Related papers: Block encoding bosons by signal processing
Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…
Modular architectures are a promising approach to scaling quantum computers to fault tolerance. Small, low-noise quantum processors connected through relatively noisy quantum links are capable of fault-tolerant operation as long as the…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a…
Bosonic codes constitute a promising route to fault-tolerant quantum computing. {Existing Floquet protocols enable analytical construction of bosonic codes but typically rely on slow adiabatic ramps with thousands of driving periods.} In…
Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to…
Quantum signal processing (QSP), which enables systematic polynomial transformations on quantum data through sequences of qubit rotations, has emerged as a fundamental building block for quantum algorithms and data re-uploading quantum…
Quantum signal processing (QSP) has emerged as a unifying subroutine in quantum algorithms. In QSP, we are given a function $f$ and a unitary black-box $U$, and the goal is to construct a quantum circuit for implementing $f(U)$ to a given…
We present a novel multi-scale embedding scheme that links conventional QM/MM embedding and bootstrap embedding (BE) to allow simulations of large chemical systems on limited quantum devices. We also propose a mixed-basis BE scheme that…
Quantum computation using qubits made of two component Bose-Einstein condensates (BECs) is analysed. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in gate operations that can be performed at a…
Quantum phase estimation (QPE) is a promising quantum algorithm for obtaining molecular ground-state energies with chemical accuracy. However, its computational cost, dominated by the Hamiltonian 1-norm $\lambda$ and the cost of the block…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
In this work, we are interested on the implementation of single-qubit gates on coupled Bose-Einstein condensates (BECs). The system, a feasible candidate for a qubit, consists on condensed atoms of different hyperfine levels coupled by a…
Block encoding lies at the core of many existing quantum algorithms. Meanwhile, efficient and explicit block encodings of dense operators are commonly acknowledged as a challenging problem. This paper presents a comprehensive study of the…
Computational cost of energy estimation for molecular electronic Hamiltonians via Quantum Phase Estimation (QPE) grows with the difference between the largest and smallest eigenvalues of the Hamiltonian. In this work we propose a…
Linear maps that are not completely positive play a crucial role in the study of quantum information, yet their non-completely positive nature renders them challenging to realize physically. The core difficulty lies in the fact that when…
Quantum linear system solvers like the Quantum Singular Value Transformation (QSVT) require a block encoding of the system matrix $A$ within a unitary operator $U_A$. Unfortunately, block encoding often results in significant…
Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as…
We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator…
We implement logically encoded three-qubit circuits for the quantum Fourier transform (QFT), using the [[7,1,3]] Steane code, and benchmark the circuits on the Quantinuum H2-1 trapped-ion quantum computer. The circuits require multiple…