arXiv subjects

Daniel Dilley

Publications and source records attributed to Daniel Dilley.

15 recordsLinked to original sources

arXiv2026

Closed form logical error rate approximations for surface codes

We propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. These results fit well known scaling laws for studied physical error rates and code distances, but break down in some other regimes. We show how to use our method to analyze hypothetical quantum computers with various configurations and select designs with lower error rates. Currently, this requires expensive classical simulations of quantum decoders for various distances and physical error rates or inaccurate extrapolation from minimal experimental data. Instead, we use the symmetry of the problem to count the configurations that result in a logical error with our novel software. Given a physical error rate, we can deduce the probability of a logical error, to provably good accuracy. We include an analysis of measurement errors to allow a more complete comparison of different surface code implementations. We extend this counting method to a particular locally-correlated error model.

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arXiv2026

A matching decomposition algorithm for simulating quantum walk Hamiltonians

In this work, we present a new algorithm for generating quantum circuits that efficiently implement continuous time quantum walks on arbitrary simple sparse graphs. The algorithm, called matching decomposition, works by decomposing a continuous-time quantum walk Hamiltonian into a collection of exactly implementable Hamiltonians corresponding to matchings in the underlying graph followed by a novel graph compression algorithm that merges edges in the graph. We develop a greedy matching heuristic and a compression-aware matching heuristic, both of which can be used in the quantum circuit algorithm. Lastly, we convert the walks to a circuit and Trotterize over these components. The dynamics of the walker on each edge in the matching can be implemented in the circuit model as sequences of CX and CRx gates. We do not use Pauli decomposition when implementing walks along each matching. Furthermore, we compare greedy (compression-aware) matching decomposition to a standard Pauli-based simulation pipeline and find that greedy (compression-aware) matching decomposition consistently yields substantial resource reductions, requiring up to 43$\%$ (70\%) fewer controlled gates and up to 54$\%$ (75\%) shallower circuits than Pauli decomposition across multiple graph families. Finally, we also present examples and theoretical results for when matching decomposition can exactly simulate a continuous-time quantum walk on a graph.

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arXiv2025

An Interacting System and Environment with Prior Correlations Plus Local Operations Can Mimic Uncorrelated Evolution

Initial system-environment correlations can induce reduced dynamics that depart from the standard completely positive (CP) description. We study when such dynamics can be reproduced by the same global unitary acting on an initial system-environment product state. We show that local preprocessing on the system, applied prior to the joint evolution, can lead to dynamics which are completely positive. We focus on two-qubit system-environment states, with a three-qubit extension when a single ancilla is used to implement Kraus channel preprocessing. We analyze three classes of local operations$-$measurements, unitaries, and Kraus channels$-$and characterize their ability to satisfy dynamics matching while minimally perturbing the initial system state. Local measurements can always enforce dynamics matching but necessarily reduce state fidelity. We numerically investigated local unitary preprocessing. Local unitaries enforce dynamics matching in all tested instances and typically preserve the system state: in 402 numerical cases the average fidelity is 99.8%, more than 92% of cases exceed 99% fidelity, and the minimum fidelity is 94.2%. We show that a two-term Kraus channel, realizable with a single ancillary qubit coupled to the system, achieves dynamics matching with unit fidelity in all tested cases. As a second contribution, we demonstrate that local preprocessing can prevent the emergence of non--completely positive (NCP) reduced dynamics in a time-dependent setting. For a correlated two-qubit experiment with a time-dependent global unitary U(t), the induced compatibility domain is fixed by the initial correlations. For every t in a nontrivial continuous interval, the reduced dynamics are NCP when defined over this domain. We then show that a single, time-independent local unitary applied prior to the joint evolution renders the reduced dynamics CP over the entire interval.

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arXiv2025

InterQnet: A Heterogeneous Full-Stack Approach to Co-designing Scalable Quantum Networks

Quantum communications have progressed significantly, moving from a theoretical concept to small-scale experiments to recent metropolitan-scale demonstrations. As the technology matures, it is expected to revolutionize quantum computing in much the same way that classical networks revolutionized classical computing. Quantum communications will also enable breakthroughs in quantum sensing, metrology, and other areas. However, scalability has emerged as a major challenge, particularly in terms of the number and heterogeneity of nodes, the distances between nodes, the diversity of applications, and the scale of user demand. This paper describes InterQnet, a multidisciplinary project that advances scalable quantum communications through a comprehensive approach that improves devices, error handling, and network architecture. InterQnet has a two-pronged strategy to address scalability challenges: InterQnet-Achieve focuses on practical realizations of heterogeneous quantum networks by building and then integrating first-generation quantum repeaters with error mitigation schemes and centralized automated network control systems. The resulting system will enable quantum communications between two heterogeneous quantum platforms through a third type of platform operating as a repeater node. InterQnet-Scale focuses on a systems study of architectural choices for scalable quantum networks by developing forward-looking models of quantum network devices, advanced error correction schemes, and entanglement protocols. Here we report our current progress toward achieving our scalability goals.

