Related papers: Multivariable quantum signal processing (M-QSP): p…
Quantum state preparation (QSP) is a key component in many quantum algorithms. In particular, the problem of sparse QSP (SQSP) $\unicode{x2013}$ the task of preparing the states with only a small number of non-zero amplitudes…
The characterization of the evolution of a quantum system is one of the main tasks to accomplish to achieve quantum information processing. The standard quantum process tomography (SQPT) has the unique property that it can be applied…
Accurate and efficient implementation of parallel quantum gates is crucial for scalable quantum information processing. However, the unavoidable crosstalk between qubits in current noisy processors impedes the achievement of high gate…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
We achieve query-optimal quantum simulations of non-Hermitian Hamiltonians $H_{\mathrm{eff}} = H_R + iH_I$, where $H_R$ is Hermitian and $H_I \succeq 0$, using a bivariate extension of quantum signal processing (QSP) with non-commuting…
We explore the use of transformers for solving quadratic programs and how this capability benefits decision-making problems that involve covariance matrices. We first show that the linear attention mechanism can provably solve unconstrained…
Solving systems of m multivariate quadratic equations in n variables (MQ-problem) over finite fields is NP-hard. The security of many cryptographic systems is based on this problem. Up to now, the best algorithm for solving the underdefined…
The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization. In this paper, we are interested in the quantum search framework for the TSP because it has robust theoretical…
Multiple quantum (MQ) NMR methods \cite{Baum} are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian \cite{Baum} describing MQ NMR dynamics is related to the…
The widely held belief that BQP strictly contains BPP raises fundamental questions: if we cannot efficiently compute predictions for the behavior of quantum systems, how can we test their behavior? In other words, is quantum mechanics…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
Quantum sequential machines (QSMs) are a quantum version of stochastic sequential machines (SSMs). Recently, we showed that two QSMs M_1 and M_2 with n_1 and n_2 states, respectively, are equivalent iff they are (n_1+n_2)^2--equivalent…
The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially…
The conventional paradigm of quantum computing is discrete: it utilizes discrete sets of gates to realize bitstring-to-bitstring mappings, some of them arguably intractable for classical computers. In parameterized quantum approaches, the…
Complex quantum simulation workflows are often hindered by incompatible wavefunction representations adopted across different algorithmic frameworks. In particular, the mismatch between the first- and second-quantization formalisms prevents…
Encoding hard-constrained optimization problems into a variational quantum algorithm often turns out to be a challenging task. In this work, we provide a solution for the class of open-shop scheduling problems (OSSPs), which we achieve by…
We discuss quantum position verification (QPV) protocols in which the verifiers create and send single-qubit states to the prover. QPV protocols using single-qubit states are known to be insecure against adversaries that share a small…
In Markov decision processes (MDPs), quantile risk measures such as Value-at-Risk are a standard metric for modeling RL agents' preferences for certain outcomes. This paper proposes a new Q-learning algorithm for quantile optimization in…