arXiv subjects

Petros Wallden

Publications and source records attributed to Petros Wallden.

At least 37 records · Page 2Linked to original sources

arXiv2024

A Brief Review of Quantum Machine Learning for Financial Services

This review paper examines state-of-the-art algorithms and techniques in quantum machine learning with potential applications in finance. We discuss QML techniques in supervised learning tasks, such as Quantum Variational Classifiers, Quantum Kernel Estimation, and Quantum Neural Networks (QNNs), along with quantum generative AI techniques like Quantum Transformers and Quantum Graph Neural Networks (QGNNs). The financial applications considered include risk management, credit scoring, fraud detection, and stock price prediction. We also provide an overview of the challenges, potential, and limitations of QML, both in these specific areas and more broadly across the field. We hope that this can serve as a quick guide for data scientists, professionals in the financial sector, and enthusiasts in this area to understand why quantum computing and QML in particular could be interesting to explore in their field of expertise.

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arXiv2024

Adiabatic quantum computing with parameterized quantum circuits

Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term devices, a number of hybrid approaches have been pursued in which a parameterized quantum circuit prepares and measures quantum states and a classical optimization algorithm minimizes an objective function that encompasses the solution to the problem of interest. In this work, we propose a different approach starting by analyzing how a small perturbation of a Hamiltonian affects the parameters that minimize the energy within a family of parameterized quantum states. We derive a set of equations that allow us to compute the new minimum by solving a constrained linear system of equations that is obtained from measuring a series of observables on the unperturbed system. We then propose a discrete version of adiabatic quantum computing that can be implemented in a near-term device while at the same time is insensitive to the initialization of the parameters and to other limitations hindered in the optimization part of variational quantum algorithms. We compare our proposed algorithm with the Variational Quantum Eigensolver on two classical optimization problems, namely MaxCut and Number Partitioning, and on a quantum-spin configuration problem, the Transverse-Field Ising Chain model, and confirm that our approach demonstrates superior performance.

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arXiv2024

Grover's oracle for the Shortest Vector Problem and its application in hybrid classical-quantum solvers

Finding the shortest vector in a lattice is a problem that is believed to be hard both for classical and quantum computers. Many major post-quantum secure cryptosystems base their security on the hardness of the Shortest Vector Problem (SVP). Finding the best classical, quantum or hybrid classical-quantum algorithms for SVP is necessary to select cryptosystem parameters that offer sufficient level of security. Grover's search quantum algorithm provides a generic quadratic speed-up, given access to an oracle implementing some function which describes when a solution is found. In this paper we provide concrete implementation of such an oracle for the SVP. We define the circuit, and evaluate costs in terms of number of qubits, number of gates, depth and T-quantum cost. We then analyze how to combine Grover's quantum search for small SVP instances with state-of-the-art classical solvers that use well known algorithms, such as the BKZ, where the former is used as a subroutine. This could enable solving larger instances of SVP with higher probability than classical state-of-the-art records, but still very far from posing any threat to cryptosystems being considered for standardization. Depending on the technology available, there is a spectrum of trade-offs in creating this combination.

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arXiv2024

Big data applications on small quantum computers

Current quantum hardware prohibits any direct use of large classical datasets. Coresets allow for a succinct description of these large datasets and their solution in a computational task is competitive with the solution on the original dataset. The method of combining coresets with small quantum computers to solve a given task that requires a large number of data points was first introduced by Harrow [arXiv:2004.00026]. In this paper, we apply the coreset method in three different well-studied classical machine learning problems, namely Divisive Clustering, 3-means Clustering, and Gaussian Mixture Model Clustering. We provide a Hamiltonian formulation of the aforementioned problems for which the number of qubits scales linearly with the size of the coreset. Then, we evaluate how the variational quantum eigensolver (VQE) performs on these problems and demonstrate the practical efficiency of coresets when used along with a small quantum computer. We perform noiseless simulations on instances of sizes up to 25 qubits on CUDA Quantum and show that our approach provides comparable performance to classical solvers.

