arXiv subjects

Chris N. Self

Publications and source records attributed to Chris N. Self.

17 recordsLinked to original sources

arXiv2026

End-to-End Quantum Algorithms for the Jones Polynomial

We present an end-to-end algorithmic pipeline where a noisy digital quantum computer is used to approximate the value of the Jones polynomial at the fifth root of unity for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we develop and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The reconfigurable tools provided in this work allow for precise resource estimation to identify minimum link sizes for near-term quantum advantage in practice for a meaningful quantum-native problem in knot theory, if a candidate set of links are provided.

quant-ph↗

arXiv2026

Computing with many encoded logical qubits beyond break-even

High-rate quantum error correcting (QEC) codes encode many logical qubits in a given number of physical qubits, making them promising candidates for quantum computation. Implementing high-rate codes at a scale that both frustrates classical computing and improves performance by encoding requires both high fidelity gates and long-range qubit connectivity -- both of which are offered by trapped-ion quantum computers. Here, we demonstrate computations that outperform their unencoded counterparts in the high-rate $[[ k+2,\, k,\, 2 ]]$ iceberg quantum error detecting (QED) and $[[ (k_2 + 2)(k_1 + 2),\, k_2k_1,\, 4 ]]$ two-level concatenated iceberg QEC codes, using the 98-qubit Quantinuum Helios trapped-ion quantum processor. Utilizing new gadgets for encoded operations, we realize this "beyond break-even" performance with reasonable postselection rates across a range of fault-tolerant (FT) and partially-fault-tolerant (pFT) component and application benchmarks with between $48$ and $94$ logical qubits. These benchmarks include FT state preparation and measurement, QEC cycle benchmarking, logical gate benchmarking, GHZ state preparation, and a pFT quantum simulation of the three-dimensional $XY$ model of quantum magnetism. Additionally, we illustrate that postselection rates can be suppressed by increasing the code distance via concatenation. Our results represent state-of-the-art logical component and state fidelities and provide evidence that high-rate QED/QEC codes are viable on contemporary quantum computers for near-term beyond-classical-scale computation.

quant-ph↗

arXiv2025

Certified randomness amplification by dynamically probing remote random quantum states

Cryptography depends on truly unpredictable numbers, but physical sources emit biased or correlated bits. Quantum mechanics enables the amplification of imperfect randomness into nearly perfect randomness, but prior demonstrations have required physically co-located, loophole-free Bell tests, constraining the feasibility of remote operation. Here we realize certified randomness amplification across a network by dynamically probing large, entangled quantum states on Quantinuum's 98-qubit Helios trapped-ion quantum processor. Our protocol is secure even if the remote device acts maliciously or is compromised by an intercepting adversary, provided the samples are generated quickly enough to preclude classical simulation of the quantum circuits. We stream quantum gates in real time to the quantum processor, maintain quantum state coherence for $\approx 0.9$ seconds, and then reveal the measurement bases to the quantum processor only milliseconds before measurement. This limits the time for classical spoofing to 30 ms and constrains the location of hypothetical adversaries to a $4{,}500$ km radius. We achieve a fidelity of 0.586 on random circuits with 64 qubits and 276 two-qubit gates, enabling the amplification of realistic imperfect randomness with a low entropy rate into nearly perfect randomness.

quant-ph↗

arXiv2025

Measuring Correlation and Entanglement between Molecular Orbitals on a Trapped-Ion Quantum Computer

Quantifying correlation and entanglement between molecular orbitals can elucidate the role of quantum effects in strongly correlated reaction processes. However, accurately storing the wavefunction for a classical computation of those quantities can be prohibitive. Here we use the Quantinuum H1-1 trapped-ion quantum computer to calculate von Neumann entropies which quantify the orbital correlation and entanglement in a strongly correlated molecular system relevant to lithium-ion batteries (vinylene carbonate interacting with an O$_2$ molecule). As shown in previous works, fermionic superselection rules decrease correlations and reduce measurement overheads for constructing orbital reduced density matrices. Taking into account superselection rules we further reduce the number of measurements by finding commuting sets of Pauli operators. Using low overhead noise reduction techniques we calculate von Neumann entropies in excellent agreement with noiseless benchmarks, indicating that correlations and entanglement between molecular orbitals can be accurately estimated from a quantum computation. Our results show that the one-orbital entanglement vanishes unless opposite-spin open shell configurations are present in the wavefunction.

quant-ph↗

arXiv2025

Estimating the Jones polynomial for Ising anyons on noisy quantum computers

The evaluation of the Jones polynomial at roots of unity is a paradigmatic problem for quantum computers. In this work we present experimental results obtained from existing noisy quantum computers for special cases of this problem, where it is classically tractable. Our approach relies on the reduction of the problem of evaluating the Jones polynomial of a knot at lattice roots of unity to the problem of computing quantum amplitudes of qudit stabiliser circuits, which are classically efficiently simulatable. More specifically, we focus on evaluation at the fourth root of unity, which is a lattice root of unity, where the problem reduces to evaluating amplitudes of qubit stabiliser circuits. To estimate the real and imaginary parts of the amplitudes up to additive error we use the Hadamard test, yielding non-Clifford circuits that nevertheless we can always efficiently compute the correct output of. Hence, we further argue that this setup defines a standard benchmark for near-term noisy quantum processors. Additionally, we study the benefit of performing quantum error mitigation with the method of zero noise extrapolation.

