Related papers: Quantum Depth in the Random Oracle Model
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…
Quantum machine learning (QML) is emerging as an application of quantum computing with the potential to deliver quantum advantage, but its realisation for practical applications remains impeded by challenges. Amongst those, a key barrier is…
Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the…
We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two new methods to achieve this, the first method involving…
We construct a quantum oracle relative to which $\mathsf{BQP} = \mathsf{QMA}$ but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom…
How could quantum cryptography help us achieve what are not achievable in classical cryptography? In this work we study the classical cryptographic problem that two parties would like to perform secure computations with long outputs. As a…
We propose a set of Bell-type nonlocal games that can be used to prove an unconditional quantum advantage in an objective and hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure a…
Simulating quantum systems using classical computing equipment has been a significant research focus. This work demonstrates that circuits as large and complex as the random circuit sampling (RCS) circuits published as a part of Google's…
A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…
Quantum theory promises computational speed-ups over classical approaches. The celebrated Gottesman-Knill Theorem implies that the full power of quantum computation resides in the specific resource of "magic" states -- the secret sauce to…
We construct a unitary oracle relative to which $\mathbf{BQP}=\mathbf{QCMA}$ but quantum-computation-classical-communication (QCCC) commitments and QCCC multiparty non-interactive key exchange exist. We also construct a unitary oracle…
In 2004, Aaronson introduced the complexity class $\mathsf{PostBQP}$ ($\mathsf{BQP}$ with postselection) and showed that it is equal to $\mathsf{PP}$. Following their line of work, we introduce two new complexity classes. The first,…
It is an established fact that for many of the interesting problems quantum algorithms based on queries of the standard oracle bring no significant improvement in comparison to known classical algorithms. It is conceivable that there are…
We present a unified quantum-classical framework for addressing NP-complete constrained combinatorial optimization problems, generalizing the recently proposed Quantum Conic Programming (QCP) approach. Accordingly, it inherits many…
We study the classical simulability of a polynomial-size quantum circuit $C_n$ on $n$ qubits followed by sparse classical post-processing (SCP) on $m$ bits, where $m \leq n \leq {\rm poly}(m)$. The SCP is described by a non-zero Boolean…
Deterministic quantum computation with one quantum bit (DQC1), or the one clean qubit model, [E. Knill and R. Laflamme, Phys. Rev. Lett. {\bf81}, 5672 (1998)] is a model of quantum computing where the input is the tensor product of a single…
Scaling bottlenecks the making of digital quantum computers, posing challenges from both the quantum and the classical components. We present a classical architecture to cope with a comprehensive list of the latter challenges {\em all at…
In this paper we consider a quantum computational variant of nondeterminism based on the notion of a quantum proof, which is a quantum state that plays a role similar to a certificate in an NP-type proof. Specifically, we consider quantum…
We investigate quantum analogues of collision resistance and obtain separations between quantum ``one-way'' and ``collision-resistant'' primitives. 1. Our first result studies one-wayness versus collision-resistance defined over quantum…
Biomarker-based prediction of clinical outcomes is challenging due to nonlinear relationships, correlated features, and the limited size of many medical datasets. Classical machine-learning methods can struggle under these conditions,…