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arXiv2025

QuantEM: The quantum error management compiler

As quantum computing advances toward fault-tolerant architectures, quantum error detection (QED) has emerged as a practical and scalable intermediate strategy in the transition from error mitigation to full error correction. By identifying and discarding faulty runs rather than correcting them, QED enables improved reliability with significantly lower overhead. Applying QED to arbitrary quantum circuits remains challenging, however, because of the need for manual insertion of detection subcircuits, ancilla allocation, and hardware-specific mapping and scheduling. We present QuantEM, a modular and extensible compiler designed to automate the integration of QED codes into arbitrary quantum programs. Our compiler consists of three key modules: (1) program analysis and transformation module to examine quantum programs in a QED-aware context and introduce checks and ancilla qubits, (2) error detection code integration module to map augmented circuits onto specific hardware backends, and (3) postprocessing and resource management for measurement results postprocessing and resource-efficient estimation techniques. The compiler accepts a high-level quantum circuit, a chosen error detection code, and a target hardware topology and then produces an optimized and executable circuit. It can also automatically select an appropriate detection code for the user based on circuit structure and resource estimates. QuantEM currently supports Pauli check sandwiching and Iceberg codes and is designed to support future QED schemes and hardware targets. By automating the complex QED compilation flow, this work reduces developer burden, enables fast code exploration, and ensures consistent and correct application of detection logic across architectures.

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arXiv2025

Efficient Entanglement Purification Circuit Design for Dual-Species Atom Arrays

Entanglement purification protocols (EPPs) are essential for generating high-fidelity entangled states in noisy quantum systems, enabling robust quantum networking and computation. Building on the circuit of the foundational recurrence protocol, we generalize two-way EPPs to arbitrary stabilizer codes. Through analytical derivations and noisy circuit simulations incorporating circuit-level noise, we demonstrate enhanced purification performance, with fidelity improvements and finite distillation rates for distillable input states. We propose efficient circuit designs for EPPs tailored to dual-species Rydberg atom arrays, leveraging species-specific laser control and interspecies Rydberg interactions. Introducing a low-overhead operation set, the dual-species atom convenient operation set, we facilitate straightforward compilation of EPP circuits without the need for ancillary atoms or complex atom rearrangements. Our framework provides practical guidance for near-term implementations on dual-species platforms, advancing towards scalable entanglement distribution in neutral atom systems and paving the way for fault-tolerant quantum technologies.

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arXiv2025

Quantum Resource Correction

Resource theories play a crucial role in characterizing states and properties essential for quantum information processing. A significant challenge is protecting resources from errors. We explore strategies for correcting quantum resources. We show that resource preserving operations in resource theory define a gauge freedom on code spaces, which allows for recovery strategies that can correct the resource while changing non-essential properties. This allows decoding to be simplified. The results are applicable to various resource theories and we provide an application to quantum sensing.

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arXiv2025

Exploring Non-Multiplicativity in the Geometric Measure of Entanglement

The geometric measure of entanglement (GME) quantifies how close a multi-partite quantum state is to the set of separable states under the Hilbert-Schmidt inner product. The GME can be non-multiplicative, meaning that the closest product state to two states is entangled across subsystems. In this work, we explore the GME in two families of states: those that are invariant under bilateral orthogonal $(O \otimes O)$ transformations, and mixtures of singlet states. In both cases, a region of GME non-multiplicativity is identified around the anti-symmetric projector state. We employ state-of-the-art numerical optimization methods and models to quantitatively analyze non-multiplicativity in these states for d = 3. We also investigate a constrained form of GME that measures closeness to the set of real product states and show that this measure can be non-multiplicative even for real separable states.

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arXiv2024

Detecting Errors in a Quantum Network with Pauli Checks

We apply the quantum error detection scheme Pauli check sandwiching (PCS) to quantum networks by turning it into a distributed multiparty protocol. PCS provides protection on the targeted qubits and generally requires less resource overhead than standard quantum error correction and detection codes. We provide analytical equations for the final fidelity and postselection rate for different PCS checks. We also introduce a recursive version of PCS that generates a family of distance 2 quantum codes that are locally equivalent to Calderbank-Shor-Steane (CSS) codes. Our analytical results are benchmarked against the Bennet-Brassard-Popescu-Schumacher-Smolin-Wooters (BBPSSW) protocol in comparable scenarios. We also perform simulations with noisy gates for entanglement swapping and attain fidelity improvements. Lastly, we discuss various setups and graph state properties of PCS.

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arXiv2023

Some Entanglement Survives Most Measurements

To prepare quantum states and extract information, it is often assumed that one can perform a perfectly projective measurement. Such measurements can achieve an uncorrelated system and environment state. However, perfectly projective measurements can be difficult or impossible to perform in practice. We investigate the limitations of repeated non-projective measurements in preparing a quantum system. For an $n$-qubit system initially entangled with its environment and subsequently prepared with measurements, using a sequence of weak measurements, we show that some entanglement remains unless one of the measurement operators becomes perfectly projective through an extreme limiting process. Removing initial (unentangled) correlations between a system and its environment and the scenario where measurement outcomes are not tracked are also discussed. We present results for $n$-qubit and $n$-dimensional input states.