quant-ph↗

arXiv2024

Protecting Expressive Circuits with a Quantum Error Detection Code

A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing quantum computers. In this context we develop a quantum error detection code for implementations on existing trapped-ion computers. By encoding $k$ logical qubits into $k+2$ physical qubits, this code presents fault-tolerant state initialisation and syndrome measurement circuits that can detect any single-qubit error. It provides a universal set of local and global logical rotations that have physical support on only two qubits. A high-fidelity -- though non fault-tolerant -- compilation of this universal gate set is possible thanks to the two-qubit physical rotations present in trapped-ion computers with all-to-all connectivity. Given the particular structure of the logical operators, we nickname it the Iceberg code. We demonstrate the protection of circuits of 8 logical qubits with up to 256 layers, saturate the logical quantum volume of $2^8$, and show the positive effect of increasing the frequency of syndrome measurements within the circuit. These results illustrate the practical usefulness of the Iceberg code to protect expressive circuits on existing trapped-ion quantum computers.

quant-ph↗

arXiv2023

Characterization of variational quantum algorithms using free fermions

We study variational quantum algorithms from the perspective of free fermions. By deriving the explicit structure of the associated Lie algebras, we show that the Quantum Approximate Optimization Algorithm (QAOA) on a one-dimensional lattice -- with and without decoupled angles -- is able to prepare all fermionic Gaussian states respecting the symmetries of the circuit. Leveraging these results, we numerically study the interplay between these symmetries and the locality of the target state, and find that an absence of symmetries makes nonlocal states easier to prepare. An efficient classical simulation of Gaussian states, with system sizes up to $80$ and deep circuits, is employed to study the behavior of the circuit when it is overparameterized. In this regime of optimization, we find that the number of iterations to converge to the solution scales linearly with system size. Moreover, we observe that the number of iterations to converge to the solution decreases exponentially with the depth of the circuit, until it saturates at a depth which is quadratic in system size. Finally, we conclude that the improvement in the optimization can be explained in terms of better local linear approximations provided by the gradients.

quant-ph↗

arXiv2022

Quantum machine learning of large datasets using randomized measurements

Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum kernels are impractical for large datasets as they scale with the square of the dataset size. Here, we measure quantum kernels using randomized measurements. The quantum computation time scales linearly with dataset size and quadratic for classical post-processing. While our method scales in general exponentially in qubit number, we gain a substantial speed-up when running on intermediate-sized quantum computers. Further, we efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth. The encoding is characterized by the quantum Fisher information metric and is related to the radial basis function kernel. Our approach is robust to noise via a cost-free error mitigation scheme. We demonstrate the advantages of our methods for noisy quantum computers by classifying images with the IBM quantum computer. To achieve further speedups we distribute the quantum computational tasks between different quantum computers. Our method enables benchmarking of quantum machine learning algorithms with large datasets on currently available quantum computers.

quant-ph↗

arXiv2021

Qubit Readout Error Mitigation with Bit-flip Averaging

Quantum computers are becoming increasingly accessible, and may soon outperform classical computers for useful tasks. However, qubit readout errors remain a significant hurdle to running quantum algorithms on current devices. We present a scheme to more efficiently mitigate these errors on quantum hardware and numerically show that our method consistently gives advantage over previous mitigation schemes. Our scheme removes biases in the readout errors allowing a general error model to be built with far fewer calibration measurements. Specifically, for reading out $n$-qubits we show a factor of $2^n$ reduction in the number of calibration measurements without sacrificing the ability to compensate for correlated errors. Our approach can be combined with, and simplify, other mitigation methods allowing tractable mitigation even for large numbers of qubits.

quant-ph↗

arXiv2021

Variational quantum algorithm with information sharing

We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining multi-dimensional energy surfaces for small molecules and a spin model. Our method solves related variational problems in parallel by exploiting the global nature of Bayesian optimisation and sharing information between different optimisers. Parallelisation makes our method ideally suited to next generation of variational problems with many physical degrees of freedom. This addresses a key challenge in scaling-up quantum algorithms towards demonstrating quantum advantage for problems of real-world interest.

quant-ph↗

arXiv2020

Quantum Delocalised-Interactions

Classical mechanics obeys the intuitive logic that a physical event happens at a definite spatial point. Entanglement however, breaks this logic by enabling interactions without a specific location. In this work we study these delocalised-interactions. These are quantum interactions that create less locational information than would be possible classically, as captured by the disturbance induced on some spatial superposition state. We introduce quantum games to capture the effect and demonstrate a direct operational use for quantum concurrence in that it bounds the non-classical performance gain. We also find a connection with quantum teleportation, and demonstrate the games using an IBM quantum processor.

