arXiv subjects

Charles D. Hill

Publications and source records attributed to Charles D. Hill.

At least 19 recordsLinked to original sources

arXiv2026

The Magic Scroll: Leveraging biased noise to improve magic state cultivation in register-based architectures

Multiple quantum computing platforms across neutral atoms [1], nitrogen vacancy centres [2, 3], gate-defined dots [4-6] and 14|15 phosphorus atom qubits [7, 8] in silicon are experimentally exploring the use of high connectivity qubits, beyond that of nearest-neighbour planar lattices. Theoretical works consider modifications to fault-tolerant codes to leverage this higher qubit connectivity, such as non-local LDPC codes [9], inspiring superconducting [10] and photonic [11] platforms to also seek non-planar connectivity. In addition, separate theoretical works consider biased noise, where bit- and phase-flip errors are not equally likely. In this work, we present efficient methods for implementing 6.6.6 and 4.8.8 colour codes, as well as bilayer and folded surface codes, using two-qubit registers. We also leverage noise bias to avoid hook errors, demonstrating comparable performance to the surface code. By combining colour and bilayer codes, we show how magic state cultivation procedures [12-14] can be improved, in a procedure we refer to as the Magic Scroll. Not only does the Magic Scroll escape to a standard surface code, it also improves cultivation volumes by 3x and supports magic $|T\rangle$ state fidelities as low as $10^{-9}$. We show that this technique can be further leveraged to improve distillation performance, showing a 3x improvement to distillation volumes for error rates of $\sim 10^{-15}$. Through these constructions, we demonstrate techniques to leverage noise bias and high qubit connectivity, showing how register-based architectures can improve error rates and reduce quantum volumes in fault-tolerant quantum computing.

quant-ph↗

arXiv2026

Practical learning of multi-time statistics in open quantum systems

Randomised measurements can efficiently characterise many-body quantum states by learning the expectation values of observables with low Pauli weights. In this paper, we generalise the theoretical tools of classical shadow tomography to the temporal domain to explore multi-time phenomena. This enables us to efficiently learn the features of multi-time processes such as correlated error rates, multi-time non-Markovianity, and temporal entanglement. We test the efficacy of these tools on a noisy quantum processor to characterise its noise features. Implementing these tools requires mid-circuit instruments, typically slow or unavailable in current quantum hardware. We devise a protocol to achieve fast and reliable instruments such that these multi-time distributions can be learned to a high accuracy. This enables a compact matrix product operator representation of large processes allowing us to showcase a reconstructed 20-step process (whose naive dimensionality is that of a 42-qubit state). Our techniques are pertinent to generic quantum stochastic dynamical processes, with a scope ranging across condensed matter physics, quantum biology, and in-depth diagnostics of noisy intermediate-scale quantum devices.

quant-ph↗

arXiv2025

Unifying non-Markovian characterisation with an efficient and self-consistent framework

Noise on quantum devices is much more complex than it is commonly given credit. Far from usual models of decoherence, nearly all quantum devices are plagued both by a continuum of environments and temporal instabilities. These induce noisy quantum and classical correlations at the level of the circuit. The relevant spatiotemporal effects are difficult enough to understand, let alone combat. There is presently a lack of either scalable or complete methods to address the phenomena responsible for scrambling and loss of quantum information. Here, we make deep strides to remedy this problem. We establish a theoretical framework that uniformly incorporates and classifies all non-Markovian phenomena. Our framework is universal, assumes no parameters values, and is written entirely in terms of experimentally accessible circuit-level quantities. We formulate an efficient reconstruction using tensor network learning, allowing also for easy modularisation and simplification based on the expected physics of the system. This is then demonstrated through both extensive numerical studies and implementations on IBM Quantum devices, estimating a comprehensive set of spacetime correlations. Finally, we conclude our analysis with applications thereof to the efficacy of control techniques to counteract these effects -- including noise-aware circuit compilation and optimised dynamical decoupling. We find significant improvements are possible in the diamond norm and average gate fidelity of arbitrary $SU(4)$ operations, as well as related decoupling improvements in contrast to off-the-shelf schemes.

quant-ph↗

arXiv2025

What can unitary sequences tell us about multi-time physics?

