Related papers: Pfaffian Circuits
Implementing quantum operations in the form of natural Hamiltonian dynamics is desirable, since they almost require no external control or feedback. In this work, we propose a NISQ-friendly quantum-classical hybrid approach to designing a…
We study the topological complexity of sets defined using Khovanskii's Pfaffian functions, in terms of an appropriate notion of format for those sets. We consider semi- and sub-Pfaffian sets, but more generally any definable set in the…
We show that Gottesman's (1998) semantics for Clifford circuits based on the Heisenberg representation gives rise to a lightweight Hoare-like logic for efficiently characterizing a common subset of quantum programs. Our applications include…
Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of Hamiltonians. The computational network of…
The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
Bosonic codes offer a hardware-efficient approach to encoding and protecting quantum information with a single continuous-variable bosonic system. In this paper, we introduce a new universal quantum gate set composed of only one type of…
We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a…
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…
We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
Spanning trees are a representative example of linear matroid bases that are efficiently countable. Perfect matchings of Pfaffian bipartite graphs are a countable example of common bases of two matrices. Generalizing these two examples,…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…
Ideas from Fourier analysis have been used in cryptography for the last three decades. Akavia, Goldwasser and Safra unified some of these ideas to give a complete algorithm that finds significant Fourier coefficients of functions on any…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
Quantum computing promises to revolutionize various fields, yet the execution of quantum programs necessitates an effective compilation process. This involves strategically mapping quantum circuits onto the physical qubits of a quantum…
Quantum fully homomorphic encryption (QFHE) allows to evaluate quantum circuits on encrypted data. We present a novel QFHE scheme, which extends Pauli one-time pad encryption by relying on the quaternion representation of SU(2). With the…
We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the input model where the entries of the Hamiltonian are stored in a data structure in a quantum random…
In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…