Related papers: Hidden Quantum Advantage near the Decoding Thresho…
Decoded Quantum Interferometry (DQI) provides a framework for superpolynomial quantum speedups by reducing certain optimization problems to reversible decoding tasks. We apply DQI to the Optimal Polynomial Intersection (OPI) problem, whose…
Decoded Quantum Interferometry (DQI) is a framework for approximating special kinds of discrete optimization problems that relies on problem structure in a way that sets it apart from other classical or quantum approaches. We show that the…
Decoded Quantum Interferometry (DQI) is a recently proposed quantum algorithm for approximating solutions to combinatorial optimization problems by reducing instances of linear satisfiability to bounded-distance decoding over superpositions…
A key issue of current quantum advantage experiments is that their verification requires a full classical simulation of the ideal computation. This limits the regime in which the experiments can be verified to precisely the regime in which…
A contemporary technological milestone is to build a quantum device performing a computational task beyond the capability of any classical computer, an achievement known as quantum adversarial advantage. In what ways can the entanglement…
We study the performance of Decoded Quantum Interferometry (DQI) on typical instances of MAX-$k$-XOR-SAT when the transpose of the constraint matrix is drawn from a standard ensemble of LDPC parity check matrices. We prove that if the…
Without large quantum computers to empirically evaluate performance, theoretical frameworks such as the quantum statistical query (QSQ) are a primary tool to study quantum algorithms for learning classical functions and search for quantum…
Many quantum mechanical experiments can be viewed as multi-round interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum "coherent" access to the unknown process is known to provide an advantage in…
In practical decoy-state quantum key distribution, the raw key length is finite. Thus, deviation of the estimated single photon yield and single photon error rate from their respective true values due to finite sample size can seriously…
We study the complexity of Decoded Quantum Interferometry (DQI), a quantum algorithm for approximate optimization. First, we show that the algorithm resists classical simulation strategies based on locating outputs with large probabilities.…
A recent paper by Jordan et al. introduced Decoded Quantum Interferometry (DQI), a novel quantum algorithm that uses the quantum Fourier transform to reduce linear optimization problems -- max-XORSAT and max-LINSAT -- to decoding problems.…
In this work, we give two results that put new limits on distributed quantum advantage in the context of the LOCAL model of distributed computing. First, we show that there is no distributed quantum advantage for any linear program. Put…
Decoded Quantum Interferometry (DQI) promises superpolynomial speedups for structured optimization; however, its practical realization is often hindered by significant sensitivity to hardware noise and spectral dispersion. To bridge this…
The Optimal Polynomial Intersection (OPI) problem is the following: Given sets $S_1, \ldots, S_m \subseteq \mathbb{F}$ and evaluation points $a_1, \ldots, a_m \in \mathbb{F}$, find a polynomial $Q \in \mathbb{F}[x]$ of degree less than $n$…
The quantum Fisher information (QFI) bounds the sensitivity of a quantum measurement, heralding the conditions for quantum advantages when compared with classical strategies. Here, we calculate analytical expressions for the QFI of…
In a recent study [Rohde et al., quant-ph/0603130 (2006)] of several quantum error correcting protocols designed for tolerance against qubit loss, it was shown that these protocols have the undesirable effect of magnifying the effects of…
We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual…
Bound secret information is classical information that contains secrecy but from which secrecy cannot be extracted. The existence of bound secrecy has been conjectured but is currently unproven, and in this work we provide analytical and…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…
Decoded Quantum Interferometry (DQI) is a recently introduced quantum algorithm that reduces discrete optimization to decoding with potential advantages over the best-known polynomial-time classical algorithms for certain Max-LINSAT…