Related papers: Unified Framework for Matchgate Classical Shadows
Matchgates are a restricted set of two-qubit gates known to be classically simulable under particular conditions. Specifically, if a circuit consists only of nearest-neighbour matchgates, an efficient classical simulation is possible if…
Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on the complexity of implementing rotations generated by fermionic…
We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian…
As quantum devices scale up, many-body quantum gates and algorithms begin to surpass what is possible to simulate classically. Validation methods which rely on such classical simulation, such as process tomography and randomized…
Schemes of classical shadows have been developed to facilitate the read-out of digital quantum devices, but similar tools for analog quantum simulators are scarce and experimentally impractical. In this work, we provide a measurement scheme…
Classical shadows (CS) has recently emerged as an important framework to efficiently predict properties of an unknown quantum state. A common strategy in CS protocols is to parametrize the basis in which one measures the state by a random…
We propose a new framework of topological complexity to study the computational complexity of quantum circuits and tensor networks. Within this framework, we establish the Quon Classical Simulation (QCS) for hybrid Clifford-Matchgate…
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…
We describe a supersymmetric Grand Unified Theory based on the gauge group $\SU(5)^3$, or $\SO(10)^3$, invariant under the interchange of any~SU(5), or~SO(10), with each family multiplet transforming non trivially under one different…
Various algorithms have been developed to simulate quantum circuits on classical hardware. Among the most prominent are approaches based on \emph{stabilizer decompositions} and \emph{tensor network contraction}. In this work, we present a…
We construct an explicit algebraic realisation of three fermion generations within a single Clifford algebra, transforming under the full Standard Model $SU(3)_C\times SU(2)_L\times U(1)_Y$ gauge group, in which an intrinsic $S_3$ family…
The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in…
Matchgates are a group of two-qubit gates associated with free fermions. They are classically simulatable if restricted to act between nearest neighbors on a one-dimensional chain, but become universal for quantum computation with…
Efficiently learning expectation values of unknown quantum states via classical shadows has become an important primitive in both theoretical and experimental aspects of quantum computation. Typically, classical shadow protocols involve…
Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication [Nature 534, 516 (2016)], we proposed and experimentally…
Achieving quantum advantage in efficiently estimating collective properties of quantum many-body systems remains a fundamental goal in quantum computing. While the quantum gradient estimation (QGE) algorithm has been shown to achieve doubly…
Performing large-scale, accurate quantum simulations of many-fermion systems is a central challenge in quantum science, with applications in chemistry, materials, and high-energy physics. Despite significant progress, realizing generic…
Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements. In this…
The Clifford hierarchy, introduced by Gottesman and Chuang in 1999, is an increasing sequence of sets of quantum gates crucial to the gate teleportation model for fault-tolerant quantum computation. Gates in the hierarchy can be…
We generalize the classical shadow tomography scheme to a broad class of finite-depth or finite-time local unitary ensembles, known as locally scrambled quantum dynamics, where the unitary ensemble is invariant under local basis…