Related papers: An Efficient Quantum Algorithm and Circuit to Gene…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Entanglement plays an important role in quantum communication, algorithms, and error correction. Schmidt coefficients are correlated to the eigenvalues of the reduced density matrix. These eigenvalues are used in Von Neumann entropy to…
We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…
We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…
An explicit algorithm for performing Schumacher's noiseless compression of quantum bits is given. This algorithm is based on a combinatorial expression for a particular bijection among binary strings. The algorithm, which adheres to the…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
Quantum dynamics can be analyzed via the structure of energy eigenstates. However, in the many-body setting, preparing eigenstates associated with finite temperatures requires time scaling exponentially with system size. In this work we…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.}, \textbf{10}, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this…
In this paper, we present a direct quantum adaptation of the classical shifted power method. The method is very similar to the iterative phase estimation algorithm; however, it does not require any initial estimate of an eigenvector and as…
It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
The phase estimation algorithm is so named because it allows the estimation of the eigenvalues associated with an operator. However it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices,…
The VQE algorithm has turned out to be quite expensive to run given the way we currently access quantum processors (i.e. over the cloud). In order to alleviate this issue, we introduce Quantum Sampling Regression (QSR), an alternative…
A major obstacle to implementing Shor's quantum number-factoring algorithm is the large size of modular-exponentiation circuits. We reduce this bottleneck by customizing reversible circuits for modular multiplication to individual runs of…
Quantum computing holds immense promise for simulating quantum systems, a critical task for advancing our understanding of complex quantum phenomena. One of the primary goals in this domain is to accurately approximate the ground state of…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…