Related papers: Quantum Period-Finding using One-Qubit Reduced Den…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…
We consider the certification of temporal quantum correlations using the pseudo-density matrix (PDM), an extension of the density matrix to the time domain, where negative eigenvalues are key indicators of temporal correlations.…
Recently, Chau introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a $2^n$-dimensional Hilbert space in the form…
The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an…
Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this…
Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence…
This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random…
Quantum computing is a promising candidate for accelerating machine learning tasks. Limited by the control accuracy of current quantum hardware, reducing the consumption of quantum resources is the key to achieving quantum advantage. Here,…
Density functional theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically…
Many quantum algorithms rely on the measurement of complex quantum amplitudes. Standard approaches to obtain the phase information, such as the Hadamard test, give rise to large overheads due to the need for global controlled-unitary…
A fast algorithm is presented for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q n p m, where p is a prime, q is a prime and a primitive root modulo p2. The algorithm presented…
This paper presents two efficient and stable algorithms for recovering phase factors in quantum signal processing (QSP), a crucial component of many quantum algorithms. The first algorithm, the ``Half Cholesky" method, which is based on…
Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to…
The matrix product state (MPS) is utilized to study the ground state properties and quantum phase transitions (QPTs) of the one-dimensional quantum compass model (QCM). The MPS wavefunctions are argued to be very efficient descriptions of…
In this work we consider practical implementations of Kitaev's algorithm for quantum phase estimation. We analyze the use of phase shifts that simplify the estimation of successive bits in the estimation of unknown phase $\varphi$. By using…
We introduce Quantum Functional Information (QFI), a new metric to quantify the rarity and utility of quantum states and circuits. Unlike standard measures such as fidelity or entropy, QFI captures the balance between functionality and…
Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations…
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…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems. In particular, we examine the computation of the cumulative distribution function (CDF) of the spectral measure…