arXiv subjects

P. A. Warburton

Publications and source records attributed to P. A. Warburton.

16 recordsLinked to original sources

arXiv2025

Enhancement of quantum annealing via n-local catalysts

The potential quantum speedup in solving optimization problems via adiabatic quantum annealing is often hindered by the closing of the energy gap during the anneal, especially when this gap scales exponentially with system size. In this work, we alleviate this bottleneck by demonstrating that for the NP-complete Maximum Weighted Independent Set (MWIS) problem, an informed choice of $n-$local catalysts (operators involving $n$ qubits) can re-open the gap during the annealing process. By analyzing first-order phase transitions in toy instances of the MWIS problem, we first identify direct-tunneling catalysts that effectively eliminate the transition and provide an analytical discussion on when the sign of the catalyst influences its impact. We then reveal that $n-$local catalysts exponentially improve gap scaling and in certain scenarios are as effective as direct tunnel coupling between two minima. Utilizing this understanding, we show that they also increase the efficiency of ground state preparation via adiabatic quantum annealing in random graphs and analytically demonstrate the necessity of their placement across unfrustrated loops in the graph for effective performance in MWIS problems. Additionally, using a circuit implementation of the $n$-local catalyst (requiring $2n$ nearest-neighbour gates), we demonstrate that both the circuit depth and the total number of gates required to solve the problem are reduced by several orders of magnitude when compared to the discrete-time version of traditional quantum annealing using local drivers. Our analysis suggests that non-local quantum fluctuations entangling multiple qubits as a catalyst are key to achieving the desired quantum advantage.

quant-ph↗

arXiv2025

Gadgets for simulating a non-native $XX$ interaction in quantum annealing

In certain scenarios, quantum annealing can be made more efficient by additional $XX$ interactions. It has been shown that the additional interactions can reduce the scaling of perturbative crossings. In traditional annealing devices these couplings do not exist natively. In this work, we develop two gadgets to achieve this: a three-body gadget that requires a strong $ZZZ$ interaction; and a one-hot gadget that uses only local $X$ drives and two-body $ZZ$ interactions. The gadgets partition the Hilbert space to effectively generate a limited number of $XX$ interactions in the low-energy subspace. We numerically verify that the one-hot gadget can mitigate a perturbative crossing on a toy problem. These gadgets establish new pathways for implementing and exploiting $XX$ interactions, enabling faster and more robust quantum annealing.

quant-ph↗

arXiv2025

Continuous-time quantum optimisation without the adiabatic principle

Continuous-time quantum algorithms for combinatorial optimisation problems, such as quantum annealing, have previously been motivated by the adiabatic principle. A number of continuous-time approaches exploit dynamics, however, and therefore are no longer physically motivated by the adiabatic principle. In this work, we take Planck's principle as the underlying physical motivation for continuous-time quantum algorithms. Planck's principle states that the energy of an isolated system cannot decrease as the result of a cyclic process. We use this principle to justify monotonic schedules in quantum annealing, which are not adiabatic. This approach also highlights the limitations of reverse quantum annealing in an isolated system.

quant-ph↗

arXiv2024

Rapid quantum approaches for combinatorial optimisation inspired by optimal state-transfer

We propose a new design heuristic to tackle combinatorial optimisation problems, inspired by Hamiltonians for optimal state-transfer. The result is a rapid approximate optimisation algorithm. We provide numerical evidence of the success of this new design heuristic. We find this approach results in a better approximation ratio than the Quantum Approximate Optimisation Algorithm at lowest depth for the majority of problem instances considered, while utilising comparable resources. This opens the door to investigating new approaches for tackling combinatorial optimisation problems, distinct from adiabatic-influenced approaches.