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arXiv2023

Quantum Multi-Solution Bernoulli Search with Applications to Bitcoin's Post-Quantum Security

A proof of work (PoW) is an important cryptographic construct enabling a party to convince others that they invested some effort in solving a computational task. Arguably, its main impact has been in the setting of cryptocurrencies such as Bitcoin and its underlying blockchain protocol, which received significant attention in recent years due to its potential for various applications as well as for solving fundamental distributed computing questions in novel threat models. PoWs enable the linking of blocks in the blockchain data structure and thus the problem of interest is the feasibility of obtaining a sequence (chain) of such proofs. In this work, we examine the hardness of finding such chain of PoWs against quantum strategies. We prove that the chain of PoWs problem reduces to a problem we call multi-solution Bernoulli search, for which we establish its quantum query complexity. Effectively, this is an extension of a threshold direct product theorem to an average-case unstructured search problem. Our proof, adding to active recent efforts, simplifies and generalizes the recording technique of Zhandry (Crypto'19). As an application, we revisit the formal treatment of security of the core of the Bitcoin consensus protocol, the Bitcoin backbone (Eurocrypt'15), against quantum adversaries, while honest parties are classical and show that protocol's security holds under a quantum analogue of the classical ``honest majority'' assumption. Our analysis indicates that the security of Bitcoin backbone is guaranteed provided the number of adversarial quantum queries is bounded so that each quantum query is worth $O(p^{-1/2})$ classical ones, where $p$ is the success probability of a single classical query to the protocol's underlying hash function. Somewhat surprisingly, the wait time for safe settlement in the case of quantum adversaries matches the safe settlement time in the classical case.

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arXiv2023

Variational quantum solutions to the Shortest Vector Problem

A fundamental computational problem is to find a shortest non-zero vector in Euclidean lattices, a problem known as the Shortest Vector Problem (SVP). This problem is believed to be hard even on quantum computers and thus plays a pivotal role in post-quantum cryptography. In this work we explore how (efficiently) Noisy Intermediate Scale Quantum (NISQ) devices may be used to solve SVP. Specifically, we map the problem to that of finding the ground state of a suitable Hamiltonian. In particular, (i) we establish new bounds for lattice enumeration, this allows us to obtain new bounds (resp.~estimates) for the number of qubits required per dimension for any lattices (resp.~random q-ary lattices) to solve SVP; (ii) we exclude the zero vector from the optimization space by proposing (a) a different classical optimisation loop or alternatively (b) a new mapping to the Hamiltonian. These improvements allow us to solve SVP in dimension up to 28 in a quantum emulation, significantly more than what was previously achieved, even for special cases. Finally, we extrapolate the size of NISQ devices that is required to be able to solve instances of lattices that are hard even for the best classical algorithms and find that with approximately $10^3$ noisy qubits such instances can be tackled.

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arXiv2022

An evolving objective function for improved variational quantum optimisation

A promising approach to useful computational quantum advantage is to use variational quantum algorithms for optimisation problems. Crucial for the performance of these algorithms is to ensure that the algorithm converges with high probability to a near-optimal solution in a small time. In Barkoutsos et al (Quantum 2020) an alternative class of objective functions, called Conditional Value-at-Risk (CVaR), was introduced and it was shown that they perform better than standard objective functions. Here we extend that work by introducing an evolving objective function, which we call Ascending-CVaR and that can be used for any optimisation problem. We test our proposed objective function, in an emulation environment, using as case-studies three different optimisation problems: Max-Cut, Number Partitioning and Portfolio Optimisation. We examine multiple instances of different sizes and analyse the performance using the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz and the Quantum Approximate Optimization Algorithm (QAOA). We show that Ascending-CVaR in all cases performs better than standard objective functions or the "constant" CVaR of Barkoutsos et al (Quantum 2020) and that it can be used as a heuristic for avoiding sub-optimal minima. Our proposal achieves higher overlap with the ideal state in all problems, whether we consider easy or hard instances -- on average it gives up to ten times greater overlap at Portfolio Optimisation and Number Partitioning, while it gives an 80% improvement at Max-Cut. In the hard instances we consider, for the number partitioning problem, standard objective functions fail to find the correct solution in almost all cases, CVaR finds the correct solution at 60% of the cases, while Ascending-CVaR finds the correct solution in 95% of the cases.