Multi-time quantum processes are endowed with the same richness as multipartite states, including temporal entanglement and exotic causal structures. However, experimentally probing these rich phenomena leans heavily on fast and clean mid-circuit measurements, which are rarely available. We show here how surprisingly accessible these phenomena are in nascent quantum processors even when faced with substantially limited control. We work within the limitation where only unitary control is allowed, followed by a terminating measurement. Within this setting, we first develop a witness for genuine multi-time entanglement, and then methods to bound (from top and bottom) multi-time entanglement, non-Markovianity, purity, entropy, and other correlative measures. Our tools are designed to be implemented on quantum information processors, which we proceed to demonstrate. Finally, we discuss the limitations of these methods by testing them across random multi-time processes. Conceptually, this broadens our understanding of the extent to which temporal correlations may be determined with only deterministic control. Our techniques are pertinent to generic quantum stochastic dynamical processes, with a scope ranging across condensed matter physics, quantum biology, and in-depth diagnostics of NISQ-era quantum devices.

quant-ph↗

arXiv2025

Grover's algorithm in a four-qubit silicon processor above the fault-tolerant threshold

Spin qubits in silicon are strong contenders for realizing a practical quantum computer. This technology has made remarkable progress with the demonstration of single and two-qubit gates above the fault-tolerant threshold and entanglement of up to three qubits. However, maintaining high fidelity operations while executing multi-qubit algorithms has remained elusive, only being achieved for two spin qubits to date due to the small qubit size, which makes it difficult to control qubits without creating crosstalk errors. Here, we use a four-qubit silicon processor with every operation above the fault tolerant limit and demonstrate Grover's algorithm with a ~95% probability of finding the marked state, one of the most successful implementations to date. Our four-qubit processor is made of three phosphorus atoms and one electron spin precision-patterned into 1.5 nm${}^2$ isotopically pure silicon. The strong resulting confinement potential, without additional confinement gates that can increase cross-talk, leverages the benefits of having both electron and phosphorus nuclear spins. Significantly, the all-to-all connectivity of the nuclear spins provided by the hyperfine interaction not only allows for efficient multi-qubit operations, but also provides individual qubit addressability. Together with the long coherence times of the nuclear and electron spins, this results in all four single qubit fidelities above 99.9% and controlled-Z gates between all pairs of nuclear spins above 99% fidelity. The high control fidelities, combined with >99% fidelity readout of all nuclear spins, allows for the creation of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state with 96.2% fidelity, the highest reported for semiconductor spin qubits so far. Such nuclear spin registers can be coupled via electron exchange, establishing a path for larger scale fault-tolerant quantum processors.

quant-ph↗

arXiv2023

Noise-robust ground state energy estimates from deep quantum circuits

In the lead up to fault tolerance, the utility of quantum computing will be determined by how adequately the effects of noise can be circumvented in quantum algorithms. Hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) have been designed for the short-term regime. However, as problems scale, VQE results are generally scrambled by noise on present-day hardware. While error mitigation techniques alleviate these issues to some extent, there is a pressing need to develop algorithmic approaches with higher robustness to noise. Here, we explore the robustness properties of the recently introduced quantum computed moments (QCM) approach to ground state energy problems, and show through an analytic example how the underlying energy estimate explicitly filters out incoherent noise. Motivated by this observation, we implement QCM for a model of quantum magnetism on IBM Quantum hardware to examine the noise-filtering effect with increasing circuit depth. We find that QCM maintains a remarkably high degree of error robustness where VQE completely fails. On instances of the quantum magnetism model up to 20 qubits for ultra-deep trial state circuits of up to ~500 CNOTs, QCM is still able to extract reasonable energy estimates. The observation is bolstered by an extensive set of experimental results. To match these results, VQE would need hardware improvement by some 2 orders of magnitude on error rates.

quant-ph↗

arXiv2023

Towards quantum enhanced adversarial robustness in machine learning

Machine learning algorithms are powerful tools for data driven tasks such as image classification and feature detection, however their vulnerability to adversarial examples - input samples manipulated to fool the algorithm - remains a serious challenge. The integration of machine learning with quantum computing has the potential to yield tools offering not only better accuracy and computational efficiency, but also superior robustness against adversarial attacks. Indeed, recent work has employed quantum mechanical phenomena to defend against adversarial attacks, spurring the rapid development of the field of quantum adversarial machine learning (QAML) and potentially yielding a new source of quantum advantage. Despite promising early results, there remain challenges towards building robust real-world QAML tools. In this review we discuss recent progress in QAML and identify key challenges. We also suggest future research directions which could determine the route to practicality for QAML approaches as quantum computing hardware scales up and noise levels are reduced.

