Related papers: Operator dynamics in k-Markov random circuits
We introduce an exact mapping of Clifford (stabilizer) random tensor networks (RTNs) and monitored quantum circuits, onto a statistical mechanics model. With Haar unitaries, the fundamental degrees of freedom ('spins') are permutations…
Topological error-correcting codes, such as surface codes and color codes, are promising because quantum operations are realized by two-dimensionally (2D) arrayed quantum bits (qubits). However, physical wiring of electrodes to qubits is…
In this paper we solve two equivalent time optimal control problems. On one hand, we design the control field to implement in minimum time the SWAP (or equivalent) operator on a two-level system, assuming that it interacts with an…
We study the problem of generating connected random graphs with no self-loops or multiple edges and that, in addition, have a given degree sequence. The generation method we focus on is the edge-switching Markov-chain method, whose…
Strongly simulating a quantum circuit, that is, computing an output amplitude, amounts to summing the circuit's Feynman paths, a weighted count over assignments to the Boolean ``path'' variables. The circuit's gates induce correlations…
We consider quantum circuit models where the gates are drawn from arbitrary gate ensembles given by probabilistic distributions over certain gate sets and circuit architectures, which we call stochastic quantum circuits. Of main interest in…
We use a novel optimization procedure that includes the temporal and spatial parameters of the pulses acting on arrays of trapped neutral atoms, to prepare entangling gates in N-qubits systems. The spatio-temporal control allows treating a…
Using the Parity Flow formalism, we show that physical SWAP gates can be eliminated in linear hardware architectures, without increasing the total number of two-qubit operations. This has a significant impact on the execution time of…
Quantum random access memories (QRAMs) are pivotal for data-intensive quantum algorithms, but existing general-purpose and domain-specific architectures are hampered by a critical bottleneck: a heavy reliance on non-Clifford gates (e.g.,…
Sampling from the stationary distribution is one of the fundamental tasks of Markov chain-based algorithms and has important applications in machine learning, combinatorial optimization and network science. For the quantum case, qsampling…
Quantum circuits are typically represented by a (ordered) sequence of gates over a set of virtual qubits. During compilation, the virtual qubits of the gates are assigned to the physical qubits of the underlying quantum hardware, a step…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
Most quantum circuits require SWAP gate insertion to run on quantum hardware with limited qubit connectivity. A promising SWAP gate insertion method for blocks of commuting two-qubit gates is a predetermined swap strategy which applies…
We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via spectral analysis of the corresponding time dependent…
Distributed quantum computing offers a potential solution to the complexity of superconducting chip hardware layouts and error correction algorithms. High-quality gates between distributed chips enable the simplification of existing error…
Nowadays quantum SWAP gate has become an integral part of quantum computing, so investigation of methods of its realization seems to be an important practical problem for various quantum-optical and information applications. In the present…
The classical simulation of quantum circuits is of central importance for benchmarking near-term quantum devices. The fact that gates belonging to the Clifford group can be simulated efficiently on classical computers has motivated a range…
In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A and B in the even and odd parity subspaces respectively, of two qubits. Using a Clifford algebra formalism we show that arbitrary uniform families of circuits of…