Related papers: On the most efficient unitary transformation for p…
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…
Block encodings are a fundamental primitive in quantum algorithms, but can often have large ancilla overhead. In this work, we introduce novel techniques for reducing this overhead in two distinct ways. In Part I, we prove the existence of…
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a…
Optimizing quantum circuits is critical: the number of quantum operations needs to be minimized for a successful evaluation of a circuit on a quantum processor. In this paper we unify two disparate ideas for optimizing quantum circuits,…
Dynamics of many-qubit systems, that may correspond to computational processing with quantum systems, can be efficiently and generally approximated by a sequence of two- and single-qubit gates. In practical applications, however, a quantum…
Any evolution described by a completely positive trace-preserving linear map can be imagined as arising from the interaction of the evolving system with an initially uncorrelated ancilla. The interaction is given by a joint unitary…
Here, we study the capacity of a quantum channel, assuming linear optical encoding, as a function of available photons and optical modes. First, we observe that substantial improvement is made possible by not restricting ourselves to a…
Combinatorial optimization problems are considered to be an application, where quantum computing can have transformative impact. In the industrial context, job shop scheduling problems that aim at finding the optimal schedule for a set of…
Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
Given the key role that quantum tunneling plays in a wide range of applications, a crucial objective is to maximize the probability of tunneling from one quantum state/level to another, while keeping the resources of the underlying physical…
Solving linear systems of equations is an important problem in science and engineering. Many quantum algorithms, such as the Harrow-Hassidim-Lloyd (HHL) algorithm (for quantum-gate computers) and the box algorithm (for quantum-annealing…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
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…
We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate…
From the set of operators for errors and its correction code, we introduce the so-called complete unitary transformation. It can be used for encoding while the inverse of it can be applied for correcting the errors of the encoded qubit. We…
Single-shot quantum channel discrimination is a fundamental task in quantum information theory. It is well known that entanglement with an ancillary system can help in this task, and furthermore that an ancilla with the same dimension as…
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit…
A $2\otimes 2$ unitary operation is called a perfect entangler if it can generate a maximally entangled state from some unentangled input. We study the following question: How many runs of a given two-qubit entangling unitary operation is…
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…
We address the fundamental task of converting $n$ uses of an unknown unitary transformation into a quantum state (i.e., storage) and later retrieval of the transformation. Specifically, we consider the case where the unknown unitary is…