arXiv subjects

Andrew C. Doherty

Publications and source records attributed to Andrew C. Doherty.

At least 19 recordsLinked to original sources

arXiv2026

Quantifying Pauli Errors in Single-Photon Resource-State Generation

We propose a scheme to compute Pauli error rates in photonics-based quantum error correction using experimental observables of single photons produced from quantum emitters. We show that first-order coherence measurements and first-order cross correlations, which can be implemented using photon counting, can extract single-photon and entangled single-photon wavefunctions in the presence of imperfections due to photon distinguishability, laser noise, and photon loss. Leveraging this, we show that the wavefunction of any entangled state of noisy photons produced from a single quantum emitter can be expressed in matrix-product-state form and can be used to analytically compute the expectation value of the stabilizer generators of the corresponding entangled state. From this we obtain analytic expressions for the Pauli error probabilities in terms of the photon noise parameters. Furthermore, we calculate Pauli error maps for entangled photons after undergoing Bell- state measurements in terms of these parameters. Our work provides a method to use experimental measurements to determine the required quality of photons produced from quantum emitters for fault-tolerant fusion-based photonics quantum computing.

quant-ph↗

arXiv2025

Ising on the donut: Regimes of topological quantum error correction from statistical mechanics

Utility-scale quantum computers require quantum error correcting codes with large numbers of physical qubits to achieve sufficiently low logical error rates. The performance of quantum error correction (QEC) is generally predicted through large-scale numerical simulations, used to estimate thresholds, finite-size scaling, and exponential suppression of logical errors below threshold. The connection of QEC to models from statistical mechanics provides an alternative tool for analysing QEC performance. However, predicting the behaviour of these models also requires large-scale numerical simulations, as analytic solutions are not generally known. Here we exploit an exact mapping, from a toric code under bit-flip noise that is post-selected on being syndrome free to the exactly-solvable two-dimensional Ising model on a torus, to derive an analytic solution for the logical failure rate across its full domain of physical error rates. In particular, this mapping provides closed-form expressions for the logical failure rate in four distinct regimes: the path-counting, below-threshold (ordered), near-threshold (critical), and above-threshold (disordered) regimes. Our framework places a number of familiar and long-standing numerical observations on firm theoretical ground. It also motivates explicit ans\"atze for the conventional QEC setting of non-post-selected codes whose statistical mechanics mappings involve random-bond disorder. Specifically, we introduce an effective surface tension model for the below-threshold regime, and a new scaling ansatz for the near-threshold regime, derived from an analysis of the ground state energy cost distribution. By bridging statistical mechanics theory and quantum error correction practice, our results offer a new toolkit for designing, benchmarking, and understanding topological codes beyond current computational limits.

quant-ph↗

arXiv2025

Explicit Instances of Quantum Tanner Codes

We construct several explicit instances of quantum Tanner codes, a class of asymptotically good quantum low-density parity check (qLDPC) codes. The codes are constructed using dihedral groups and random pairs of classical codes and exhibit high encoding rates, relative distances, and pseudo-thresholds. Using the BP+OSD decoder, we demonstrate good performance in the phenomenological and circuit-level noise settings, comparable to the surface code with similar distances. Finally, we conduct an analysis of the space-time overhead incurred by these codes.

quant-ph↗

arXiv2025

Improving error suppression with noise-aware decoding

We demonstrate that the performance of quantum error correction can be improved with noise-aware decoders that are calibrated to the likelihood of physical error configurations in a device. We show that noise-aware decoding increases the error suppression factor of the surface code, yielding reductions in the logical error rate that increase exponentially with the code distance. Our calibration protocol involves circuit-level Pauli noise characterisation experiments with averaged circuit eigenvalue sampling. This enables decoder calibration at the scales required for fault-tolerant quantum computation and near-optimal decoding when compared to the true noise model. Our results indicate that these noise characterisation experiments could be performed and processed in seconds for superconducting quantum computers. This establishes the practicality and utility of noise-aware decoding for quantum error correction at scale.

quant-ph↗

arXiv2025

Near-deterministic photon entanglement from a spin qudit in silicon using third quantisation

