|$, and for the conditions under which pausing can improve the time to solution. Here, through demonstrations on an updated annealing architecture that has higher connectivity than previous annealers, and on multiple embedded problem classes, we are able to confirm various aspects of this picture. We demonstrate the robustness of the optimal pause parameters across platforms and problem classes, explore how to set $|J_F|$ to optimize performance in different scenarios, and provide empirical evidence that short pauses trump longer overall annealing times in time to solution. We also identify the number of different coefficients in a problem as a predictor of problem hardness, and explore its interplay with the optimal $|J_F|$ and embedding size. Based on these results we are able to present qualitative guidelines for parameter setting in quantum annealers.

quant-ph↗

arXiv2022

A Parameter Setting Heuristic for the Quantum Alternating Operator Ansatz

Parameterized quantum circuits are widely studied approaches for tackling optimization problems. A prominent example is the Quantum Alternating Operator Ansatz (QAOA), an approach that builds off the structure of the Quantum Approximate Optimization Algorithm. Finding high-quality parameters efficiently for QAOA remains a major challenge in practice. In this work, we introduce a classical strategy for parameter setting, suitable for common cases in which the number of distinct cost values grows only polynomially with the problem size. The crux of our strategy is that we replace the cost function expectation value step of QAOA with a parameterized model that can be efficiently evaluated classically. This model is based on empirical observations that QAOA states have large overlaps with states where variable configurations with the same cost have the same amplitude, which we define as Perfect Homogeneity. We thus define a Classical Homogeneous Proxy for QAOA in which Perfect Homogeneity holds exactly, and which yields information describing both states and expectation values. We classically determine high-quality parameters for this proxy, and use these parameters in QAOA, an approach we label the Homogeneous Heuristic for Parameter Setting. We numerically examine this heuristic for MaxCut on random graphs. For up to $3$ QAOA levels we are easily able to find parameters that match approximation ratios returned by previous globally optimized approaches. For levels up to $20$ we obtain parameters with approximation ratios monotonically increasing with depth, while a strategy that uses parameter transfer instead fails to converge with comparable classical resources. These results suggest that our heuristic may find good parameters in regimes that are intractable with noisy intermediate-scale quantum devices. Finally, we outline how our heuristic may be applied to wider classes of problems.

quant-ph↗

arXiv2022

Towards solving the Fermi-Hubbard model via tailored quantum annealers

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.

quant-ph↗

arXiv2022

Logical shadow tomography: Efficient estimation of error-mitigated observables

We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density matrix. Using efficient classical post-processing, one can mitigate errors by projecting a general nonlinear function of the noisy density matrix into the codespace. The subspace expansion and virtual distillation can be viewed as special cases of the new framekwork. We show our method is favorable in the quantum and classical resources overhead. Relative to subspace expansion which requires $O\left(2^{N} \right)$ samples to estimate a logical Pauli observable with $[[N, k]]$ error correction code, our technique requires only $O\left(4^{k} \right)$ samples. Relative to virtual distillation, our technique can compute powers of the density matrix without additional copies of quantum states or quantum memory. We present numerical evidence using logical states encoded with up to sixty physical qubits and show fast convergence to error-free expectation values with only $10^5$ samples under 1% depolarizing noise.

quant-ph↗

arXiv2022

Mixer-Phaser Ansätze for Quantum Optimization with Hard Constraints

We introduce multiple parametrized circuit ansätze and present the results of a numerical study comparing their performance with a standard Quantum Alternating Operator Ansatz approach. The ansätze are inspired by mixing and phase separation in the QAOA, and also motivated by compilation considerations with the aim of running on near-term superconducting quantum processors. The methods are tested on random instances of a weighted quadratic binary constrained optimization problem that is fully connected for which the space of feasible solutions has constant Hamming weight. For the parameter setting strategies and evaluation metric used, the average performance achieved by the QAOA is effectively matched by the one obtained by a "mixer-phaser" ansatz that can be compiled in less than half-depth of standard QAOA on most superconducting qubit processors.

quant-ph↗

arXiv2021

Dual Map Framework for Noise Characterization of Quantum Computers

In order to understand the capabilities and limitations of quantum computers, it is necessary to develop methods that efficiently characterize and benchmark error channels present on these devices. In this paper, we present a method that faithfully reconstructs a marginal (local) approximation of the effective noise (MATEN) channel, that acts as a single layer at the end of the circuit. We first introduce a dual map framework that allows us to analytically derive expectation values of observables with respect to noisy circuits. These findings are supported by numerical simulations of the quantum approximate optimization algorithm (QAOA) that also justify the MATEN, even in the presence of non-local errors that occur during a circuit. Finally, we demonstrate the performance of the method on Rigetti's Aspen-9 quantum computer for QAOA circuits up to six qubits, successfully predicting the observed measurements on a majority of the qubits.

