Research in Optical Sciences

Ancilla-based quantum simulation

Katherine L. Brown, Suvabrata De, Viv M. Kendon, William J. Munro

Published Jan 1, 2012• 4 citations

Abstract

We describe in detail how a qubus quantum computer using a continuous variable ancilla to control the qubits can provide significant efficiency savings for quantum simulation. We illustrate this by using as an example the simulation of the Bardeen, Cooper and Schrieffer (BCS) Hamiltonian, a model of low-temperature superconductivity. We demonstrate an O(Ns) improvement over previous studies conducted on an NMR computer [1, 2] for nearest- neighbour and completely general cases. We make these results controlled on an ancilla qubit so that we can apply the phase estimation algorithm, and hence show that when N ≥ 5, our qubus simulation requires significantly fewer operations than a similar simulation conducted on an NMR computer.

DOI: 10.1364/qim.2012.qw4a.5

Related papers

Ancilla-based quantum simulation

Katherine L. Brown, Suvabrata De, Viv M. Kendon +1 more

We consider the simulation of the Bardeen, Cooper and Schrieffer (BCS) Hamiltonian, a model of low-temperature superconductivity, on a quantum computer. In particular, we consider conducting the simulation on the qubus quantum computer, which uses a continuous variable ancilla to generate interactions between qubits. We demonstrate an O ( N 3 ) improvement over previous studies conducted on an NMR computer (Wu et al 2002 Phys. Rev. Lett. 89 057904 and Brown et al 2006 Phys. Rev. Lett. 97 050504) for the nearest-neighbour and completely general cases. We then proceed to show methods for minimizing the number of operations needed per time step using the qubus in three cases: the completely general case, the case of exponentially decaying interactions and the case of fixed range interactions. We make these results controlled on an ancilla qubit so that we can apply the phase estimation algorithm, and hence show that when N ⩾5, our qubus simulation requires significantly fewer operations than a similar simulation conducted on an NMR computer.

arXiv:1011.2984New Journal of PhysicsSep 14, 201119 citations

Qubus ancilla-driven quantum computation

Katherine Louise Brown, Suvabrata De, Viv M. Kendon +1 more

Hybrid matter-optical systems offer a robust, scalable path to quantum computation. Such systems have an ancilla which acts as a bus connecting the qubits. We demonstrate how using a continuous variable qubus as the ancilla provides savings in the total number of operations required when computing with many qubits.

AIP conference proceedingsJan 1, 20141 citation

Using the qubus for quantum computing

Katherine Louise Brown

In this thesis I explore using the qubus for quantum computing. The qubus is an architecture of quantum computing, where a continuous variable ancilla is used to generate operations between matter qubits. I concentrate on using the qubus for two purposes - quantum simulation, and generating cluster states. Quantum simulation is the idea of using a quantum computer to simulate a quantum system. I focus on conducting a simulation of the BCS Hamiltonian. I demonstrate how to perform the necessary two qubit operations in a controlled fashion using the qubus. In particular I demonstrate an O(N3) saving over an implementation on an NMR computer, and a factor of 2 saving over a naıve technique. I also discuss how to perform the quantum Fourier transform on the qubus quantum computer. I show that it is possible to perform the quantum Fourier transform using just, 24⌊N/2⌋ + 7N − 6, this is an O(N) saving over a naıve method. In the second part of the thesis, I move on, and consider generating cluster states using the qubus. A cluster state, is a universal resource for one-way or measurement-based computation. In one-way computation, the pre-generated, entangled resource is used to perform calculations, which only require local corrections and measurement. I demonstrate that the qubus can generate cluster states deterministically, and in a relatively short time. I discuss several techniques of cluster state generation, one of which is optimal, given the physical architecture we are using. This can generate an n × m cluster in only 3nm − 2n − 2m + 4 operations. The alternative techniques look at generating a cluster using layers or columns, allowing it to be built dynamically, while the cluster is used to perform calculations. I then move on, and discuss problems with error accumulation in the generation process.

Apr 1, 20117 citations

Quantum phase processing and its applications in estimating phase and entropies

Youle Wang, Lei Zhang, Zhan Yu +1 more

Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates and make quantum algorithms fundamentally different from their classical counterparts. Based on this unique principle of quantum computing, we develop an algorithmic toolbox, quantum phase processing, that can directly apply arbitrary trigonometric transformations to eigenphases of a unitary operator. The quantum phase processing circuit is constructed simply, consisting of single-qubit rotations and controlled unitaries, typically using only one ancilla qubit. Besides the capability of phase transformation, quantum phase processing in particular can extract the eigeninformation of quantum systems by simply measuring the ancilla qubit, making it naturally compatible with indirect measurement. Quantum phase processing complements another powerful framework known as quantum singular value transformation and leads to more intuitive and efficient quantum algorithms for solving problems that are particularly phase related. As a notable application, we propose a quantum phase estimation algorithm without quantum Fourier transform, which requires the fewest ancilla qubits and matches the best performance so far. We further exploit the power of our method by investigating a plethora of applications in Hamiltonian simulation, entanglement spectroscopy, and quantum entropy estimation, demonstrating improvements or optimality for almost all cases.

arXiv:2209.14278Physical Review ADec 13, 202330 citations

Parallelizing gates with high-dimensional ancillas

Katherine L. Brown, Suvabrata De, Viv M. Kendon

A qubus quantum computer can perform a quantum Fourier transform with a linear number of operations. This implies continuous-variable ancilla-driven quantum computation is equivalent to the quantum circuit model plus unbounded fan-out.

Conference on Lasers and Electro-OpticsJan 1, 20120 citations

Minimal ancilla-controlled quantum computation

Timothy J Proctor, Erika Andersson, Viv M. Kendon

We characterise a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is required to the computational register and the dynamics of both the register and ancilla are unitary. This scheme is inspired by the measurement-based ancilla-driven quantum computation of Anders et al. [PRA 82, 020301(R), 2010], but does not require measurements of the ancillas, and in this respect is similar to the original gate based model of quantum computation. We consider what possible forms this ancilla-register interaction can take, with a proof that the interaction is necessarily locally equivalent to SWAP combined with an entangling controlled gate. We further show which Hamiltonians can create such interactions and discuss two examples; the two-qubit XY Hamiltonian and a particular case of the XXZ Hamiltonian. We then give an example of a simple, finite and fault tolerant gate set for universal quantum computation in this model.

Jul 23, 20130 citations