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Richard Jozsa

Publications and source records attributed to Richard Jozsa.

At least 19 recordsLinked to original sources

Taming Volatility: Stable and Private QUIC Classification with Federated Learning

Federated Learning (FL) is a promising approach for privacy-preserving network traffic analysis, but its practical deployment is challenged by the non-IID nature of real-world data. While prior work has addressed statistical heterogeneity, the impact of temporal traffic volatility-the natural daily ebb and flow of network activity-on model stability remains largely unexplored. This volatility can lead to inconsistent data availability at clients, destabilizing the entire training process. In this paper, we systematically address the problem of temporal volatility in federated QUIC classification. We first demonstrate the instability of standard FL in this dynamic setting. We then propose and evaluate a client-side data buffer as a practical mechanism to ensure stable and consistent local training, decoupling it from real-time traffic fluctuations. Using the real-world CESNET-QUIC22 dataset partitioned into 14 autonomous clients, we then demonstrate that this approach enables robust convergence. Our results show that a stable federated system achieves a 95.2% F1 score, a mere 2.3 percentage points below a non-private centralized model. This work establishes a blueprint for building operationally stable FL systems for network management, proving that the challenges of dynamic network environments can be overcome with targeted architectural choices.

cs.NI

IQP computations with intermediate measurements

We consider the computational model of IQP circuits (in which all computational steps are $X$ basis diagonal gates), supplemented by intermediate $X$ or $Z$ basis measurements. We show that if we allow non-adaptive or adaptive $X$ basis measurements, or allow non-adaptive $Z$ basis measurements, then the computational power remains the same as that of the original IQP model; and with adaptive $Z$ basis measurements the model becomes quantum universal. Furthermore we show that the computational model having circuits of only $CZ$ gates and adaptive $X$ basis measurements, with input states that are tensor products of 1-qubit states from the set $\{ |+\rangle, |1\rangle,\frac{1}{\sqrt{2}}(|0\rangle+i|1\rangle), \frac{1}{\sqrt{2}}(|0\rangle+e^{i\pi/4}|1\rangle) \} $, is quantum universal. In contrast to the relation of IQP to PH collapse, all our results here are manifestly stable under small additive implementational errors.

quant-ph

Early-Stage Anomaly Detection: A Study of Model Performance on Complete vs. Partial Flows

This study investigates the efficacy of machine learning models in network security threat detection through the critical lens of partial versus complete flow information, addressing a common gap between research settings and real-time operational needs. We systematically evaluate how a standard benchmark model, Random Forest, performs under varying training and testing conditions (complete/complete, partial/partial, complete/partial), quantifying the performance impact when dealing with the incomplete data typical in real-time environments. Our findings demonstrate a significant performance difference, with precision and recall dropping by up to 30% under certain conditions when models trained on complete flows are tested against partial flows. The study also reveals that, for the evaluated dataset and model, a minimum threshold around 7 packets in the test set appears necessary for maintaining reliable detection rates, providing valuable, quantified insights for developing more realistic real-time detection strategies.

cs.LG

Evaluating ML-Based Anomaly Detection Across Datasets of Varied Integrity: A Case Study

Cybersecurity remains a critical challenge in the digital age, with network traffic flow anomaly detection being a key pivotal instrument in the fight against cyber threats. In this study, we address the prevalent issue of data integrity in network traffic datasets, which are instrumental in developing machine learning (ML) models for anomaly detection. We introduce two refined versions of the CICIDS-2017 dataset, NFS-2023-nTE and NFS-2023-TE, processed using NFStream to ensure methodologically sound flow expiration and labeling. Our research contrasts the performance of the Random Forest (RF) algorithm across the original CICIDS-2017, its refined counterparts WTMC-2021 and CRiSIS-2022, and our NFStream-generated datasets, in both binary and multi-class classification contexts. We observe that the RF model exhibits exceptional robustness, achieving consistent high-performance metrics irrespective of the underlying dataset quality, which prompts a critical discussion on the actual impact of data integrity on ML efficacy. Our study underscores the importance of continual refinement and methodological rigor in dataset generation for network security research. As the landscape of network threats evolves, so must the tools and techniques used to detect and analyze them.