Unlike other quantum hardware, photonic quantum architectures can produce millions of qubits from a single device. However, controlling photonic qubits remains challenging, even at small scales, due to their weak interactions, making non-deterministic gates in linear optics unavoidable. Nevertheless, a single photon can readily spread over multiple modes and create entanglement within the multiple modes deterministically. Rudolph's concept of third quantization leverages this feature by evolving multiple single-photons into multiple modes, distributing them uniformly and randomly to different parties, and creating multipartite entanglement without interactions between photons or non-deterministic gates. This method requires only classical communication and deterministic entanglement within multi-mode single-photon states and enables universal quantum computing. The multipartite entanglement generated within the third quantization framework is nearly deterministic, where ``deterministic'' is achieved in the asymptotic limit of a large system size. In this work, we propose a near-term experiment using antimony donor in a silicon chip to realize third quantization. Utilizing the eight energy levels of antimony, one can generate two eight-mode single-photon states independently and distribute them to parties. This enables a random multipartite Bell-state experiment, achieving a Bell state with an upper-bound efficiency of 87.5% among 56 random pairs without non-deterministic entangling gates. This approach opens alternative pathways for silicon-based photonic quantum computing.

quant-ph↗

arXiv2024

On the energy barrier of hypergraph product codes

A macroscopic energy barrier is a necessary condition for self-correcting quantum memory. In this paper, we prove tight bounds on the energy barrier applicable to any quantum code obtained from the hypergraph product of two classical codes. If the underlying classical codes are low-density parity-check codes (LDPC), the energy barrier of the quantum code is shown to be the minimum energy barrier of the underlying classical codes (and their transposes) up to an additive $O(1)$ constant.

quant-ph↗

arXiv2024

Scalable noise characterization of syndrome-extraction circuits with averaged circuit eigenvalue sampling

Characterising the performance of noisy quantum circuits is central to the production of prototype quantum computers and can enable improved quantum error correction that exploits noise biases identified in a quantum device. We develop a scalable noise characterisation protocol suited to characterising the syndrome extraction circuits of quantum error correcting codes, a key component of fault-tolerant architectures. Our protocol builds upon averaged circuit eigenvalue sampling (ACES), a framework for noise characterisation experiments that simultaneously estimates the Pauli error probabilities of all gates in a Clifford circuit and captures averaged spatial correlations between gates implemented simultaneously in the layers of the circuit. By rigorously analysing the performance of noise characterisation experiments in the ACES framework, we derive a figure of merit for their expected performance, allowing us to optimise their experimental design and improve the precision to which we estimate noise given fixed experimental resources. We demonstrate the scalability and performance of our protocol through circuit-level numerical simulations of the entire noise characterisation procedure for the syndrome extraction circuit of a distance-25 surface code with over 1000 qubits. Our results indicate that detailed noise characterisation methods are scalable to near-term quantum devices. We release our code in the form of the Julia package QuantumACES.

quant-ph↗

arXiv2024

Logical Gates and Read-Out of Superconducting Gottesman-Kitaev-Preskill Qubits

The Gottesman-Kitaev-Preskill (GKP) code is an exciting route to fault-tolerant quantum computing since Gaussian resources and GKP Pauli-eigenstate preparation are sufficient to achieve universal quantum computing. In this work, we provide a practical proposal to perform Clifford gates and state read-out in GKP codes implemented with active error correction in superconducting circuits. We present a method of performing Clifford circuits without physically implementing any single-qubit gates, reducing the potential for them to spread errors in the system. In superconducting circuits, all the required two-qubit gates can be implemented with a single piece of hardware. We analyze the error-spreading properties of GKP Clifford gates and describe how a modification in the decoder following the implementation of each gate can reduce the gate infidelity by multiple orders of magnitude. Moreover, we develop a simple analytical technique to estimate the effect of loss and dephasing on GKP codes that matches well with numerics. Finally, we consider the effect of homodyne measurement inefficiencies on logical state read-out and present a scheme that implements a measurement with a $0.1\%$ error rate in $630$ ns assuming an efficiency of just~$75\%$.

quant-ph↗

arXiv2023

Concatenating Binomial Codes with the Planar Code

Rotation symmetric bosonic codes are an attractive encoding for qubits into oscillator degrees of freedom, particularly in superconducting qubit experiments. While these codes can tolerate considerable loss and dephasing, they will need to be combined with higher level codes to achieve large-scale devices. We investigate concatenating these codes with the planar code in a measurement-based scheme for fault-tolerant quantum computation. We focus on binomial codes as the base level encoding, and estimate break-even points for such encodings under loss for various types of measurement protocol. These codes are more resistant to photon loss errors, but require both higher mean photon numbers and higher phase resolution for gate operations and measurements. We find that it is necessary to implement adaptive phase measurements, maximum likelihood quantum state inference, and weighted minimum weight decoding to obtain good performance for a planar code using binomial code qubits.