quant-ph↗

arXiv2024

Continuous-time quantum walks for MAX-CUT are hot

By exploiting the link between time-independent Hamiltonians and thermalisation, heuristic predictions on the performance of continuous-time quantum walks for MAX-CUT are made. The resulting predictions depend on the number of triangles in the underlying MAX-CUT graph. We extend these results to the time-dependent setting with multi-stage quantum walks and Floquet systems. The approach followed here provides a novel way of understanding the role of unitary dynamics in tackling combinatorial optimisation problems with continuous-time quantum algorithms.

quant-ph↗

arXiv2023

Effects of XX-catalysts on quantum annealing spectra with perturbative crossings

In adiabatic quantum annealing the required run-time to reach a given ground-state fidelity is dictated by the size of the minimum gap that appears between the ground and first excited state in the annealing spectrum. In general the presence of avoided level crossings demands an exponential increase in the annealing time with the system size which has consequences both for the efficiency of the algorithm and the required qubit coherence times. One promising avenue being explored to produce more favourable gap scaling is the introduction of non-stoquastic XX-couplings in the form of a catalyst - of particular interest are catalysts which utilise accessible information about the optimisation problem in their construction. Here we show extreme sensitivity of the effect of an XX-catalyst to subtle changes in the encoding of the optimisation problem. In particular, we observe that a targeted catalyst containing a single coupling at constant strength can significantly reduce the gap closing with system size at an avoided level crossing. For slightly different encodings of the same problems however, these same catalysts result in closing gaps in the annealing spectrum. To understand the origin of these closing gaps, we study how the evolution of the ground-state vector is altered by the presence of the catalyst and find that the negative components of the ground-state vector are key to understanding the response of the gap spectrum. We also consider how and when these closing gaps could be utilised in diabatic quantum annealing protocols - a promising alternative to adiabatic quantum annealing in which transitions to higher energy levels are exploited to reduce the run time of the algorithm.

quant-ph↗

arXiv2022

A Cost and Power Feasibility Analysis of Quantum Annealing for NextG Cellular Wireless Networks

In order to meet mobile cellular users' ever-increasing data demands, today's 4G and 5G networks are designed mainly with the goal of maximizing spectral efficiency. While they have made progress in this regard, controlling the carbon footprint and operational costs of such networks remains a long-standing problem among network designers. This paper takes a long view on this problem, envisioning a NextG scenario where the network leverages quantum annealing for cellular baseband processing. We gather and synthesize insights on power consumption, computational throughput and latency, spectral efficiency, operational cost, and feasibility timelines surrounding quantum technology. Armed with these data, we analyze and project the quantitative performance targets future quantum annealing hardware must meet in order to provide a computational and power advantage over CMOS hardware, while matching its whole-network spectral efficiency. Our quantitative analysis predicts that with quantum annealing hardware operating at a 102 $μ$s problem latency and 3.1M qubits, quantum annealing will achieve a spectral efficiency equal to CMOS computation while reducing power consumption by 41 kW (45% lower) in a representative 5G base station scenario with 400 MHz bandwidth and 64 antennas, and an 8 kW power reduction (16% lower) using 1.5M qubits in a 200 MHz-bandwidth 5G scenario.

cs.NI↗

arXiv2019

Minimizing minor embedding energy: an application in quantum annealing

A significant challenge in quantum annealing is to map a real-world problem onto a hardware graph of limited connectivity. If the maximum degree of the problem graph exceeds the maximum degree of the hardware graph, one employs minor embedding in which each logical qubit is mapped to a tree of physical qubits. Pairwise interactions between physical qubits in the tree are set to be ferromagnetic with some coupling strength $F<0$. Here we address the question of what value $F$ should take in order to maximise the probability that the annealer finds the correct ground-state of an Ising problem. The sum of $|F|$ for each logical qubit is defined as minor embedding energy. We confirm experimentally that the ground-state probability is maximised when the minor embedding energy is minimised, subject to the constraint that no domain walls appear in every tree of physical qubits associated with each embedded logical qubit. We further develop an analytical lower bound on $|F|$ which satisfies this constraint and show that it is a tighter bound than that previously derived by Choi (Quantum Inf. Proc. 7 193 (2008)).