quant-ph↗

arXiv2022

Practical parallel self-testing of Bell states via magic rectangles

Self-testing is a method to verify that one has a particular quantum state from purely classical statistics. For practical applications, such as device-independent delegated verifiable quantum computation, it is crucial that one self-tests multiple Bell states in parallel while keeping the quantum capabilities required of one side to a minimum. In this work, we use the $3 \times n$ magic rectangle games (generalizations of the magic square game) to obtain a self-test for $n$ Bell states where the one side needs only to measure single-qubit Pauli observables. The protocol requires small input sizes [constant for Alice and $O(\log n)$ bits for Bob] and is robust with robustness $O(n^{5/2} \sqrt{\varepsilon})$, where $\varepsilon$ is the closeness of the ideal (perfect) correlations to those observed. To achieve the desired self-test, we introduce a one-side-local quantum strategy for the magic square game that wins with certainty, we generalize this strategy to the family of $3 \times n$ magic rectangle games, and we supplement these nonlocal games with extra check rounds (of single and pairs of observables).

quant-ph↗

arXiv2021

The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry

Variational quantum algorithms are suitable for use on noisy quantum systems. One of the most important use-cases is the quantum simulation of materials, using the variational quantum eigensolver (VQE). To optimize VQE performance, a suitable parameterized quantum circuit (ansatz) must be selected. We investigate a class of ansatze that incorporates knowledge of the quantum hardware, namely the hardware efficient ansatze. The performance of hardware efficient ansatze is affected differently by noise, and our goal is to study the effect of noise on evaluating which ansatz gives more accurate results in practice. First, we study the effect of noise on the different hardware efficient ansatze by benchmarking and ranking the performance of each ansatz family (i) on a chemistry application using VQE and (ii) by the recently established metric of "expressibility". The results demonstrate the ranking of optimal circuits does not remain constant in the presence of noise. Second, we evaluate the suitability of the expressibility measure in this context by performing a correlation study between expressibility and the performance of the same circuits on a chemistry application using VQE. Our simulations reveal a weak correlation and therefore demonstrate that expressibility is not an adequate measure to quantify the effectiveness of parameterized quantum circuits for quantum chemistry. Third, we evaluate the effect of different quantum device noise models on the ordering of which ansatz family is best. Interestingly, we see that to decide which ansatz is optimal for use, one needs to consider the specific hardware used even within the same family of quantum hardware.

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arXiv2021

Imperfect 1-out-of-2 quantum oblivious transfer: bounds, a protocol, and its experimental implementation

Oblivious transfer is an important primitive in modern cryptography. Applications include secure multiparty computation, oblivious sampling, e-voting, and signatures. Information-theoretically secure perfect 1-out-of 2 oblivious transfer is impossible to achieve. Imperfect variants, where both participants' ability to cheat is still limited, are possible using quantum means while remaining classically impossible. Precisely what security parameters are attainable remains unknown. We introduce a theoretical framework for studying semirandom quantum oblivious transfer, which is shown to be equivalent to regular oblivious transfer in terms of cheating probabilities. We then use it to derive bounds on cheating. We also present a protocol with lower cheating probabilities than previous schemes, together with its optical realization. We show that a lower bound of 2/3 on the minimum achievable cheating probability can be directly derived for semirandom protocols using a different method and definition of cheating than used previously. The lower bound increases from 2/3 to approximately 0.749 if the states output by the protocol are pure and symmetric. The oblivious transfer scheme we present uses unambiguous state elimination measurements and can be implemented with the same technological requirements as standard quantum cryptography. The cheating probabilities are 3/4 and approximately 0.729 for sender and receiver respectively, which is lower than in existing protocols. Using a photonic test-bed, we have implemented the protocol with honest parties, as well as optimal cheating strategies.

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arXiv2020

Quantum Magic Rectangles: Characterization and Application to Certified Randomness Expansion

We study a generalization of the Mermin-Peres magic square game to arbitrary rectangular dimensions. After exhibiting some general properties, these rectangular games are fully characterized in terms of their optimal win probabilities for quantum strategies. We find that for $m \times n$ rectangular games of dimensions $m,n \geq 3$ there are quantum strategies that win with certainty, while for dimensions $1 \times n$ quantum strategies do not outperform classical strategies. The final case of dimensions $2 \times n$ is richer, and we give upper and lower bounds that both outperform the classical strategies. Finally, we apply our findings to quantum certified randomness expansion to find the noise tolerance and rates for all magic rectangle games. To do this, we use our previous results to obtain the winning probability of games with a distinguished input for which the devices give a deterministic outcome, and follow the analysis of C. A. Miller and Y. Shi [SIAM J. Comput. 46, 1304 (2017)].