quant-ph↗

arXiv2023

Universal flux-based control of a $\pi$-SQUID

We describe a protocol for the universal control of non-ideal $\pi$-periodic superconducting qubits. Our proposal relies on a $\pi$-SQUID: a superconducting loop formed by two $\pi$-periodic circuit elements, with an external magnetic flux threading the circuit. The system exhibits an extensive sweet spot around half-flux where residual $2\pi$-periodic Cooper pair tunneling is highly suppressed. We demonstrate that universal single-qubit operations can be realised by tuning the flux adiabatically and diabatically within this broad sweet spot. We also assess how residual $2\pi$-periodicity in $\pi$-SQUIDs impacts holonomic phase gates.

quant-ph↗

arXiv2023

No Strings Attached: Boundaries and Defects in the Cubic Code

Haah's cubic code is the prototypical type-II fracton topological order. It instantiates the no string-like operator property that underlies the favorable scaling of its code distance and logical energy barrier. Previously, the cubic code was only explored in translation-invariant systems on infinite and periodic lattices. In these settings, the code distance scales superlinearly with the linear system size, while the number of logical qubits within the degenerate ground space exhibits a complicated functional dependence that undergoes large fluctuations within a linear envelope. Here, we extend the cubic code to systems with open boundary conditions and crystal lattice defects. We characterize the condensation of topological excitations in the vicinity of these boundaries and defects, finding that their inclusion can introduce local string-like operators and enhance the mobility of otherwise fractonic excitations. Despite this, we use these boundaries and defects to define new encodings where the number of logical qubits scales linearly without fluctuations, and the code distance scales superlinearly, with the linear system size. These include a subsystem encoding with open boundary conditions and a subspace encoding using lattice defects.

quant-ph↗

arXiv2023

Edge Theories for Anyon Condensation Phase Transitions

The algebraic tools used to study topological phases of matter are not clearly suited to studying processes in which the bulk energy gap closes, such as phase transitions. We describe an elementary two edge thought experiment which reveals the effect of an anyon condensation phase transition on the robust edge properties of a sample, bypassing a limitation of the algebraic description. In particular, the two edge construction allows some edge degrees of freedom to be tracked through the transition, despite the bulk gap closing. The two edge model demonstrates that bulk anyon condensation induces symmetry breaking in the edge model. Further, the construction recovers the expected result that the number of chiral current carrying modes at the edge cannot change through anyon condensation. We illustrate the construction through detailed analysis of anyon condensation transitions in an achiral phase, the toric code, and in chiral phases, the Kitaev spin liquids.

cond-mat.str-el↗

arXiv2023

Gottesman-Kitaev-Preskill state preparation using periodic driving

The Gottesman-Kitaev-Preskill (GKP) code may be used to overcome noise in continuous variable quantum systems. However, preparing GKP states remains experimentally challenging. We propose a method for preparing GKP states by engineering a time-periodic Hamiltonian whose Floquet states are GKP states. This Hamiltonian may be realized in a superconducting circuit comprising a SQUID shunted by a superinductor and a capacitor, with a characteristic impedance twice the resistance quantum. The GKP Floquet states can be prepared by adiabatically tuning the frequency of the external magnetic flux drive. We predict that highly squeezed $>11.9$ dB ($10.8$ dB) GKP magic states can be prepared on a microsecond timescale, given a quality factor of $10^6$ ($10^5$) and flux noise at typical rates.

quant-ph↗

arXiv2022

Testing Generalised Uncertainty Principles through Quantum Noise

Motivated by several approaches to quantum gravity, there is a considerable literature on generalised uncertainty principles particularly through modification of the canonical position-momentum commutation relations. Some of these modified relations are also consistent with general principles that may be supposed of any physical theory. Such modified commutators have significant observable consequences. Here we study the noisy behaviour of an optomechanical system assuming a certain commonly studied modified commutator. From recent observations of radiation pressure noise in tabletop optomechanical experiments as well as the position noise spectrum of Advanced LIGO we derive bounds on the modified commutator. We find how such experiments can be adjusted to provide significant improvements in such bounds, potentially surpassing those from sub-atomic measurements.

