Related papers: Quantum Circuits for Matrix-Product Unitaries
Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the…
Monitored random circuits, consisting of alternating layers of entangling two-qubit gates and projective single-qubit measurements applied to some fraction $p$ of the qubits, have been a topic of recent interest. In particular, the…
Data representation in quantum state space offers an alternative function space for machine learning tasks. However, benchmarking these algorithms at a practical scale has been limited by ineffective simulation methods. We develop a quantum…
Finite-depth quantum circuits preserve the long-range entanglement structure in quantum states and map between states within a gapped phase. To map between states of different gapped phases, we can use Sequential Quantum Circuits which…
Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most…
We extend quantum circuit cutting to heterogeneous registers comprising mixed-dimensional qudits. By decomposing non-local interactions into tensor products of local generalised Gell-Mann matrices, we enable the simulation and execution of…
We exhibit some simple gadgets useful in designing shallow parallel circuits for quantum algorithms. We prove that any quantum circuit composed entirely of controlled-not gates or of diagonal gates can be parallelized to logarithmic depth,…
We define a map from an arbitrary quantum circuit to a local Hamiltonian whose ground state encodes the quantum computation. All previous maps relied on the Feynman-Kitaev construction, which introduces an ancillary `clock register' to…
We propose a method for the implementation of one-way quantum computing in superconducting circuits. Measurement-based quantum computing is a universal quantum computation paradigm in which an initial cluster-state provides the quantum…
The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to…
We show how to explicitly construct an $O(nd)$ size and constant quantum depth circuit which encodes any given $n$-qubit stabilizer code with $d$ generators. Our construction is derived using the graphic description for stabilizer codes and…
Many-body ground state preparation is an important subroutine used in the simulation of physical systems. In this paper, we introduce a flexible and efficient framework for obtaining a state preparation circuit for a large class of…
Quantum computing has been revolutionizing the development of algorithms. However, only noisy intermediate-scale quantum devices are available currently, which imposes several restrictions on the circuit implementation of quantum…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the…
This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to…
In the age of noisy quantum processors, the exploitation of quantum symmetries can be quite beneficial in the efficient preparation of trial states, an important part of the variational quantum eigensolver algorithm. The benefits include…
Quantum circuits are time dependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable and heuristic methods must…
Modular quantum computing architectures are a promising alternative to monolithic QPU (Quantum Processing Unit) designs for scaling up quantum devices. They refer to a set of interconnected QPUs or cores consisting of tightly coupled…
Measurement-based uncomputation (MBU) is a technique used to perform probabilistic uncomputation of quantum circuits. We formalize this technique for the case of single-qubit registers, and we show applications to modular arithmetic. First,…