Related papers: Pfaffian Circuits
High-fidelity and robust quantum manipulation is the key for scalable quantum computation. Therefore, due to the intrinsic operational robustness, quantum manipulation induced by geometric phases is one of the promising candidates. However,…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
Homogenous Boolean function is an essential part of any cryptographic system. The ability to construct an optimized reversible circuits for homogeneous Boolean functions might arise the possibility of building cryptographic system on novel…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
Recent work on Euclidean quantum gravity, black hole thermodynamics, and the holographic principle has seen the return of random matrix models as a powerful tool. It is explained how they allow for the study of the physics well beyond the…
Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems using parameterized quantum circuits (PQCs). The design of these circuits influences the ability of…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
Holographic functional methods are introduced as probes of discrete time-stepped maps that lead to chaotic behavior. The methods provide continuous time interpolation between the time steps, thereby revealing the maps to be…
The concept of the quantum Pfaffian is rigorously examined and refurbished using the new method of quantum exterior algebras. We derive a complete family of Pl\"ucker relations for the quantum linear transformations, and then use them to…
In this work we study quantum algorithms for Hopcroft's problem which is a fundamental problem in computational geometry. Given $n$ points and $n$ lines in the plane, the task is to determine whether there is a point-line incidence. The…
We present a quantum algorithm for approximating the linear structures of a Boolean function $f$. Different from previous algorithms (such as Simon's and Shor's algorithms) which rely on restrictions on the Boolean function, our algorithm…
Quantum simulation is a popular application of quantum computing, but its practical realization is hindered by the technical limitations of current devices. In this work, we focus on preprocessing Hamiltonians before Trotterization to…
We investigate pfaffian trial wave functions with singlet and triplet pair orbitals by quantum Monte Carlo methods. We present mathematical identities and the key algebraic properties necessary for efficient evaluation of pfaffians.…
In a calculation of rotated matrix elements with angular momentum projection, the generalized Wick's theorem may encounter a practical problem of combinatorial complexity when the configurations have more than four quasi-particles (qps).…
We present a general technique to implement products of many qubit operators communicating via a joint harmonic oscillator degree of freedom in a quantum computer. By conditional displacements and rotations we can implement Hamiltonians…
We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
Fermionic Gaussian operators are foundational tools in quantum many-body theory, numerical simulation of fermionic dynamics, and fermionic linear optics. While their structure is fully determined by two-point correlations, evaluating their…