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Quantum ptychography is a method for estimating an unknown pure quantum state by subjecting it to overlapping projections, each one followed by a projective measurement on a single prescribed basis. Here, we present a comprehensive study of…
We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) to…
By encoding a qudit in a harmonic oscillator and investigating the infinite limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators for…
We found that the actual computational time-cost of the QFT is O(n 2^n) for large n in a quantum computer using nuclear spins. The computational cost of a quantum algorithm has usually been estimated as the sum of the universal gates…
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 addition based on the quantum Fourier transform can be an integral part of a quantum circuit and proved to be more efficient than the existing classical ripple carry adder. Our study includes identifying the quantum resource…
Many quantum algorithms make use of ancilla, additional qubits used to store temporary information during computation, to reduce the total execution time. Quantum computers will be resource-constrained for years to come so reducing ancilla…
This paper proposes a method of quantum Monte Carlo integration that retains the full quadratic quantum advantage, without requiring any arithmetic or quantum phase estimation to be performed on the quantum computer. No previous proposal…
Prime factorization (P = M*N) is considered to be a promising application in quantum computations. We perform 4-bit factorization in experiments using a superconducting flux qubit toward quantum annealing. Our proposed method uses a…
We present a method for estimating the probabilities of outcomes of a quantum circuit using Monte Carlo sampling techniques applied to a quasiprobability representation. Our estimate converges to the true quantum probability at a rate…
The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are…
This paper presents a method for constructing quantum circuits for schoolbook multiplication using controlled add-subtract circuits, asymptotically halving the Toffoli count compared to traditional controlled-adder-based constructions.…
The use of mid-circuit measurement and qubit reset within quantum programs has been introduced recently and several applications demonstrated that perform conditional branching based on these measurements. In this work, we go a step further…
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…
We present two methods for the construction of quantum circuits for quantum error-correcting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC…
The synthesis of a quantum circuit consists in decomposing a unitary matrix into a series of elementary operations. In this paper, we propose a circuit synthesis method based on the QR factorization via Householder transformations. We…
We present a scalable set of universal gates and multiply controlled gates in a qudit basis through a bijective mapping from N qubits to qudits with D = 2^N levels via rotations in U(2). For each of the universal gates (H, CNOT, and T), as…
We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls applying $n$ single-qubit arbitrary phase rotations from $4n b+\mathcal{O}(\sqrt{cn b})$ to $2n b+\mathcal{O}(\sqrt{cn…
We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive…
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis…