Related papers: Taming Quantum Time Complexity
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
Quantum linear system (QLS) solvers are a fundamental class of quantum algorithms used in many potential quantum computing applications, including machine learning and solving differential equations. The performance of quantum algorithms is…
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model…
We define a new query measure we call quantum distinguishing complexity, denoted QD(f) for a Boolean function f. Unlike a quantum query algorithm, which must output a state close to |0> on a 0-input and a state close to |1> on a 1-input, a…
A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and lower variance than the individual classifiers that…
A series of work [GKK+08, Kal22, KPV24] has shown that asymptotic advantages in space complexity are possible for quantum algorithms over their classical counterparts in the streaming model. We give a simple quantum sketch that encompasses…
Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyse quantum networks performing AQFT in the presence of decoherence and show that extensive…
Quantum computing has garnered attention for its potential to solve complex computational problems with considerable speedup. Despite notable advancements in the field, achieving meaningful scalability and noise control in quantum hardware…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
The quest for effective quantum feature maps for data encoding presents significant challenges, particularly due to the flat training landscapes and lengthy training processes associated with parameterised quantum circuits. To address these…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
Most existing quantum programming languages are based on the quantum circuit model of computation, as higher-level abstractions are particularly challenging to implement - especially ones relating to quantum control flow. The Qunity…
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to…
We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious…
Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…
Although quantum control typically relies on greedy (local) optimization, traps (irregular critical points) in the control landscape can make optimization hard by foiling local search strategies. We demonstrate the failure of greedy…
More computational resources (i.e., more physical qubits and qubit connections) on a superconducting quantum processor not only improve the performance but also result in more complex chip architecture with lower yield rate. Optimizing both…