Related papers: Efficient quantum circuits for dense and non-unita…
The standard paradigm for state preparation on quantum computers for the simulation of physical systems in the near term has been widely explored with different algorithmic methods. One such approach is the optimization of parameterized…
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis…
Producing and maintaining entanglement reside at the heart of the optimal construction of quan- tum operations and are fundamental issues in the realization of universal quantum computation. We here introduce a setup of spin qubits that…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Block encoding is a successful technique used in several powerful quantum algorithms. In this work we provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure. The proposed methodology is…
Quantum entanglement lies at the heart of quantum mechanics in both fundamental and practical aspects. The entanglement of quantum states has been studied widely, however, the entanglement of operators has not been studied much in spite of…
We define and construct efficient depth-universal and almost-size-universal quantum circuits. Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
Numerical simulation is an important method for verifying the quantum circuits used to simulate low-energy nuclear states. However, real-world applications of quantum computing for nuclear theory often generate deep quantum circuits that…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…
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…
This work proposes double-bracket iterations as a framework for obtaining diagonalizing quantum circuits. Their implementation on a quantum computer consists of interlacing evolutions generated by the input Hamiltonian with diagonal…
Diagonal quantum circuits are quantum circuits comprising only diagonal gates in the computational basis. In spite of a classical feature of diagonal quantum circuits in the sense of commutativity of all gates, their computational power is…
Quantum simulation traditionally relies on unitary dynamics, inherently imposing efficiency constraints on the generation of intricate entangled states. In principle, these limitations can be superseded by non-unitary, dynamic circuits.…
The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less…
The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with $n$ wires, each corresponding to one…
We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where non-local cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase…
While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular…
Block-encodings of matrices have become an essential element of quantum algorithms derived from the quantum singular value transformation. This includes a variety of algorithms ranging from the quantum linear systems problem to quantum…