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arXiv2022

Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms

The computational capabilities of near-term quantum computers are limited by the noisy execution of gate operations and a limited number of physical qubits. Hybrid variational algorithms are well-suited to near-term quantum devices because they allow for a wide range of tradeoffs between the amount of quantum and classical resources used to solve a problem. This paper investigates tradeoffs available at both the algorithmic and hardware levels by studying a specific case -- applying the Quantum Approximate Optimization Algorithm (QAOA) to instances of the Maximum Independent Set (MIS) problem. We consider three variants of the QAOA which offer different tradeoffs at the algorithmic level in terms of their required number of classical parameters, quantum gates, and iterations of classical optimization needed. Since MIS is a constrained combinatorial optimization problem, the QAOA must respect the problem constraints. This can be accomplished by using many multi-controlled gate operations which must be decomposed into gates executable by the target hardware. We study the tradeoffs available at this hardware level, combining the gate fidelities and decomposition efficiencies of different native gate sets into a single metric called the gate decomposition cost.

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arXiv2022

Identifying Quantum Correlations Using Explicit SO(3) to SU(2) Maps

Quantum state manipulation of two-qubits on the local systems by special unitaries induces special orthogonal rotations on the Bloch spheres. An exact formula is given for determining the local unitaries for some given rotation on the Bloch sphere. The solution allows for easy manipulation of two-qubit quantum states with a single definition that is programmable. With this explicit formula, modifications to the correlation matrix are made simple. Using our solution, it is possible to diagonalize the correlation matrix without solving for the parameters in SU(2) that define the local unitary that induces the special orthogonal rotation in SO(3). Since diagonalization of the correlation matrix is equivalent to diagonalization of the interaction Hamiltonian, manipulating the correlation matrix is important in time-optimal control of a two-qubit state. The relationship between orthogonality conditions on SU(2) and SO(3) are given and manipulating the correlation matrix when only one qubit can be accessed is discussed.

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arXiv2021

Guaranteeing Completely Positive Quantum Evolution

In open quantum systems, it is known that if the system and environment are in a product state, the evolution of the system is given by a linear completely positive (CP) Hermitian map. CP maps are a subset of general linear Hermitian maps, which also include non completely positive (NCP) maps. NCP maps can arise in evolutions such as non-Markovian evolution, where the CP divisibility of the map (writing the overall evolution as a composition of CP maps) usually fails. Positive but NCP maps are also useful as entanglement witnesses. In this paper, we focus on transforming an initial NCP map to a CP map through composition with the asymmetric depolarizing map. We use separate asymmetric depolarizing maps acting on the individual subsystems. Previous work have looked at structural physical approximation (SPA), which is a CP approximation of a NCP map using a mixture of the NCP map with a completely depolarizing map. We prove that the composition can always be made CP without completely depolarizing in any direction. It is possible to depolarize less in some directions. We give the general proof by using the Choi matrix and an isomorphism from a maximally entangled two qudit state to a set of qubits. We also give measures that describe the amount of disturbance the depolarization introduces to the original map. Given our measures, we show that asymmetric depolarization has many advantages over SPA in preserving the structure of the original NCP map. Finally, we give some examples. For some measures and examples, completely depolarizing (while not necessary) in some directions can give a better approximation than keeping the depolarizing parameters bounded by the required depolarization if symmetric depolarization is used.

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arXiv2020

Sufficient Conditions and Constraints for Reversing General Quantum Errors

Reversing the effects of a quantum evolution, for example as is done in error correction, is an important task for controlling quantum systems in order to produce reliable quantum devices. When the evolution is governed by a completely positive map, there exist reversibility conditions, known as the quantum error correcting code conditions, which are necessary and sufficient conditions for the reversibility of a quantum operation on a subspace, the code space. However, if we suppose that the evolution is not described by a completely positive map, necessary and sufficient conditions are not known. Here we consider evolutions that do not necessarily correspond to a completely positive map. We prove that the completely positive map error correcting code conditions can lead to a code space that is not in the domain of the map, meaning that the output of the map is not positive. A corollary to our theorem provides a class of relevant examples. Finally, we provide a set of sufficient conditions that will enable the use of quantum error correcting code conditions while ensuring positivity.

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arXiv2018

More Nonlocality with Less Entanglement in CHSH Experiments using Inefficient Detectors

It is well-known that in certain scenarios weakly entangled states can generate stronger nonlocal effects than their maximally entangled counterparts. In this paper, we consider violations of the CHSH Inequality when one party has inefficient detectors, a scenario known as an asymmetric Bell experiment. %We show that violations can occur if and only if the detection efficiency is above $50\%$. For any fixed detection efficiency, we derive a simple upper bound on the entanglement needed to violate the inequality by more than some specified amount $κ\geq 0$. When $κ=0$, the amount of entanglement in all states violating the inequality goes to zero as the detection efficiency approaches $50\%$ from above. %This provides another scenario in which weakly entangled states are advantageous for violating the CHSH Inequality in the presence of detection inefficiency. We finally consider the scenario in which detection inefficiency arises for only one choice of local measurement. In this case, it is shown that the CHSH Inequality can always be violated for any nonzero detection efficiency and any choice of non-commuting measurements.

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