cs.LG

Computational power of matchgates with supplementary resources

We study the classical simulation complexity in both the weak and strong senses, of matchgate (MG) computations supplemented with all combinations of settings involving inclusion of intermediate adaptive or nonadaptive computational basis measurements, product state or magic and general entangled state inputs, and single- or multi-line outputs. We find a striking parallel to known results for Clifford circuits, after some rebranding of resources. We also give bounds on the amount of classical simulation effort required in case of limited access intermediate measurements and entangled inputs. In further settings we show that adaptive MG circuits remain classically efficiently simulable if arbitrary two-qubit entangled input states on consecutive lines are allowed, but become quantum universal for three or more lines. And if adaptive measurements in non-computational bases are allowed, even with just computational basis inputs, we get quantum universal power again.

quant-ph

All pure fermionic non-Gaussian states are magic states for matchgate computations

Magic states were introduced in the context of Clifford circuits as a resource that elevates classically simulatable computations to quantum universal capability, while maintaining the same gate set. Here we study magic states in the context of matchgate (MG) circuits, where the notion becomes more subtle, as MGs are subject to locality constraints and also the SWAP gate is not available. Nevertheless a similar picture of gate-gadget constructions applies, and we show that every pure fermionic state which is non-Gaussian, i.e. which cannot be generated by MGs from a computational basis state, is a magic state for MG computations. This result has significance for prospective quantum computing implementation in view of the fact that MG circuit evolutions coincide with the quantum physical evolution of non-interacting fermions.

quant-ph

Quantum advantage of unitary Clifford circuits with magic state inputs

We study the computational power of unitary Clifford circuits with solely magic state inputs (CM circuits), supplemented by classical efficient computation. We show that CM circuits are hard to classically simulate up to multiplicative error (assuming PH non-collapse), and also up to additive error under plausible average-case hardness conjectures. Unlike other such known classes, a broad variety of possible conjectures apply. Along the way we give an extension of the Gottesman-Knill theorem that applies to universal computation, showing that for Clifford circuits with joint stabiliser and non-stabiliser inputs, the stabiliser part can be eliminated in favour of classical simulation, leaving a Clifford circuit on only the non-stabiliser part. Finally we discuss implementational advantages of CM circuits.

quant-ph

Implementing smooth functions of a Hermitian matrix on a quantum computer

We review existing methods for implementing smooth functions f(A) of a sparse Hermitian matrix A on a quantum computer, and analyse a further combination of these techniques which has some advantages of simplicity and resource consumption in some cases. Our construction uses the linear combination of unitaries method with Chebyshev polynomial approximations. The query complexity we obtain is O(log C/eps) where eps is the approximation precision, and C>0 is an upper bound on the magnitudes of the derivatives of the function f over the domain of interest. The success probability depends on the 1-norm of the Taylor series coefficients of f, the sparsity d of the matrix, and inversely on the smallest singular value of the target matrix f(A).

quant-ph

Efficient classical verification of quantum computations

We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious adversarial behaviour in the misfunctioning of the quantum computing device. Our scheme is not secure against arbitrarily adversarial behaviour, but may nevertheless be sufficiently acceptable in many practical situations. With this concession we gain in manifest simplicity and transparency, and in contrast to previous schemes, our verifier is entirely classical. It is based on the fact that adaptive Clifford circuits on general product state inputs provide universal quantum computation, while the same processes without adaptation are always classically efficiently simulatable.

quant-ph

Quantum conditional query complexity

We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups over the best known quantum algorithms for identity testing, equivalence testing and uniformity testing of probability distributions; (b) study the power of these oracles for testing properties of boolean functions, and obtain an algorithm for checking whether an $n$-input $m$-output boolean function is balanced or $ε$-far from balanced; and (c) give a sub-linear algorithm, requiring $\tilde{O}(n^{3/4}/ε)$ queries, for testing whether an $n$-dimensional quantum state is maximally mixed or not.

quant-ph

Jordan-Wigner formalism for arbitrary 2-input 2-output matchgates and their classical simulation

