Related papers: Quantum Information and the PCP Theorem
One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems…
We show two results about the relationship between quantum and classical messages. Our first contribution is to show how to replace a quantum message in a one-way communication protocol by a deterministic message, establishing that for all…
Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of $N$ spins (qubits). We find that the quality of this optimal…
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…
The general stable quantum memory unit is a hybrid consisting of a classical digit with a quantum digit (qudit) assigned to each classical state. The shape of the memory is the vector of sizes of these qudits, which may differ. We determine…
Quantum computing becomes viable when a quantum state can be preserved from environmentally-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) is capable of identifying…
We present a construction of one-time memories (OTMs) using classical-accessible stateless hardware, building upon the work of Broadbent et al. and Behera et al.. Unlike the aforementioned work, our approach leverages quantum random access…
Ensuring security and integrity of elections constitutes an important challenge with wide-ranging societal implications. Classically, security guarantees can be ensured based on computational complexity, which may be challenged by quantum…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
In recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine.…
Recent work has extended Bell's theorem by quantifying the amount of communication required to simulate entangled quantum systems with classical information. The general scenario is that a bipartite measurement is given from a set of…
Quantum mechanics enables information-processing advantages even at the level of a single qubit. A paradigmatic example is the 2$\to$1 random access code (RAC), where a qubit outperforms a classical bit in retrieving encoded information. In…
We present upper and lower bounds of the computational complexity of the two-way communication model of multiple-prover quantum interactive proof systems whose verifiers are limited to measure-many two-way quantum finite automata. We prove…
In this paper we consider the following question: how many bits of classical communication and shared random bits are necessary to simulate a quantum protocol involving Alice and Bob where they share k entangled quantum bits and do not…
We demonstrate that a high fidelity approximation to $| \Psi_b \rangle$, the quantum superposition over all bit strings within Hamming distance $b$ of the codewords of a dimension-$k$ linear code over $\mathbb{Z}_2^n$, can be efficiently…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
Quantum information offers the promise of being able to perform certain communication and computation tasks that cannot be done with conventional information technology (IT). Optical Quantum Information Processing (QIP) holds particular…
This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any…
The no-masking theorem for quantum information proves that it is impossible to encode an arbitrary input state into a larger bipartite entangled state such that the full information is stored in the correlation but the individual subsystems…
Quantum Merlin-Arthur proof systems are believed to be stronger than both their classical counterparts and ``stand-alone'' quantum computers when Arthur is assumed to operate in $\Omega(\log n)$ space. No hint of such an advantage over…