Probabilistic nonunitary quantum computing

Colin P. Williams

doi:10.1117/12.542413

24 August 2004 Probabilistic nonunitary quantum computing

Colin P. Williams

Proceedings Volume 5436, Quantum Information and Computation II; (2004) https://doi.org/10.1117/12.542413
Event: Defense and Security, 2004, Orlando, Florida, United States

Abstract

In [1] 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.

Citation Download Citation

Colin P. Williams "Probabilistic nonunitary quantum computing", Proc. SPIE 5436, Quantum Information and Computation II, (24 August 2004); https://doi.org/10.1117/12.542413

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available