quant-ph↗

arXiv2020

Geometric description of the Kitaev honeycomb lattice model

It is widely accepted that topological superconductors can only have an effective interpretation in terms of curved geometry rather than gauge fields due to their charge neutrality. This approach is commonly employed in order to investigate their properties, such as the behaviour of their energy currents. Nevertheless, it is not known how accurately curved geometry can describe actual microscopic models. Here, we demonstrate that the low-energy properties of the Kitaev honeycomb lattice model, a topological superconductor that supports localised Majorana zero modes at its vortex excitations, are faithfully described in terms of Riemann-Cartan geometry. In particular, we show analytically that the continuum limit of the model is given in terms of the Majorana version of the Dirac Hamiltonian coupled to both curvature and torsion. We numerically establish the accuracy of the geometric description for a wide variety of couplings of the microscopic model. Our work opens up the opportunity to accurately predict dynamical properties of the Kitaev model from its effective geometric description.

cond-mat.str-el↗

arXiv2020

Topological bulk states and their currents

We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localised bulk states deep in their valance and conduction bands. These states manifest when local potential gradients are applied to the bulk, while all parts of the system remain adiabatically connected to the same phase. In turn, the bulk states produce bulk current transverse to the strain. This occurs even when the potential is always below the energy gap, where one expects only edge currents to appear. Bulk currents are topologically protected and behave like edge currents under external influence, such as temperature or local disorder. Detecting topologically resilient bulk currents offers a direct means to probe the localised bulk states.

cond-mat.mes-hall↗

arXiv2019

Seeing topological edge and bulk currents in time-of-flight images

Here we provide a general methodology to directly measure the topological currents emerging in the optical lattice implementation of the Haldane model. Alongside the edge currents supported by gapless edge states, transverse currents can emerge in the bulk of the system whenever the local potential is varied in space, even if it does not cause a phase transition. In optical lattice implementations the overall harmonic potential that traps the atoms provides the boundaries of the topological phase that supports the edge currents, as well as providing the potential gradient across the topological phase that gives rise to the bulk current. Both the edge and bulk currents are resilient to several experimental parameters such as trapping potential, temperature and disorder. We propose to investigate the properties of these currents directly from time-of-flight images with both short-time and long-time expansions.

cond-mat.mes-hall↗

arXiv2018

Thermally induced metallic phase in a gapped quantum spin liquid - a Monte Carlo study of the Kitaev model with parity projection

Thermalisation is a probabilistic process. As such, it is generally expected that when we increase the temperature of a system its classical behaviour dominates its quantum coherences. By employing the Gibbs state of a translationally invariant quantum spin liquid - Kitaev's honeycomb lattice model - we demonstrate that an insulating phase at $T=0$ becomes metallic purely by increasing temperature. In particular, we compute the finite temperature distribution of energies and show that it diverges logarithmically, as we move to small energies. The corresponding wave functions become critical alike as at Anderson transitions. These characteristics are obtained within a new exact Monte Carlo method that simulates the finite temperature behaviour of the Kitaev model. In particular, we take into account the projection onto the physical parity sectors, required for identifying the topological degeneracy of the model. Our work opens the possibility to detect thermal metal behaviour in spin liquid experiments.

cond-mat.str-el↗

arXiv2017

Conformal energy currents on the edge of a topological superconductor

The boundary of a 2D topological superconductor can be modeled by a conformal field theory. Here we demonstrate the behaviors of this high level description emerging from a microscopic model at finite temperatures. To achieve that, we analyze the low energy sector of Kitaev's honeycomb lattice model and probe its energy current. We observe that the scaling of the energy current with temperature reveals the central charge of the conformal field theory, which is in agreement with the Chern number of the bulk. Importantly, these currents can discriminate between distinct topological phases at finite temperatures. We assess the resilience of this measurement of the central charge under coupling disorder, bulk dimerisation and defects at the boundary, thus establishing it as a favorable means of experimentally probing topological superconductors.

cond-mat.str-el↗

arXiv2016

Quantum memories at finite temperature

To use quantum systems for technological applications we first need to preserve their coherence for macroscopic timescales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a quantum memory. An attractive scenario is the construction of passive storage of quantum information with minimal active support. Indeed, passive protection is the basis of robust and scalable classical technology, physically realized in the form of the transistor and the ferromagnetic hard disk. The discovery of an analogous quantum system is a challenging open problem, plagued with a variety of no-go theorems. Several approaches have been devised to overcome these theorems by taking advantage of their loopholes. Here we review the state-of-the-art developments in this field in an informative and pedagogical way. We give the main principles of self-correcting quantum memories and we analyze several milestone examples from the literature of two-, three- and higher-dimensional quantum memories.

quant-ph↗