Related papers: Realization of quantum signal processing on a nois…
Quantum Signal Processing (QSP) is a technique that can be used to implement a polynomial transformation $P(x)$ applied to the eigenvalues of a unitary $U$, essentially implementing the operation $P(U)$, provided that $P$ satisfies some…
Quantum signal processing (QSP) provides a representation of scalar polynomials of degree $d$ as products of matrices in $\mathrm{SU}(2)$, parameterized by $(d+1)$ real numbers known as phase factors. QSP is the mathematical foundation of…
Simulating open quantum systems on quantum computers presents a fundamental challenge: open quantum dynamics are intrinsically nonunitary, whereas quantum computers operate through unitary evolution. Conventional approaches overcome this…
Today's experimental noisy quantum processors can compete with and surpass all known algorithms on state-of-the-art supercomputers for the computational benchmark task of Random Circuit Sampling [1-5]. Additionally, a circuit-based quantum…
Quantum signal processing (QSP), originally developed for composite pulse sequences in nuclear magnetic resonance systems, has recently attracted attention as a unified framework for quantum algorithms. A pioneering study applied QSP to…
Quantum simulation is a potentially powerful application of quantum computing, holding the promise to be able to emulate interesting quantum systems beyond the reach of classical computing methods. Despite such promising applications, and…
Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated…
Quantum signal processing (QSP) is a highly successful algorithmic primitive in quantum computing which leads to conceptually simple and efficient quantum algorithms using the block-encoding framework of quantum linear algebra. Multivariate…
Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom and arbitrarily long coherence time. In Noisy Intermediate-Scale Quantum (NISQ) devices, however, the…
Simulating noisy quantum circuits is vital in designing and verifying quantum algorithms in the current NISQ (Noisy Intermediate-Scale Quantum) era, where quantum noise is unavoidable. However, it is much more inefficient than the classical…
Quantum Signal Processing (QSP), together with the quantum singular value transformation, is one of the central quantum algorithms due to its efficiency and generality in many fields including quantum simulation, quantum machine learning,…
Analog quantum simulators can directly emulate time-dependent Hamiltonian dynamics, enabling the exploration of diverse physical phenomena such as phase transitions, quench dynamics, and non-equilibrium processes. Realizing accurate analog…
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…
We achieve query-optimal quantum simulations of non-Hermitian Hamiltonians $H_{\mathrm{eff}} = H_R + iH_I$, where $H_R$ is Hermitian and $H_I \succeq 0$, using a bivariate extension of quantum signal processing (QSP) with non-commuting…
Rydberg atom arrays have recently emerged as one of the most promising platforms for quantum simulation and quantum information processing. However, as is the case for other experimental platforms, the longer-term success of the Rydberg…
Noise in quantum devices is generally considered detrimental to computational accuracy. However, the recent proposal of noise-assisted simulation has demonstrated that noise can be an asset in digital quantum simulations of open systems on…
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…
Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest…
Quantum computing promises an effective way to solve targeted problems that are classically intractable. Among them, quantum computers built with superconducting qubits are considered one of the most advanced technologies, but they suffer…
Quantum signal processing (QSP), a framework for implementing matrix-valued polynomials, is a fundamental primitive in various quantum algorithms. Despite its versatility, a potentially underappreciated challenge is that all systematic…