Related papers: Quantum Logspace Algorithm for Powering Matrices w…
We construct an efficient classical analogue of the quantum matrix inversion algorithm (HHL) for low-rank matrices. Inspired by recent work of Tang, assuming length-square sampling access to input data, we implement the pseudoinverse of a…
As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new…
Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…
While quantum computers hold the promise of significant computational speedups, the limited size of early quantum machines motivates the study of space-bounded quantum computation. We relate the quantum space complexity of computing a…
Polynomial-time quantum Turing machines are provably superior to their classical counterparts within a common space bound in $o(\log \log n)$. For $\Omega(\log \log n)$ space, the only known quantum advantage result has been the fact…
We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to…
Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known…
Given an algorithm that outputs the correct answer with bounded error, say $1/3$, it is sometimes desirable to reduce this error to some arbitrarily small $\varepsilon$ -- e.g., if one wants to call the algorithm many times as a subroutine.…
We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground…
Convolution operations are foundational to classical image processing and modern deep learning architectures, yet their extension into the quantum domain has remained algorithmically and physically costly due to inefficient data encoding…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy,…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
We present a quantum algorithm for computing the period lattice of infrastructures of fixed dimension. The algorithm applies to infrastructures that satisfy certain conditions. The latter are always fulfilled for infrastructures obtained…
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
We present classical sublinear-time algorithms for solving low-rank linear systems of equations. Our algorithms are inspired by the HHL quantum algorithm for solving linear systems and the recent breakthrough by Tang of dequantizing the…