Related papers: Low-depth unitary quantum circuits for dualities i…
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters…
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an…
Whether a given target state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit is a key question in condensed matter physics and quantum information science. It underpins classifications…
The $U(1)$ quantum link model on the triangular lattice has two rotation-symmetry-breaking nematic confined phases. Static external charges are connected by confining strings consisting of individual strands with fractionalized electric…
This paper addresses the problem of designing universal quantum circuits to transform $k$ uses of a $d$-dimensional unitary input-operation into a unitary output-operation in a probabilistic heralded manner. Three classes of protocols are…
Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that…
Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous…
We introduce an extended framework for the simultaneous gauging of modulated symmetries in $(d+1)$ dimensions, employing {\it multiple} gauge symmetry operators whose corresponding gauging procedures must be carried out simultaneously.…
Unitarity serves as a fundamental concept for characterizing linear and conservative wave phenomena in both classical and quantum systems. Developing platforms that perform unitary operations on light waves in a uni-versal and programmable…
A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multi-body observables. One strategy to reduce circuit depth in such algorithms involves…
Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…
Current quantum devices have unutilized high-level quantum resources. More and more attention has been paid to the qudit quantum systems with larger than two dimensions to maximize the potential computing power of quantum computation. Then,…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
Classical planar vertex models afford transfer matrices with real and positive entries, which makes this class of models suitable for quantum simulations. In this work, we support this statement by building explicit quantum circuits that…
Quantum circuits offer a versatile platform for simulating digital quantum dynamics and uncovering novel states of non-equilibrium quantum matter. One principal example are measurement-induced phase transitions arising from non-unitary…
The development of large-scale, programmable photonic circuits capable of performing generic matrix-vector multiplication is essential for both classical and quantum information processing. However, this goal is hindered by high losses,…
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing…
We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be…
Implementing many important sub-circuits on near-term quantum devices remains a challenge due to the high levels of noise and the prohibitive depth on standard nearest-neighbour topologies. Overcoming these barriers will likely require…