Related papers: On the Constant Depth Implementation of Pauli Expo…
We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the…
The cost of measuring quantum expectation values of an operator can be reduced by grouping the Pauli string ($SU(2)$ tensor product) decomposition of the operator into maximally commuting sets. We detail an algorithm, presented in [1], to…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators $H=\sum_k A_k$, for…
We elaborate on the recent idea of a direct decomposition of Feynman integrals onto a basis of master integrals on maximal cuts using intersection numbers. We begin by showing an application of the method to the derivation of contiguity…
Decoupling systems into independently evolving components has a long history of simplifying seemingly complex systems. They enable a better understanding of the underlying dynamics and causal structures while providing more efficient means…
As quantum devices continue to grow in size but remain affected by noise, it is crucial to determine when and how they can outperform classical computers on practical tasks. A central piece in this effort is to develop the most efficient…
We show that some common and important global constraints like ALL-DIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These…
Clifford circuits play an important role in quantum computation. Gottesman and Chuang proposed a gate teleportation protocol so that a quantum circuit can be implemented by the teleportation circuit with specific ancillary qubits. In…
Pauli-based computation (PBC) is a universal model for quantum computation with qubits where the input state is a magic (resource) state and the computation is driven by a sequence of adaptively chosen and compatible multiqubit Pauli…
Effective spin-spin interactions between N+1 qubits enable the determination of the eigenvalue of an arbitrary Pauli product of dimension N with a constant, small number of multi-qubit gates that is independent of N and encodes the…
We present an optimization of the reduction algorithm of one-loop amplitudes in terms of master integrals. It is based on the exploitation of the polynomial structure of the integrand when evaluated at values of the loop-momentum fulfilling…
Quantum computers can efficiently simulate Lindbladian dynamics, enabling powerful applications in open system simulation, thermal and ground-state preparation, autonomous quantum error correction, dissipative engineering, and more. Despite…
We investigate deep composite polynomial approximations of continuous but non-differentiable functions with algebraic cusp singularities. The functions in focus consist of finitely many cusp terms of the form $|x-a_j|^{\alpha_j}$ with…
Recently, Nielsen et al have proposed a geometric approach to quantum computation. They've shown that the size of the minimum quantum circuits implementing a unitary U, up to polynomial factors, equals to the length of minimal geodesic from…
We propose a method for decomposing continuous-variable operations into a universal gate set, without the use of any approximations. We fully characterize a set of transformations admitting exact decompositions and describe a process for…
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…
The Pauli channel acting on 2 x 2 matrices is generalized to an n-level quantum system. When the full matrix algebra M is decomposed into pairwise complementary subalgebras, then trace-preserving linear mappings from M to M are constructed…
While 2-level systems, aka qubits, are a natural choice to perform a logical quantum computation, the situation is less clear at the physical level. Encoding information in higher-dimensional physical systems can indeed provide a first…
We introduce a coefficient-decoupled matrix product operator (MPO) representation for Pauli-sum operators that separates reusable symbolic operator support from a tunable coefficient bridge across a fixed bipartition. This representation…
The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome…