In  Gingrich and Williams extended the standard quantum circuit model of quantum computation to include gates that perform arbitrary linear, yet non-unitary, transformations of their input state. In this paper we use this theory to construct quantum circuits that perform desired non-unitary state transformations of the sort arising in lattice-based quantum search. Such n-qubit non-unitary gates cannot be achieved deterministically, but they can be achieved probabilistically using a single ancilla. Our approach is to use the n-qubit non-unitary gate to design an (n+1)-qubit Hamiltonian that can be seen to induce a suitable conditional dynamics such that whenever the output value of the ancilla qubit is measured and found to be |O>, then the remaining (unmeasured) n qubits will contain the desired non-unitary transform of the n-qubit input state. The scheme is necessarily probabilistic because we cannot force the measurement on the ancilla qubit to return the value we want. Fortunately, however, failed attempts are found to disturb the n-qubit input state very little. This allows us to re-use the result of successive “failed” attempts until the success condition is finally attained, and we give analytic expressions for the success probability and net fidelity in this case. By using our previous method for designing a quantum circuit for an arbitrary n-qubit gate in conjunction with our new probabilistic non-unitary procedure we are able to compute an explicit quantum circuit sufficient to implement an arbitrary linear, yet non-unitary, transformation of an input pure or mixed n-qubit state, using only a single copy of the input state. This allows us to extend the repertoire of computations that may be performed on a quantum computer, and in particular, gives the first explicit construction of the quantum circuits needed to perform some of the key operations arising in quantum lattice search.
Future quantum information processing devices will require the use of exotic quantum states, such as specially crafted entangled states, to achieve certain desired computations on demand. Thus far, synthesis schemes for such states have been devised on a case-by-case basis using ad hoc techniques. In this paper we present a systematic method for finding a quantum circuit that can synthesize any pure or mixed n-qubit state. We then give examples of the use of our algorithm for finding synthesis pathways for especially exotic quantum states such as maximal mixed states. It is not known how to prepare general instances of such states by other means. Thus our quantum state synthesis algorithm should be of use not only in quantum information processing, but also in experimental quantum physics.
We show how to beat the `fundamental' noise limits in optical lithography using entangled quantum states. In this talk we will give the theoretical background to optical lithography and its quantum formulation. A proof-in-principle experimental demonstration is described.
The technique of projective measurements in linear optics can provide apparent, efficient nonlinear interaction between photons, which is technically problematic otherwise. We present an application of such a technique to prepare large photon-number path entanglement. Large photon-number path entanglement is an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. A similar technique can also be applied to signal the presence of a single photon without destroying it. We further show how to build a quantum repeater for long-distance quantum communication.
Conference Committee Involvement (2)
Quantum Communications and Quantum Imaging II
4 August 2004 | Denver, Colorado, United States
Quantum Communications and Quantum Imaging
6 August 2003 | San Diego, California, United States