quant-ph↗

arXiv2018

Emergence of Quantum Phase-Slip Behaviour in Superconducting NbN Nanowires: DC Electrical Transport and Fabrication Technologies

Superconducting nanowires undergoing quantum phase-slips have potential for impact in electronic devices, with a high-accuracy quantum current standard among a possible toolbox of novel components. A key element of developing such technologies is to understand the requirements for, and control the production of, superconducting nanowires that undergo coherent quantum phase-slips. We present three fabrication technologies, based on using electron-beam lithography or neon focussed ion-beam lithography, for defining narrow superconducting nanowires, and have used these to create nanowires in niobium nitride with widths in the range of 20-250 nm. We present characterisation of the nanowires using DC electrical transport at temperatures down to 300 mK. We demonstrate that a range of different behaviours may be obtained in different nanowires, including bulk-like superconducting properties with critical-current features, the observation of phase-slip centres and the observation of zero conductance below a critical voltage, characteristic of coherent quantum phase-slips. We observe critical voltages up to 5 mV, an order of magnitude larger than other reports to date. The different prominence of quantum phase-slip effects in the various nanowires may be understood as arising from the differing importance of quantum fluctuations. Control of the nanowire properties will pave the way for routine fabrication of coherent quantum phase-slip nanowire devices for technology applications.

cond-mat.supr-con↗

arXiv2017

Effect of lithographically-induced strain relaxation on the magnetic domain configuration in microfabricated epitaxially grown Fe81Ga19

We investigate the role of lithographically-induced strain relaxation in a micron-scaled device fabricated from epitaxial thin films of the magnetostrictive alloy Fe81Ga19. The strain relaxation due to lithographic patterning induces a magnetic anisotropy that competes with the magnetocrystalline and shape induced anisotropies to play a crucial role in stabilising a flux-closing domain pattern. We use magnetic imaging, micromagnetic calculations and linear elastic modelling to investigate a region close to the edges of an etched structure. This highly-strained edge region has a significant influence on the magnetic domain configuration due to an induced magnetic anisotropy resulting from the inverse magnetostriction effect. We investigate the competition between the strain-induced and shape-induced anisotropy energies, and the resultant stable domain configurations, as the width of the bar is reduced to the nanoscale range. Understanding this behaviour will be important when designing hybrid magneto-electric spintronic devices based on highly magnetostrictive materials.

cond-mat.mes-hall↗

arXiv2014

Compact chromium oxide thin film resistors for use in nanoscale quantum circuits

We report on the electrical characterisation of a series of thin chromium oxide films, grown by dc sputtering, to evaluate their suitability for use as on-chip resistors in nanoelectronics. By increasing the level of oxygen doping, the room-temperature sheet resistance of the chromium oxide films was varied from 28$Ω/ \square$ to 32.6k$Ω/ \square$. The variation in resistance with cooling to 4.2K in liquid helium was investigated; the sheet resistance at 4.2K varied with composition from 65$Ω/ \square$ to above 20G$Ω/ \square$. All of the films measured displayed ohmic behaviour at all measured temperatures. For on-chip devices for quantum phase-slip measurements using niobium-silicon nanowires, interfaces between niobium-silicon and chromium oxide are required. By characterising the interface contact resistance, we found that a gold intermediate layer is favourable: the specfic contact resistivity of chromium-oxide-to-gold interfaces was 0.15 m$Ω$cm$^2$, much lower than the value for direct chromium-oxide to niobium-silicon interfaces, 65m$Ω$cm$^2$. We conclude that these chromium oxide films are suitable for use in nanoscale circuits as high-value resistors, with resistivity tunable by oxygen content.

cond-mat.mes-hall↗

arXiv2014

Quantum and Classical in Adiabatic Computation

Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialised state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose groundstate encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimisation algorithms and quantum adiabatic optimisation. This new perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing - though inconclusive - results.

