Related papers: A Cautionary Note on Quantum Oracles
We initiate the study of the relationship between two complexity classes, BQP (Bounded-Error Quantum Polynomial-Time) and PPAD (Polynomial Parity Argument, Directed). We first give a conjecture that PPAD is contained in BQP, and show a…
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. 1. BQP is low for PP, i.e.,…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
The analysis of quantum algorithms which query random, invertible permutations has been a long-standing challenge in cryptography. Many techniques which apply to random oracles fail, or are not known to generalize to this setting. As a…
The simulation of the spectra measured in nuclear magnetic resonance (NMR) spectroscopy experiments is a computationally non-trivial problem which, due to its natural interpretation as a quantum spin problem, maps in a straightforward way…
Grover's algorithm is a well-known contribution to quantum computing. It searches one value within an unordered sequence faster than any classical algorithm. A fundamental part of this algorithm is the so-called oracle, a quantum circuit…
Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete problems for the complexity classes NP and QMA which are believed to be intractable for classical and quantum computers, respectively. Statistical ensembles of…
Ring signatures are a powerful primitive that allows a member to sign on behalf of a group, without revealing their identity. Recently, ring signatures have received additional attention as an ingredient for post-quantum deniable…
This paper introduces a novel lower bound on communication complexity using quantum relative entropy and mutual information, refining previous classical entropy-based results. By leveraging Uhlmann's lemma and quantum Pinsker inequalities,…
Public-key quantum money is a cryptographic proposal for using highly entangled quantum states as currency that is publicly verifiable yet resistant to counterfeiting due to the laws of physics. Despite significant interest, constructing…
Pairwise "same-cluster" queries are one of the most widely used forms of supervision in semi-supervised clustering. However, it is impractical to ask human oracles to answer every query correctly. In this paper, we study the influence of…
Quantum reservoir computing has emerged as a promising paradigm within the field of quantum machine learning, harnessing the inherent properties of quantum systems to optimise and enhance information processing capabilities. Here, we…
Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime…
This paper considers the quantum query complexity of {\it $\eps$-biased oracles} that return the correct value with probability only $1/2 + \eps$. In particular, we show a quantum algorithm to compute $N$-bit OR functions with…
As an important branch of quantum secure multiparty computation, quantum private comparison (QPC) has attracted more and more attention recently. In this paper, according to the quantum implementation mechanism that these protocols used, we…
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…
Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the…
The $P$ versus $NP$ problem is still unsolved. But there are several oracles with $P$ unequal $NP$ relative to them. Here we will prove, that $P\not=NP$ relative to a $P$-complete oracle. In this paper, we use padding arguments as the proof…
As simulations of quantum systems cross the limits of classical computability, both quantum and classical approaches become hard to verify. Scaling predictions are therefore based on local structure and asymptotic assumptions, typically…
This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running…