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The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits to the attention of the EDA community [10, 17, 4, 16, 9]. We discuss efficient circuits to initialize quantum registers and implement generic quantum computations. Our techniques yield circuits that… (More)

A unitary operator U = ∑ j,k u j,k |k j| is called diagonal when u j,k = 0 unless j = k. The definition extends to quantum computations , where j and k vary over the 2 n binary expressions for integers 0, 1 · · · , 2 n − 1, given n qubits. Such operators do not affect outcomes of the projective measurement { j| ; 0 ≤ j ≤ 2 n − 1} but rather create arbitrary… (More)

- Stephen S Bullock, Igor L Markov
- 2008

Quantum circuits currently constitute a dominant model for quantum computation [14]. Our work addresses the problem of constructing quantum circuits to implement an arbitrary given quantum computation, in the special case of two qubits. We pursue circuits without ancilla qubits and as small a number of elementary quantum gates [1, 15] as possible. Our lower… (More)

Scalability of a quantum computation requires that the information be processed on multiple subsystems. However, it is unclear how the complexity of a quantum algorithm, quantified by the number of entangling gates, depends on the subsystem size. We examine the quantum circuit complexity for exactly universal computation on many d-level systems (qudits).… (More)

We show how to implement an arbitrary two-qubit unitary operation using any of several quantum gate libraries with small a priori upper bounds on gate counts. In analogy to library-less logic synthesis, we consider circuits and gates in terms of the underlying model of quantum computation, and do not assume any particular technology. As increasing the… (More)

- Vivek V Shende, Stephen S Bullock, Igor L Markov

Operators acting on a collection of two-level quantum-mechanical systems can be represented by quantum circuits. This work presents a new universal quantum circuit capable of implementing any unitary operator. The circuit has a top-down structure, and the parameters for individual unitaries can be computed using standard matrix analysis algorithms. The… (More)

- Vivek V Shende, Igor L Markov, Stephen S Bullock
- 2004

An important result from the mid nineties shows that any unitary evolution may be realized as a sequence of controlled-not and one-qubit gates. This work surveys especially efficient circuits in this library, in the special case of evolutions on two-quantum bits. In particular, we show that to construct an arbitrary two-qubit state from |00, one CNOT gate… (More)

- Vivek V Shende, Igor L Markov, Stephen S Bullock
- 2003

Recently, Vatan and Williams utilize a matrix decomposition of SU(2 n) introduced by Khaneja and Glaser to produce CNOT-efficient circuits for arbitrary three-qubit unitary evolutions. In this note, we place the Khaneja Glaser Decomposition (KGD) in context as a SU(2 n) = KAK decomposition by proving that its Cartan invo-lution is type AIII, given n ≥ 3.… (More)

This paper concerns the efficient implementation of quantum circuits for qudits. We show that controlled two-qudit gates can be implemented without ancillas and prove that the gate library containing arbitrary local unitaries and one two-qudit gate, CINC, is exact-universal. A recent paper [S.Bullock,] describes quantum circuits for qudits which require O(d… (More)