quant-ph↗

arXiv2022

Stabilizer subsystem decompositions for single- and multi-mode Gottesman-Kitaev-Preskill codes

The Gottesman-Kitaev-Preskill (GKP) error correcting code encodes a finite dimensional logical space in one or more bosonic modes, and has recently been demonstrated in trapped ions and superconducting microwave cavities. In this work we introduce a new subsystem decomposition for GKP codes that we call the stabilizer subsystem decomposition, analogous to the usual approach to quantum stabilizer codes. The decomposition has the defining property that a partial trace over the non-logical stabilizer subsystem is equivalent to an ideal decoding of the logical state. We describe how to decompose arbitrary states across the subsystem decomposition using a set of transformations that move between the decompositions of different GKP codes. Besides providing a convenient theoretical view on GKP codes, such a decomposition is also of practical use. We use the stabilizer subsystem decomposition to efficiently simulate noise acting on single-mode GKP codes, and in contrast to more conventional Fock basis simulations, we are able to to consider essentially arbitrarily large photon numbers for realistic noise channels such as loss and dephasing.

quant-ph↗

arXiv2019

Performance of quantum error correction with coherent errors

We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes we analytically compute the effective logical channel that results when the error correction steps are performed noiselessly. Our examples include the entire family of repetition codes, the 5-qubit, Steane, Shor, and surface codes. When errors are measured in terms of the diamond norm, we find that the error correction is typically much more effective for unitary errors than for dephasing. We observe this behavior for a wide range of codes after a single level of encoding, and in the thresholds of concatenated codes using hard decoders. We show that this holds with great generality by proving a bound on the performance of any stabilizer code when the noise at the physical level is unitary. By comparing the diamond norm error $D'_\diamond$ of the logical qubit with the same quantity at the physical level $D_\diamond$, we show that $D'_\diamond \le c D^d_\diamond $ where $d$ is the distance of the code and $c$ is constant that depends on the code but not on the error. This bound compares very favorably to the performance of error correction for dephasing noise and other Pauli channels, where an error correcting code of odd distance $d$ will exhibit a scaling $D'_\diamond \sim D_\diamond^{(d+1)/2}$.

quant-ph↗

arXiv2018

Fast spin exchange between two distant quantum dots

The Heisenberg exchange interaction between neighboring quantum dots allows precise voltage control over spin dynamics, due to the ability to precisely control the overlap of orbital wavefunctions by gate electrodes. This allows the study of fundamental electronic phenomena and finds applications in quantum information processing. Although spin-based quantum circuits based on short-range exchange interactions are possible, the development of scalable, longer-range coupling schemes constitutes a critical challenge within the spin-qubit community. Approaches based on capacitative coupling and cavity-mediated interactions effectively couple spin qubits to the charge degree of freedom, making them susceptible to electrically-induced decoherence. The alternative is to extend the range of the Heisenberg exchange interaction by means of a quantum mediator. Here, we show that a multielectron quantum dot with 50-100 electrons serves as an excellent mediator, preserving speed and coherence of the resulting spin-spin coupling while providing several functionalities that are of practical importance. These include speed (mediated two-qubit rates up to several gigahertz), distance (of order of a micrometer), voltage control, possibility of sweet spot operation (reducing susceptibility to charge noise), and reversal of the interaction sign (useful for dynamical decoupling from noise).

cond-mat.mes-hall↗

arXiv2018

Optimizing practical entanglement distillation

The goal of entanglement distillation is to turn a large number of weakly entangled states into a smaller number of highly entangled ones. Practical entanglement distillation schemes offer a tradeoff between the fidelity to the target state, and the probability of successful distillation. Exploiting such tradeoffs is of interest in the design of quantum repeater protocols. Here, we present a number of methods to assess and optimize entanglement distillation schemes. We start by giving a numerical method to compute upper bounds on the maximum achievable fidelity for a desired probability of success. We show that this method performs well for many known examples by comparing it to well-known distillation protocols. This allows us to show optimality for many well-known distillation protocols for specific states of interest. As an example, we analytically prove optimality of the distillation protocol utilized within the Extreme Photon Loss (EPL) entanglement generation scheme, even in the asymptotic limit. We proceed to present a numerical method that can improve an existing distillation scheme for a given input state, and we present an example for which this method finds an optimal distillation protocol. An implementation of our numerical methods is available as a Julia package.

quant-ph↗