Related papers: Clifford Circuits Augmented Grassmann Matrix Produ…
We present an efficient protocol leveraging classical computation to support Initial State Preparation for strongly correlated fermionic systems, a critical bottleneck for fault-tolerant quantum simulation. Focusing on nuclear shell model…
We present a simple but general framework for constructing quantum circuits that implement the multiply-controlled unitary $\text{Select}(H) \equiv \sum_\ell |\ell\rangle\langle\ell|\otimes H_\ell$, where $H = \sum_\ell H_\ell$ is the…
Estimating quantum fermionic properties is a computationally difficult yet crucial task for the study of electronic systems. Recent developments have begun to address this challenge by introducing classical shadows protocols relying on…
We present a discussion of the generalized Clifford group over non-cyclic finite abelian groups. These Clifford groups appear naturally in the theory of topological error correction and abelian anyon models. We demonstrate a generalized…
Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in…
Variational quantum algorithms are considered to be appealing applications of near-term quantum computers. However, it has been unclear whether they can outperform classical algorithms or not. To reveal their limitations, we must seek a…
The study of fermionic quantum field theories is an important problem for realizing the standard model of particle physics on a quantum computer. As a step towards this goal, we consider the massive Thirring and Gross--Neveu models with…
We present a new technique for efficiently simulating (in polynomial time) a class of one-dimensional (1D) dissipative spin chains that, when mapped to fermions, have quadratic Hamiltonians, with the only nonlinearity coming from…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
We present an algorithm for the approximate decomposition of diagonal operators, focusing specifically on decompositions over the Clifford+$T$ basis, that minimize the number of phase-rotation gates in the synthesized approximation circuit.…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
Hamiltonian simulation represents an important module in a large class of quantum algorithms and simulations such as quantum machine learning, quantum linear algebra methods, and modeling for physics, material science and chemistry. One of…
The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be simulated efficiently on a classical computer. This paper improves that theorem in…
We construct a Grassmann tensor network representing the partition function of (1+1)-dimensional two-color QCD with staggered fermions. The Grassmann path integral is rewritten as the trace of a Grassmann tensor network by introducing…
For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate…
The threshold theorem promises a path to fault-tolerant quantum computation, provided the physical error rate is below a critical threshold. While transversal gates efficiently implement logical operations, they propagate errors and can…
In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli…
A decision diagram (DD) is a graph-like data structure for homomorphic compression of Boolean and pseudo-Boolean functions. Over the past decades, decision diagrams have been successfully applied to verification, linear algebra, stochastic…
We consider the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works this approach has been used to derive upper bounds to fault tolerance thresholds - usually by identifying a…
The design and optimization of a large-scale fault-tolerant quantum computer architecture relies extensively on numerical simulations to assess the performance of each component of the architecture. The simulation of fault-tolerant gadgets,…