Related papers: Unitarization Through Approximate Basis
Quantum symmetrization is the task of transforming a non-strictly increasing list of $n$ integers into an equal superposition of all permutations of the list (or more generally, performing this operation coherently on a superposition of…
The accurate evaluation of diagonal unitary operators is often the most resource-intensive element of quantum algorithms such as real-space quantum simulation and Grover search. Efficient circuits have been demonstrated in some cases but…
A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor…
The initial state creation is a starting point of many quantum algorithms and usually is considered as a separate subroutine not included into the algorithm itself. There are many algorithms aimed on creation of special class of states. Our…
Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all one-qubit…
Understanding the complexity of quantum states and circuits is a central challenge in quantum information science, with broad implications in many-body physics, high-energy physics and quantum learning theory. A common way to model the…
This work presents an optimization-based scalable quantum neural network framework for approximating $n$-qubit unitaries through generic parametric representation of unitaries, which are obtained as product of exponential of basis elements…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
Experiments in coherent nuclear and electron magnetic resonance,and quantum computing in general correspond to control of quantum mechanical systems, guiding them from initial to final target states by unitary transformations. The control…
A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
Implementing a quantum circuit on specific hardware with a reduced available gate set is often associated with a substantial increase in the length of the equivalent circuit. This process is also known as transpilation and due to…
Preparing the ground state of a local Hamiltonian is a crucial problem in understanding quantum many-body systems, with applications in a variety of physics fields and connections to combinatorial optimization. While various quantum…
We investigate protocols for generating a state $t$-design by using a fixed separable initial state and a diagonal-unitary $t$-design in the computational basis, which is a $t$-design of an ensemble of diagonal unitary matrices with random…
We present a formulation of the problem of finding the smallest T -Count circuit that implements a given unitary as a binary search over a sequence of continuous minimization problems, and demonstrate that these problems are numerically…
We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…
The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work…
Noise poses a challenge for any real-world implementation in quantum information science. The theory of quantum error correction deals with this problem via methods to encode and recover quantum information in a way that is resilient…