Untitled

Nebe, Gabriele; Rains, Eric M.; Sloane, N. J. A.

doi:10.1023/a:1011233615437

Cited by 84 publications

(39 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…VII C, is to circuits containing a few nonstabilizer gates. The qualifier "few" is essential here, since it is known that unitary stabilizer circuits plus any additional gate yields a universal set of quantum gates [35,36]. The running time of our simulation procedure is polynomial in n, the number of qubits, but is exponential in the d, the number of nonstabilizer gates.…”

Section: Beyond Stabilizer Circuitsmentioning

confidence: 99%

Improved simulation of stabilizer circuits

2004

View full text Add to dashboard Cite

The Gottesman-Knill theorem says that a stabilizer circuit-that is, a quantum circuit consisting solely of controlled-NOT (CNOT), Hadamard, and phase gates-can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. First, by removing the need for Gaussian elimination, we make the simulation algorithm much faster at the cost of a factor of 2 increase in the number of bits needed to represent a state. We have implemented the improved algorithm in a freely available program called CHP (CNOT-Hadamard-phase), which can handle thousands of qubits easily. Second, we show that the problem of simulating stabilizer circuits is complete for the classical complexity class L, which means that stabilizer circuits are probably not even universal for classical computation. Third, we give efficient algorithms for computing the inner product between two stabilizer states, putting any n-qubit stabilizer circuit into a "canonical form" that requires at most O͑n 2 / log n͒ gates, and other useful tasks. Fourth, we extend our simulation algorithm to circuits acting on mixed states, circuits containing a limited number of nonstabilizer gates, and circuits acting on general tensor-product initial states but containing only a limited number of measurements.

show abstract

Section: Beyond Stabilizer Circuitsmentioning

confidence: 99%

Improved simulation of stabilizer circuits

2004

View full text Add to dashboard Cite

show abstract

“…Jim Harrington corrected a mistaken omission of Z in S 0,1,2,3 , and Daniel Gottesman drew our attention to Ref. [26]. We thank Allen Knutson and Eric Rains for insightful ideas on the universality of the set P, U † P U …”

Section: Acknowledgmentsmentioning

confidence: 96%

“…It is known that the Clifford group generated by {cnot, h, p} together with any other gate are universal [26]. Thus {cnot, h, p, u} is universal for any 1-qubit gate u outside the Clifford group.…”

Section: Universality Of 2-qubit Measurementsmentioning

confidence: 99%

Quantum Computation by Measurements

Leung

2004

Int. J. Quantum Inform.

View full text Add to dashboard Cite

We first consider various methods for the indirect implementation of unitary gates. We apply these methods to rederive the universality of 4-qubit measurements based on a scheme much simpler than Nielsen's original construction [quant-ph/0108020]. Then, we prove the universality of simple discrete sets of 2-qubit measurements, again using a scheme simplifying the initial construction [quant-ph/0111122]. Finally, we show how to use a single 4-qubit measurement to achieve universal quantum computation, and outline a proof for the universality of almost all maximally entangling 4-qubit measurements.

show abstract

“…It is well known that computations using only gates from the Clifford group are not universal and are efficiently classically simulatable when QVs are only measured and prepared in the computational basis [45,47,[50][51][52]. However, for prime dimension qudits the addition of any non-Clifford gate to a set of generators for the Clifford group is sufficient for universality [4,53,54] and for QCVs the addition of any continuous power of a non-Clifford gate is sufficient for universality [30,43]. In these cases, the gate normally considered is a so-called cubic phase gate of some sort, which may be defined in general by…”

Section: Universal Quantum Computationmentioning

confidence: 99%

Ancilla-driven quantum computation for qudits and continuous variables

et al. 2017

View full text Add to dashboard Cite

(2017) 'Ancilla-driven quantum computation for qudits and continuous variables. ', Physical review A., 95 (5). 052317.Further information on publisher's website:https://doi.org/10.1103/PhysRevA.95.052317Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review A 95, 052317 c (2017) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Although qubits are the leading candidate for the basic elements in a quantum computer, there are also a range of reasons to consider using higher-dimensional qudits or quantum continuous variables (QCVs). In this paper, we use a general "quantum variable" formalism to propose a method of quantum computation in which ancillas are used to mediate gates on a well-isolated "quantum memory" register and which may be applied to the setting of qubits, qudits (for d > 2), or QCVs. More specifically, we present a model in which universal quantum computation may be implemented on a register using only repeated applications of a single fixed two-body ancilla-register interaction gate, ancillas prepared in a single state, and local measurements of these ancillas. In order to maintain determinism in the computation, adaptive measurements via a classical feed forward of measurement outcomes are used, with the method similar to that in measurement-based quantum computation (MBQC). We show that our model has the same hybrid quantum-classical processing advantages as MBQC, including the power to implement any Clifford circuit in essentially one layer of quantum computation. In some physical settings, high-quality measurements of the ancillas may be highly challenging or not possible, and hence we also present a globally unitary model which replaces the need for measurements of the ancillas with the requirement for ancillas to be prepared in states from a fixed orthonormal basis. Finally, we discuss settings in which these models may be of practical interest.

show abstract

Untitled

Cited by 84 publications

References 48 publications

Improved simulation of stabilizer circuits

Improved simulation of stabilizer circuits

Quantum Computation by Measurements

Ancilla-driven quantum computation for qudits and continuous variables

Contact Info

Product

Resources

About