Related papers: Quantum Depth in the Random Oracle Model

A recent line of work has shown the unconditional advantage of constant-depth quantum computation, or $\mathsf{QNC^0}$, over $\mathsf{NC^0}$, $\mathsf{AC^0}$, and related models of classical computation. Problems exhibiting this advantage…

The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate…

Quantum computing promises to revolutionize various fields, yet the execution of quantum programs necessitates an effective compilation process. This involves strategically mapping quantum circuits onto the physical qubits of a quantum…

We continue the study of the circuit class GC^0, which augments AC^0 with unbounded-fan-in gates that compute arbitrary functions inside a sufficiently small Hamming ball but must be constant outside it. While GC^0 can compute functions…

Classical shadows are a versatile tool to probe many-body quantum systems, consisting of a combination of randomised measurements and classical post-processing computations. In a recently introduced version of the protocol, the…

Variational quantum algorithms are the centerpiece of modern quantum programming. These algorithms involve training parameterized quantum circuits using a classical co-processor, an approach adapted partly from classical machine learning.…

We present a compact quantum circuit for factoring a large class of integers, including some whose classical hardness is expected to be equivalent to RSA (but not including RSA integers themselves). Most notably, we factor $n$-bit integers…

We present characterisations of "exact" gap-definable classes, in terms of indeterministic models of computation which slightly modify the standard model of quantum computation. This follows on work of Aaronson [arXiv:quant-ph/0412187], who…

In the quantum computation verification problem, a quantum server wants to convince a client that the output of evaluating a quantum circuit $C$ is some result that it claims. This problem is considered very important both theoretically and…

We generalize quantum-classical PCPs, first introduced by Weggemans, Folkertsma and Cade (TQC 2024), to allow for $q$ quantum queries to a polynomially-sized classical proof ($\mathsf{QCPCP}_{Q,c,s}[q]$). Exploiting a connection with the…

Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…

The optimization of quantum circuit depth is crucial for practical quantum computing, as limited coherence times and error-prone operations constrain executable algorithms. Measurement and feedback operations are fundamental in quantum…

Quantum circuit simulators running on classical computers offer a vital platform for designing, testing, and optimizing quantum algorithms, driving innovation despite limited access to real quantum hardware. However, their scalability is…

It is a longstanding open problem to devise an oracle relative to which BQP does not lie in the Polynomial-Time Hierarchy (PH). We advance a natural conjecture about the capacity of the Nisan-Wigderson pseudorandom generator [NW94] to fool…

We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the…

Boson sampling, a computational task believed to be classically hard to simulate, is expected to hold promise for demonstrating quantum computational advantage using near-term quantum devices. However, noise in experimental implementations…

So far, only the results on 3 qubit spaces (both on superconducting and ion-trap realisations of quantum processors) have beaten the classical unstructured search in the expected number of oracle calls using optimal protocols in both…

One can fix the randomness used by a randomized algorithm, but there is no analogous notion of fixing the quantumness used by a quantum algorithm. Underscoring this fundamental difference, we show that, in the black-box setting, the…

Quantum deep learning (QDL) explores the use of both quantum and quantum-inspired resources to determine when deep learning's core capabilities, such as expressivity, generalization, and scalability, can be enhanced based on specific…

The limited computational power of constant-depth quantum circuits can be boosted by adapting future gates according to the outcomes of mid-circuit measurements. We formulate computation of a variety of Boolean functions in the framework of…