quant-ph↗

arXiv2023

Filtering crosstalk from bath non-Markovianity via spacetime classical shadows

From an open system perspective non-Markovian effects due to a nearby bath or neighbouring qubits are dynamically equivalent. However, there is a conceptual distinction to account for: neighbouring qubits may be controlled. We combine recent advances in non-Markovian quantum process tomography with the framework of classical shadows to characterise spatiotemporal quantum correlations. Observables here constitute operations applied to the system, where the free operation is the maximally depolarising channel. Using this as a causal break, we systematically erase causal pathways to narrow down the progenitors of temporal correlations. We show that one application of this is to filter out the effects of crosstalk and probe only non-Markovianity from an inaccessible bath. It also provides a lens on spatiotemporally spreading correlated noise throughout a lattice from common environments. We demonstrate both examples on synthetic data. Owing to the scaling of classical shadows, we can erase arbitrarily many neighbouring qubits at no extra cost. Our procedure is thus efficient and amenable to systems even with all-to-all interactions.

quant-ph↗

arXiv2023

GASP -- A Genetic Algorithm for State Preparation

The efficient preparation of quantum states is an important step in the execution of many quantum algorithms. In the noisy intermediate-scale quantum (NISQ) computing era, this is a significant challenge given quantum resources are scarce and typically only low-depth quantum circuits can be implemented on physical devices. We present a genetic algorithm for state preparation (GASP) which generates relatively low-depth quantum circuits for initialising a quantum computer in a specified quantum state. The method uses a basis set of R_x, R_y, R_z, and CNOT gates and a genetic algorithm to systematically generate circuits to synthesize the target state to the required fidelity. GASP can produce more efficient circuits of a given accuracy with lower depth and gate counts than other methods. This variability of the required accuracy facilitates overall higher accuracy on implementation, as error accumulation in high-depth circuits can be avoided. We directly compare the method to the state initialisation technique based on an exact synthesis technique by implemented in IBM Qiskit simulated with noise and implemented on physical IBM Quantum devices. Results achieved by GASP outperform Qiskit's exact general circuit synthesis method on a variety of states such as Gaussian states and W-states, and consistently show the method reduces the number of gates required for the quantum circuits to generate these quantum states to the required accuracy.

quant-ph↗

arXiv2023

A kernel-based quantum random forest for improved classification

The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to attain expressional and computational advantage. In this work we extend the linear quantum support vector machine (QSVM) with kernel function computed through quantum kernel estimation (QKE), to form a decision tree classifier constructed from a decision directed acyclic graph of QSVM nodes - the ensemble of which we term the quantum random forest (QRF). To limit overfitting, we further extend the model to employ a low-rank Nyström approximation to the kernel matrix. We provide generalisation error bounds on the model and theoretical guarantees to limit errors due to finite sampling on the Nyström-QKE strategy. In doing so, we show that we can achieve lower sampling complexity when compared to QKE. We numerically illustrate the effect of varying model hyperparameters and finally demonstrate that the QRF is able obtain superior performance over QSVMs, while also requiring fewer kernel estimations.

quant-ph↗

arXiv2022

On the sampling complexity of open quantum systems

Open quantum systems are ubiquitous in the physical sciences, with widespread applications in the areas of chemistry, condensed matter physics, material science, optics, and many more. Not surprisingly, there is significant interest in their efficient simulation. However, direct classical simulation quickly becomes intractable with coupling to an environment whose effective dimension grows exponentially. This raises the question: can quantum computers help model these complex dynamics? A first step in answering this question requires understanding the computational complexity of this task. Here, we map the temporal complexity of a process to the spatial complexity of a many-body state using a computational model known as the process tensor framework. With this, we are able to explore the simulation complexity of an open quantum system as a dynamic sampling problem: a system coupled to an environment can be probed at successive points in time -- accessing multi-time correlations. The complexity of multi-time sampling, which is an important and interesting problem in its own right, contains the complexity of master equations and stochastic maps as a special case. Our results show how the complexity of the underlying quantum stochastic process corresponds to the complexity of the associated family of master equations for the dynamics. We present both analytical and numerical examples whose multi-time sampling is as complex as sampling from a many-body state that is classically hard. This also implies that the corresponding family of master equations are classically hard. Our results pave the way for studying open quantum systems from a complexity-theoretic perspective, highlighting the role quantum computers will play in our understanding of quantum dynamics.