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arXiv2020

Security Limitations of Classical-Client Delegated Quantum Computing

Secure delegated quantum computing allows a computationally weak client to outsource an arbitrary quantum computation to an untrusted quantum server in a privacy-preserving manner. One of the promising candidates to achieve classical delegation of quantum computation is classical-client remote state preparation ($RSP_{CC}$), where a client remotely prepares a quantum state using a classical channel. However, the privacy loss incurred by employing $RSP_{CC}$ as a sub-module is unclear. In this work, we investigate this question using the Constructive Cryptography framework by Maurer and Renner (ICS'11). We first identify the goal of $RSP_{CC}$ as the construction of ideal RSP resources from classical channels and then reveal the security limitations of using $RSP_{CC}$. First, we uncover a fundamental relationship between constructing ideal RSP resources (from classical channels) and the task of cloning quantum states. Any classically constructed ideal RSP resource must leak to the server the full classical description (possibly in an encoded form) of the generated quantum state, even if we target computational security only. As a consequence, we find that the realization of common RSP resources, without weakening their guarantees drastically, is impossible due to the no-cloning theorem. Second, the above result does not rule out that a specific $RSP_{CC}$ protocol can replace the quantum channel at least in some contexts, such as the Universal Blind Quantum Computing (UBQC) protocol of Broadbent et al. (FOCS '09). However, we show that the resulting UBQC protocol cannot maintain its proven composable security as soon as $RSP_{CC}$ is used as a subroutine. Third, we show that replacing the quantum channel of the above UBQC protocol by the $RSP_{CC}$ protocol QFactory of Cojocaru et al. (Asiacrypt '19), preserves the weaker, game-based, security of UBQC.

quant-ph↗

arXiv2020

Randomized Benchmarking in the Analogue Setting

Current development in programmable analogue quantum simulators (AQS), whose physical implementation can be realised in the near-term compared to those of large-scale digital quantum computers, highlights the need for robust testing techniques in analogue platforms. Methods to properly certify or benchmark AQS should be efficiently scalable, and also provide a way to deal with errors from state preparation and measurement (SPAM). Up to now, attempts to address this combination of requirements have generally relied on model-specific properties. We put forward a new approach, applying a well-known digital noise characterisation technique called randomized benchmarking (RB) to the analogue setting. RB is a scalable experimental technique that provides a measure of the average error-rate of a gate-set on a quantum hardware, incorporating SPAM errors. We present the original form of digital RB, the necessary alterations to translate it to the analogue setting and introduce the analogue randomized benchmarking protocol (ARB). In ARB we measure the average error-rate per time evolution of a family of Hamiltonians and we illustrate this protocol with two case-studies of analogue models; classically simulating the system by incorporating several physically motivated noise scenarios. We find that for the noise models tested, the data fit with the theoretical predictions and we gain values for the average error rate for differing unitary sets. We compare our protocol with other relevant RB methods, where both advantages (physically motivated unitaries) and disadvantages (difficulty in reversing the time-evolution) are discussed.

quant-ph↗

arXiv2019

Methods for Classically Simulating Noisy Networked Quantum Architectures

As research on building scalable quantum computers advances, it is important to be able to certify their correctness. Due to the exponential hardness of classically simulating quantum computation, straight-forward verification through classical simulation fails. However, we can classically simulate small scale quantum computations and hence we are able to test that devices behave as expected in this domain. This constitutes the first step towards obtaining confidence in the anticipated quantum-advantage when we extend to scales which can no longer be simulated. Realistic devices have restrictions due to their architecture and limitations due to physical imperfections and noise. Here we extend the usual ideal simulations by considering those effects. We provide a general methodology for constructing realistic simulations emulating the physical system which will both provide a benchmark for realistic devices, and guide experimental research in the quest for quantum-advantage. We exemplify our methodology by simulating a networked architecture and corresponding noise-model; in particular that of the device developed in the Networked Quantum Information Technologies Hub (NQIT). For our simulations we use, with suitable modification, the classical simulator of of Bravyi and Gosset. The specific problems considered belong to the class of Instantaneous Quantum Polynomial-time (IQP) problems, a class believed to be hard for classical computing devices, and to be a promising candidate for the first demonstration of quantum-advantage. We first consider a subclass of IQP, defined by Bermejo-Vega et al, involving two-dimensional dynamical quantum simulators, before moving to more general instances of IQP, but which are still restricted to the architecture of NQIT.

