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Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications…
This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulae, written in terms of matrix coefficients, characterizing operators implementable…
Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly.…
The execution of quantum circuits on real systems has largely been limited to those which are simply time-ordered sequences of unitary operations followed by a projective measurement. As hardware platforms for quantum computing continue to…
While the ability to build quantum computers is improving dramatically, developing quantum algorithms is limited and relies on human insight and ingenuity. Although a number of quantum programming languages have been developed, it is…
A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all one-qubit…
Artificial neural networks are becoming an integral part of digital solutions to complex problems. However, employing neural networks on quantum processors faces challenges related to the implementation of non-linear functions using quantum…
The Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of…
We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum table reads, to…
Quantum machine learning deals with leveraging quantum theory with classic machine learning algorithms. Current research efforts study the advantages of using quantum mechanics or quantum information theory to accelerate learning time or…
The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that…
We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be…
We derive a set of composite pulse sequences that generates CNOT gates and correct all systematic errors within the logical subspace to arbitrary order. These sequences are applicable for any two-qubit interaction Hamiltonian, and make no…
Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It…
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm…
A quantum algorithm is exact if, on any input data, it outputs the correct answer with certainty (probability 1). A key question is: how big is the advantage of exact quantum algorithms over their classical counterparts: deterministic…
We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise…
Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…
We provide a simple framework for the synthesis of quantum circuits based on a numerical optimization algorithm. This algorithm is used in the context of the trapped-ions technology. We derive theoretical lower bounds for the number of…
Gate-model quantum computers provide an experimentally implementable architecture for near term quantum computations. To design a reduced quantum circuit that can simulate a high complexity reference quantum circuit, an optimization should…