quant-ph↗

arXiv2022

Comparative analysis of error mitigation techniques for variational quantum eigensolver implementations on IBM quantum system

Quantum computers are anticipated to transcend classical supercomputers for computationally intensive tasks by exploiting the principles of quantum mechanics. However, the capabilities of the current generation of quantum devices are limited due to noise or errors, and therefore implementation of error mitigation and/or correction techniques is pivotal to reliably process quantum algorithms. In this work, we have performed a comparative analysis of the error mitigation capability of the [[4,2,2]] quantum error-detecting code (QEC method), duplicate circuit technique, and the Bayesian read-out error mitigation (BREM) approach in the context of proof-of-concept implementations of variational quantum eigensolver (VQE) algorithm for determining the ground state energy of H$_2$ molecule. Based on experiments on IBM quantum device, our results show that the duplicate circuit approach performs superior to the QEC method in the presence of the hardware noise. A significant impact of cross-talk noise was observed when multiple mappings of the duplicate circuit and the QEC method were implemented simultaneously $-$ again the duplicate circuit approach overall performed better than the QEC method. To gain further insights into the performance of the studied error mitigation techniques, we also performed quantum simulations on IBM system with varying strengths of depolarising circuit noise and read-out errors which further supported the main finding of our work that the duplicate circuit offer superior performance towards mitigating of errors when compared to the QEC method. Our work reports a first assessment of the duplicate circuit approach for a quantum algorithm implementation and the documented evidence will pave the way for future scalable implementations of the duplicated circuit techniques for the error-mitigated practical applications of near-term quantum computers.

quant-ph↗

arXiv2022

Non-Markovian Quantum Process Tomography

Characterisation protocols have so far played a central role in the development of noisy intermediate-scale quantum (NISQ) computers capable of impressive quantum feats. This trajectory is expected to continue in building the next generation of devices: ones that can surpass classical computers for particular tasks -- but progress in characterisation must keep up with the complexities of intricate device noise. A missing piece in the zoo of characterisation procedures is tomography which can completely describe non-Markovian dynamics over a given time frame. Here, we formally introduce a generalisation of quantum process tomography, which we call process tensor tomography. We detail the experimental requirements, construct the necessary post-processing algorithms for maximum-likelihood estimation, outline the best-practice aspects for accurate results, and make the procedure efficient for low-memory processes. The characterisation is a pathway to diagnostics and informed control of correlated noise. As an example application of the hardware-agnostic technique, we show how its predictive control can be used to substantially improve multi-time circuit fidelities on superconducting quantum devices. Our methods could form the core for carefully developed software that may help hardware consistently pass the fault-tolerant noise threshold.

quant-ph↗

arXiv2022

Inducing Heat Reversal in a Three-Qubit Spin Chain

By the standard second law of thermodynamics, heat spontaneously flows from a hotter body to a colder body. However, quantum systems in which quantum correlations play a prominent role can exhibit a non-classical reversal of such heat flow. We propose a quantum system consisting of a chain of qubits, each in local Gibbs states, where only adjacent qubits are allowed to thermally interact. By controlling initial quantum correlations along the chain, we then demonstrate non-classical heat reversal for the special case of a three-qubit chain on a quantum computer. We explore multiple initial conditions for the spin chain to showcase exotic behaviour such as the preferential pumping of heat afforded by unequal initial correlations between adjacent pairs of qubits, reinforcing the role that initial correlations play in influencing the dynamics of heat flow.

quant-ph↗

arXiv2021

Process Tomography on a 7-Qubit Quantum Processor via Tensor Network Contraction Path Finding