quant-ph↗

arXiv2013

NbSi nanowire quantum-phase-slip circuits: dc supercurrent blockade, microwave measurements and thermal analysis

We present a detailed report of microwave irradiation of ultra-narrow superconducting nanowires. In our nanofabricated circuits containing a superconducting NbSi nanowire, a dc blockade of current flow was observed at low temperatures below a critical voltage Vc, a strong indicator of the existence of quantum phase-slip (QPS) in the nanowire. We describe the results of applying microwaves to these samples, using a range of frequencies and both continuous-wave and pulsed drive, in order to search for dual Shapiro steps which would constitute an unambiguous demonstration of quantum phase-slip. We observed no steps, and our subsequent thermal analysis suggests that the electron temperature in the series CrO resistors was significantly elevated above the substrate temperature, resulting in sufficient Johnson noise to wash out the steps. To understand the system and inform future work, we have constructed a numerical model of the dynamics of the circuit for dc and ac bias (both continuous wave and pulsed drive signals) in the presence of Johnson noise. Using this model, we outline important design considerations for device and measurement parameters which should be used in any future experiment to enable the observation of dual Shapiro steps at experimentally accessible temperatures and thus lead to the development of a QPS-based quantum current standard.

cond-mat.supr-con↗

arXiv2012

Fano resonance resulting from a tunable interaction between molecular vibrational modes and a double-continuum of a plasmonic metamolecule

Coupling between tuneable broadband modes of an array of plasmonic metamolecules and a vibrational mode of carbonyl bond of poly(methyl methacrylate) is shown experimentally to produce a Fano resonance, which can be tuned in situ by varying the polarization of incident light. The interaction between the plasmon modes and the molecular resonance is investigated using both rigorous electromagnetic calculations and a quantum mechanical model describing the quantum interference between a discrete state and two continua. The predictions of the quantum mechanical model are in good agreement with the experimental data and provide an intuitive interpretation, at the quantum level, of the plasmon-molecule coupling.

cond-mat.mes-hall↗

arXiv2008

Thermal fluctuations in moderately damped Josephson junctions: Multiple escape and retrapping, switching- and return-current distributions and hysteresis

A crossover at a temperature T* in the temperature dependence of the width s of the distribution of switching currents of moderately damped Josephson junctions has been reported in a number of recent publications, with positive ds/dT and IV characteristics associated with underdamped behaviour for lower temperatures T T*. We have investigated in detail the behaviour of Josephson junctions around the temperature T* by using Monte Carlo simulations including retrapping from the running state into the supercurrent state as given by the model of Ben-Jacob et al. We develop discussion of the important role of multiple escape and retrapping events in the moderate-damping regime, in particular considering the behaviour in the region close to T*. We show that the behaviour is more fully understood by considering two crossover temperatures, and that the shape of the distribution and s(T) around T*, as well as at lower T<T*, are largely determined by the shape of the conventional thermally activated switching distribution. We show that the characteristic temperatures T* are not unique for a particular Josephson junction, but have some dependence on the ramp rate of the applied bias current. We also consider hysteresis in moderately damped Josephson junctions and discuss the less commonly measured distribution of return currents for a decreasing current ramp. We find that some hysteresis should be expected to persist above T* and we highlight the importance, even well below T*, of accounting properly for thermal fluctuations when determining the damping parameter Q.

cond-mat.supr-con↗

arXiv2003

Decoupling of a Current-Biased Intrinsic Josephson Junction from its Environment

We have observed a dissipative phase diffusion branch in arrays of hysteretic high-Tc intrinsic Josephson junctions. By comparing the data with a thermal activation model we extract the impedance seen by the junction in which phase diffusion is occurring. At the plasma frequency this junction is isolated from its environment and it sees its own large (~ kilo Ohm) impedance. Our results suggest that stacks of Josephson junctions may be used for isolation purposes in the development of a solid state quantum computer.

cond-mat.supr-con↗