Related papers: Possibilistic simulation of quantum circuits by cl…
A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantum-computational gate, then topological…
Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable…
We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof…
Classical simulation of quantum circuits is a critical tool for validating quantum hardware and probing the boundary between classical and quantum computational power. Existing state-of-the-art methods, notably tensor network approaches,…
We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…
We introduce a framework for simulating, on an $(n+1)$-qubit quantum computer, the action of a Gaussian Bosonic (GB) circuit on a state over $2^n$ modes. Specifically, we encode the initial bosonic state's expectation values over quadrature…
This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any…
It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes…
Current quantum computing hardware is restricted by the availability of only few, noisy qubits which limits the investigation of larger, more complex molecules in quantum chemistry calculations on quantum computers in the near-term. In this…
We give an efficient algorithm to evaluate a certain class of exponential sums, namely the periodic, quadratic, multivariate half Gauss sums. We show that these exponential sums become $\#\mathsf{P}$-hard to compute when we omit either the…
The reversible implementation of classical functions accounts for the bulk of most known quantum algorithms. As a result, a number of reversible circuit constructions over the Clifford+$T$ gate set have been developed in recent years which…
In order to evaluate, validate, and refine the design of new quantum algorithms or quantum computers, researchers and developers need methods to assess their correctness and fidelity. This requires the capabilities of quantum circuit…
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model…
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…
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 show that a classical algorithm based on sparse Pauli dynamics can efficiently simulate quantum circuits studied in a recent experiment on 127 qubits of IBM's Eagle processor [Nature 618, 500 (2023)]. Our classical simulations on a…
We show that the quantum parity gate on $n > 3$ qubits cannot be cleanly simulated by a quantum circuit with two layers of arbitrary C-SIGN gates of any arity and arbitrary 1-qubit unitary gates, regardless of the number of allowed ancilla…
A general quantum circuit can be simulated classically in exponential time. If it has a planar layout, then a tensor-network contraction algorithm due to Markov and Shi has a runtime exponential in the square root of its size, or more…
It is shown that the fault testing for quantum circuits does not follow conventional classical techniques. If probabilistic gate like Hadamard gate is included in a circuit then the classical notion of test vector is shown to fail. We have…
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…