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- Vivek V. Shende, Stephen S. Bullock, Igor L. Markov
- IEEE Transactions on Computer-Aided Design of…
- 2005

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)

- Stephen S. Bullock, Igor L. Markov
- Quantum Information & Computation
- 2004

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)

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)

- Stephen S Bullock, Dianne P O'Leary, Gavin K Brennen
- Physical review letters
- 2005

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)

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
- Proceedings Design, Automation and Test in Europe…
- 2004

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)

We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare favorably to previously published results. Temporary storage is not used because it tends to be expensive in physical… (More)

- G. K. Brennen, Stephen S. Bullock, Dianne P. O'Leary
- Quantum Information & Computation
- 2006

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)

On pure states of n quantum bits, the concurrence entanglement monotone returns the norm of the inner product of a pure state with its spin-flip. The monotone vanishes for n odd, but for n even there is an explicit formula for its value on mixed states, i.e., a closed-form expression computes the minimum over all ensemble decompositions of a given density.… (More)