Quantum process tomography (QPT), where a quantum channel is reconstructed through the analysis of repeated quantum measurements, is an important tool for validating the operation of a quantum processor. We detail the combined use of an existing QPT approach based on tensor networks (TNs) and unsupervised learning with TN contraction path finding algorithms in order to use TNs of arbitrary topologies for reconstruction. Experiments were conducted on the 7-qubit IBM Quantum Falcon Processor ibmq_casablanca, where we demonstrate this technique by matching the topology of the tensor networks used for reconstruction with the topology of the processor, allowing us to extend past the characterisation of linear nearest neighbour circuits. Furthermore, we conduct single-qubit gate set tomography (GST) on each individual qubit to correct for separable errors during the state preparation and measurement phases of QPT, which are separate from the channel under consideration but may negatively impact the quality of its reconstruction. We are able to report a fidelity of 0.89 against the ideal unitary channel of a single-cycle random quantum circuit performed on ibmq_casablanca, after obtaining just $1.1 \times 10^5$ measurements for the reconstruction of this 7-qubit process. This represents more than five orders of magnitude fewer total measurements than the number needed to conduct full, traditional QPT on a 7-qubit process.

quant-ph↗

arXiv2021

A silicon qubit platform for in situ single molecule structure determination

Imaging individual conformational instances of generic, inhomogeneous, transient or intrinsically disordered protein systems at the single molecule level in situ is one of the notable challenges in structural biology. Present techniques access averaged structural information by measuring over large ensembles of proteins in nearly uniform conformational states in synthetic environments. This poses significant implications for diagnostics and drug design which require a detailed understanding of subtle conformational changes, small molecule interactions and ligand dynamics. Here we tackle the problem by designing a single molecule imaging platform technology embracing the advantages silicon-based spin qubits offer in terms of quantum coherence and established fabrication pathways. We demonstrate through detailed simulation, that this platform enables scalable atomic-level structure-determination of individual molecular systems in native environments. The approach is particularly well suited to the high-value lipid-membrane context, and as such its experimental implementation could have far-reaching consequences for the understanding of membrane biology and drug development.

quant-ph↗

arXiv2021

Chemistry beyond the Hartree-Fock limit via quantum computed moments

Quantum computers hold promise to circumvent the limitations of conventional computing for difficult molecular problems. However, the accumulation of quantum logic errors on real devices represents a major challenge, particularly in the pursuit of chemical accuracy requiring the inclusion of dynamical effects. In this work we implement the quantum computed moments (QCM) approach for hydrogen chain molecular systems up to H$_6$. On a superconducting quantum processor, Hamiltonian moments, $\langle \mathcal{H}^p\rangle$ are computed with respect to the Hartree-Fock state, which are then employed in Lanczos expansion theory to determine an estimate for the ground-state energy which incorporates electronic correlations and manifestly improves on the variational result. Post-processing purification of the raw QCM data takes the estimate through the Hartree-Fock variational limit to within 99.9% of the exact electronic ground-state energy for the largest system studied, H$_6$. Calculated dissociation curves indicate precision at about 10mH for this system and as low as 0.1mH for molecular hydrogen, H$_2$, over a range of bond lengths. In the context of stringent precision requirements for chemical problems, these results provide strong evidence for the error suppression capability of the QCM method, particularly when coupled with post-processing error mitigation. Greater emphasis on more efficient representations of the Hamiltonian and classical preprocessing steps may enable the solution of larger systems on near-term quantum processors.

physics.chem-ph↗

arXiv2021

Whole-device entanglement in a 65-qubit superconducting quantum computer

The ability to generate large-scale entanglement is an important progenitor of quantum information processing capability in noisy intermediate-scale quantum (NISQ) devices. In this paper, we investigate the extent to which entangled quantum states over large numbers of qubits can be prepared on current superconducting quantum devices. We prepared native-graph states on the IBM Quantum 65-qubit $\textit{ibmq_manhattan}$ device and the 53-qubit $\textit{ibmq_rochester}$ device and applied quantum readout-error mitigation (QREM). Connected entanglement graphs spanning each of the full devices were detected, indicating bipartite entanglement over the whole of each device. The application of QREM was shown to increase the observed entanglement within all measurements, in particular, the detected number of entangled pairs of qubits found within $\textit{ibmq_rochester}$ increased from 31 to 56 of the total 58 connected pairs. The results of this work indicate full bipartite entanglement in two of the largest superconducting devices to date.

quant-ph↗