quant-ph↗

arXiv2021

Inter-generational comparison of quantum annealers in solving hard scheduling problems

We compare the performance of four quantum annealers, the D-Wave Two, 2X, 2000Q, and Advantage in solving an identical ensemble of a parametrized family of scheduling problems. These problems are NP-complete and, in fact, equivalent to vertex coloring problems. They are also practically motivated and closely connected to planning problems from artificial intelligence. We examine factors contributing to the performance differences while separating the contributions from hardware upgrades, support for shorter anneal times, and possible optimization of ferromagnetic couplings. While shorter anneal times can improve the time to solution (TTS) at any given problem size, the scaling of TTS with respect to the problem size worsens for shorter anneal times. In contrast, optimizing the ferromagnetic coupling improves both the absolute TTS and the scaling. There is a statistically significant improvement in performance between D-Wave Two and 2X and from all older generation annealers to Advantage, even when operated under identical anneal time and ferromagnetic couplings. However, the performance improvement from 2X to 2000Q requires the anneal time and ferromagnetic couplings to be optimized. Overall, owing to these inter-generational hardware improvements and optimizations, the scaling exponent reduces from $1.01 \pm 0.01$ on Two to $0.173 \pm 0.009$ on Advantage.

quant-ph↗

arXiv2021

Quantum-accelerated constraint programming

Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking tree search augmented with logical inference. In this paper, we show how quantum algorithms can accelerate CP, at both the levels of inference and search. Leveraging existing quantum algorithms, we introduce a quantum-accelerated filtering algorithm for the $\texttt{alldifferent}$ global constraint and discuss its applicability to a broader family of global constraints with similar structure. We propose frameworks for the integration of quantum filtering algorithms within both classical and quantum backtracking search schemes, including a novel hybrid classical-quantum backtracking search method. This work suggests that CP is a promising candidate application for early fault-tolerant quantum computers and beyond.

quant-ph↗

arXiv2021

Simulations of state-of-the-art fermionic neural network wave functions with diffusion Monte Carlo

Recently developed neural network-based \emph{ab-initio} solutions (Pfau et. al arxiv:1909.02487v2) for finding ground states of fermionic systems can generate state-of-the-art results on a broad class of systems. In this work, we improve the results for this Ansatz with Diffusion Monte Carlo. Additionally, we introduce several modifications to the network (Fermi Net) and optimization method (Kronecker Factored Approximate Curvature) that reduce the number of required resources while maintaining or improving the modelling performance. In terms of the model, we remove redundant computations and alter the way data is handled in the permutation equivariant function. The Diffusion Monte Carlo results exceed or match state-of-the-art performance for all systems investigated: atomic systems Be-Ne, and the carbon cation C$^+$.

physics.chem-ph↗

arXiv2021

Character randomized benchmarking for non-multiplicity-free groups with applications to subspace, leakage, and matchgate randomized benchmarking

Randomized benchmarking (RB) is a powerful method for determining the error rate of experimental quantum gates. Traditional RB, however, is restricted to gatesets, such as the Clifford group, that form a unitary 2-design. The recently introduced character RB can benchmark more general gates using techniques from representation theory; up to now, however, this method has only been applied to "multiplicity-free" groups, a mathematical restriction on these groups. In this paper, we extend the original character RB derivation to explicitly treat non-multiplicity-free groups, and derive several applications. First, we derive a rigorous version of the recently introduced subspace RB, which seeks to characterize a set of one- and two-qubit gates that are symmetric under SWAP. Second, we develop a new leakage RB protocol that applies to more general groups of gates. Finally, we derive a scalable RB protocol for the matchgate group, a group that like the Clifford group is non-universal but becomes universal with the addition of one additional gate. This example provides one of the few examples of a scalable non-Clifford RB protocol. In all three cases, compared to existing theories, our method requires similar resources, but either provides a more accurate estimate of gate fidelity, or applies to a more general group of gates. In conclusion, we discuss the potential, and challenges, of using non-multiplicity-free character RB to develop new classes of scalable RB protocols and methods of characterizing specific gates.

quant-ph↗