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arXiv2019

QFactory: classically-instructed remote secret qubits preparation

The functionality of classically-instructed remotely prepared random secret qubits was introduced in (Cojocaru et al 2018) as a way to enable classical parties to participate in secure quantum computation and communications protocols. The idea is that a classical party (client) instructs a quantum party (server) to generate a qubit to the server's side that is random, unknown to the server but known to the client. Such task is only possible under computational assumptions. In this contribution we define a simpler (basic) primitive consisting of only BB84 states, and give a protocol that realizes this primitive and that is secure against the strongest possible adversary (an arbitrarily deviating malicious server). The specific functions used, were constructed based on known trapdoor one-way functions, resulting to the security of our basic primitive being reduced to the hardness of the Learning With Errors problem. We then give a number of extensions, building on this basic module: extension to larger set of states (that includes non-Clifford states); proper consideration of the abort case; and verifiablity on the module level. The latter is based on "blind self-testing", a notion we introduced, proved in a limited setting and conjectured its validity for the most general case.

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arXiv2018

On the possibility of classical client blind quantum computing

We define the functionality of delegated pseudo-secret random qubit generator (PSRQG), where a classical client can instruct the preparation of a sequence of random qubits at some distant party. Their classical description is (computationally) unknown to any other party (including the distant party preparing them) but known to the client. We emphasize the unique feature that no quantum communication is required to implement PSRQG. This enables classical clients to perform a class of quantum communication protocols with only a public classical channel with a quantum server. A key such example is the delegated universal blind quantum computing. Using our functionality one could achieve a purely classical-client computational secure verifiable delegated universal quantum computing (also referred to as verifiable blind quantum computation). We give a concrete protocol (QFactory) implementing PSRQG, using the Learning-With-Errors problem to construct a trapdoor one-way function with certain desired properties (quantum-safe, two-regular, collision-resistant). We then prove the security in the Quantum-Honest-But-Curious setting and briefly discuss the extension to the malicious case.

cs.CR↗

arXiv2017

Measurement-Device-Independent Quantum Digital Signatures

Digital signatures play an important role in software distribution, modern communication and financial transactions, where it is important to detect forgery and tampering. Signatures are a cryptographic technique for validating the authenticity and integrity of messages, software, or digital documents. The security of currently used classical schemes relies on computational assumptions. Quantum digital signatures (QDS), on the other hand, provide information-theoretic security based on the laws of quantum physics. Recent work on QDS shows that such schemes do not require trusted quantum channels and are unconditionally secure against general coherent attacks. However, in practical QDS, just as in quantum key distribution (QKD), the detectors can be subjected to side-channel attacks, which can make the actual implementations insecure. Motivated by the idea of measurement-device-independent quantum key distribution (MDI-QKD), we present a measurement-device-independent QDS (MDI-QDS) scheme, which is secure against all detector side-channel attacks. Based on the rapid development of practical MDI-QKD, our MDI-QDS protocol could also be experimentally implemented, since it requires a similar experimental setup.

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arXiv2017

Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

The relationship between correlations and entanglement has played a major role in understanding quantum theory since the work of Einstein, Podolsky and Rosen (1935). Tsirelson (1980) proved that Bell states, shared among two parties, when measured suitably, achieve the maximum non-local correlations allowed by quantum mechanics. Conversely, Reichardt, Unger and Vazirani (2013) showed that observing the maximal correlation value over a sequence of repeated measurements, implies that the underlying quantum state is close to a tensor product of maximally entangled states and, moreover, that it is measured according to an ideal strategy. However, this strong rigidity result comes at a high price, requiring a large number of entangled pairs to be tested. In this paper, we present a significant improvement in terms of the overhead by instead considering quantum steering where the device of the one side is trusted. We first demonstrate a robust one-sided device-independent version of self-testing, which characterises the shared state and measurement operators of two parties up to a certain bound. We show that this bound is optimal up to constant factors and we generalise the results for the most general attacks. This leads us to a rigidity theorem for maximal steering correlations. As a key application we give a one-sided device-independent protocol for verifiable delegated quantum computation, and compare it to other existing protocols, to highlight the cost of trust assumptions. Finally, we show that under reasonable assumptions, the states shared in order to run a certain type of verification protocol must be unitarily equivalent to perfect Bell states.

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