Related papers: Efficient quantum circuits for binary elliptic cur…
In this work, we report on a novel quantum gate approximation algorithm based on the application of parametric two-qubit gates in the synthesis process. The utilization of these parametric two-qubit gates in the circuit design allows us to…
In this paper, we give quantum circuits for calculating two closely related linear transforms that we refer to jointly as Mobius-like transforms. The first is the Mobius transform of a function $f^{-}(S^-)\in \mathbb{C}$, where $S^-\subset…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing's tket compiler. We present…
A new approach to discretization of the Duffing equation is presented. Integrable discrete maps are obtained by using well-studied encrypting operations in elliptic curve cryptography and, therefore, they do not depend upon standard small…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
We study in detail the algebraic structures underlying quantum circuits generated by CNOT gates. Our results allow us to propose polynomial-time heuristics to reduce the number of gates used in a given CNOT circuit and we also give…
Quantum circuits for basic mathematical functions such as the square root are required to implement scientific computing algorithms on quantum computers. Quantum circuits that are based on Clifford+T gates can easily be made fault tolerant…
A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e.,…
Gate set tomography (GST) is a self-consistent and highly accurate method for the tomographic reconstruction of a quantum information processor's quantum logic operations, including gates, state preparations, and measurements. However,…
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…
Complex quantum simulation workflows are often hindered by incompatible wavefunction representations adopted across different algorithmic frameworks. In particular, the mismatch between the first- and second-quantization formalisms prevents…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed…
All quantum gates with one and two qubits may be described by elements of $Spin$ groups due to isomorphisms $Spin(3) \simeq SU(2)$ and $Spin(6) \simeq SU(4)$. However, the group of $n$-qubit gates $SU(2^n)$ for $n > 2$ has bigger dimension…
Current techniques for formally verifying circuits implemented in Galois field (GF) arithmetic are limited to those with a known irreducible polynomial P(x). This paper presents a computer algebra based technique that extracts the…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…
Quantum algorithms to solve practical problems in quantum chemistry, materials science, and matrix inversion often involve a significant amount of arithmetic operations which act on a superposition of inputs. These have to be compiled to a…
Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy…
We perform logical and physical resource estimation for computing binary elliptic curve discrete logarithms using Shor's algorithm on fault-tolerant quantum computers. We adopt a windowed approach to design our circuit implementation of the…