In Valiant's matchgate theory, 2-input 2-output matchgates are 4x4 matrices that satisfy ten so-called matchgate identities. We prove that the set of all such matchgates (including non-unitary and non-invertible ones) coincides with the topological closure of the set of all matrices obtained as exponentials of linear combinations of the 2-qubit Jordan-Wigner (JW) operators and their quadratic products, extending a previous result of Knill. In Valiant's theory, outputs of matchgate circuits can be classically computed in poly-time. Via the JW formalism, Terhal & DiVincenzo and Knill established a relation of a unitary class of these circuits to the efficient simulation of non-interacting fermions. We describe how the JW formalism may be used to give an efficient simulation for all cases in Valiant's simulation theorem, which in particular includes the case of non-interacting fermions generalised to allow arbitrary 1-qubit gates on the first line at any stage in the circuit. Finally we give an exposition of how these simulation results can be alternatively understood from some basic Lie algebra theory, in terms of a formalism introduced by Somma et al.

quant-ph

Symmetric polynomials in information theory: entropy and subentropy

Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities, and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore we see that H and the intrinsically quantum informational quantity Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials we also derive a series of further properties of H and Q.

quant-ph

Entropy, subentropy and the elementary symmetric functions

We use complex contour integral techniques to study the entropy H and subentropy Q as functions of the elementary symmetric polynomials, revealing a series of striking properties. In particular for these variables, derivatives of -Q are equal to derivatives of H of one higher order and the first derivatives of H and Q are seen to be completely monotone functions. It then follows that exp (-H) and exp(-Q) are Laplace transforms of infinitely divisible probability distributions.

quant-ph

Properties of subentropy

Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's theorem. Here we establish a series of properties of subentropy, paralleling the well-developed analogous theory for von Neumann entropy. Further, we show that subentropy is a lower bound for min-entropy. We introduce a notion of conditional subentropy and show that it can be used to provide an upper bound for the guessing probability of any classical-quantum state of two qubits; we conjecture that the bound applies also in higher dimensions. Finally we give an operational interpretation of subentropy within classical information theory.

quant-ph

On exact quantum query complexity

We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these functions cannot be obtained by simply computing parities of pairs of bits. We also characterise the model of nonadaptive exact quantum query complexity in terms of coding theory and completely characterise the query complexity of symmetric boolean functions in this context. These results were originally inspired by numerically solving the semidefinite programs characterising quantum query complexity for small problem sizes. We include numerical results giving the optimal success probabilities achievable by quantum algorithms computing all boolean functions on up to 4 bits, and all symmetric boolean functions on up to 6 bits.

quant-ph

Classical simulation complexity of extended Clifford circuits

Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true only in a suitably restricted setting. Here we consider Clifford computations with a variety of additional ingredients: (a) strong vs. weak simulation, (b) inputs being computational basis states vs. general product states, (c) adaptive vs. non-adaptive choices of gates for circuits involving intermediate measurements, (d) single line outputs vs. multi-line outputs. We consider the classical simulation complexity of all combinations of these ingredients and show that many are not classically efficiently simulatable (subject to common complexity assumptions such as P not equal to NP). Our results reveal a surprising proximity of classical to quantum computing power viz. a class of classically simulatable quantum circuits which yields universal quantum computation if extended by a purely classical additional ingredient that does not extend the class of quantum processes occurring.

quant-ph

Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient classical means. More specifically we introduce the class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection, and prove first that post-IQP equals the classical class PP. Using this result we show that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, even up to 41% multiplicative error in the probabilities, then the infinite tower of classical complexity classes known as the polynomial hierarchy, would collapse to its third level. We mention some further results on the classical simulation properties of IQP circuit families, in particular showing that if the output distribution results from measurements on only O(log n) lines then it may in fact be classically efficiently sampled.

quant-ph

Matchgate and space-bounded quantum computations are equivalent

Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and one-dimensional spin chains. We show that the computational power of circuits of matchgates is equivalent to that of space-bounded quantum computation with unitary gates, with space restricted to being logarithmic in the width of the matchgate circuit. In particular, for the conventional setting of polynomial-sized (logarithmic-space generated) families of matchgate circuits, known to be classically simulatable, we characterise their power as coinciding with polynomial-time and logarithmic-space bounded universal unitary quantum computation.

quant-ph