Algorithmic cooling and scalable NMR quantum computers

Boykin, P. Oscar; Mor, Tal; Roychowdhury, Vwani P.; Vatan, Farrokh; Vrijen, R. B.

doi:10.1073/pnas.241641898

Cited by 170 publications

(220 citation statements)

References 12 publications

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“…(20), it is first necessary to derive a suitable approximation for the superoperator L(t), defined by Eq. (9). As will be shown below, when H 0 (t) generates sufficiently rapid oscillations inṼ (t), a leading-order Magnus expansion can be performed on the time-ordered exponential in Eq.…”

Section: Fig 1 (Color Online) (A)mentioning

confidence: 99%

“…As will be shown below, when H 0 (t) generates sufficiently rapid oscillations inṼ (t), a leading-order Magnus expansion can be performed on the time-ordered exponential in Eq. (9). For a sufficiently large environment with initial state described by many uncorrelated degrees of freedom, the moments associated with the average · · · E will be approximately Gaussian.…”

Section: Fig 1 (Color Online) (A)mentioning

confidence: 99%

“…Pure ancillas are required to introduce redundancy into quantum errorcorrecting codes, [1][2][3][4][5][6] for the preparation of GreenbergerHorne-Zeilinger (GHZ) states for quantum-enhanced precision measurements, 7,8 as a low-entropy resource for algorithmic cooling, [9][10][11] and to perform high-fidelity qubit readout. [12][13][14][15] Despite the importance of having high-quality ancillas, it is often taken for granted that high-purity ancillas can be prepared by allowing a physical qubit system to fall into its non-interacting ground state in contact with a thermal bath at low temperature.…”

Section: Introductionmentioning

confidence: 99%

“…This topic has become especially interesting in the context of spin-bath dynamics. [17][18][19][20] For slowly-evolving nuclear-spin baths, it is indeed possible to approach pure-state initial conditions through algorithmic cooling [9][10][11] or direct measurement of the bath state, 13,[21][22][23][24][25] so studying the purity for these systems is especially important from both a practical and a fundamental point of view.…”

Section: Introductionmentioning

confidence: 99%

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Maximizing the purity of a qubit evolving in an anisotropic environment

2015

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We provide a general method to calculate and maximize the purity of a qubit interacting with an anisotropic non-Markovian environment. Counter to intuition, we find that the purity is often maximized by preparing and storing the qubit in a superposition of non-interacting eigenstates. For a model relevant to decoherence of a heavy-hole spin qubit in a quantum dot or for a singlettriplet qubit for two electrons in a double quantum dot, we show that preparation of the qubit in its non-interacting ground state can actually be the worst choice to maximize purity. We further give analytical results for spin-echo envelope modulations of arbitrary spin components of a hole spin in a quantum dot, going beyond a standard secular approximation. We account for general dynamics in the presence of a pure-dephasing process and identify a crossover timescale at which it is again advantageous to initialize the qubit in the non-interacting ground state. Finally, we consider a general two-axis dynamical decoupling sequence and determine initial conditions that maximize purity, minimizing leakage to the environment.

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Section: Fig 1 (Color Online) (A)mentioning

confidence: 99%

Section: Fig 1 (Color Online) (A)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Maximizing the purity of a qubit evolving in an anisotropic environment

2015

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“…

We introduce a scheme to perform the cooling algorithm, first presented by Boykin et al in 2002, for an arbitrary number of times on the same set of qbits. We achieve this goal by adding an additional SWAP-gate and a bath contact to the algorithm.

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confidence: 99%

Cyclic cooling algorithm

2007

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We introduce a scheme to perform the cooling algorithm, first presented by Boykin et al. in 2002, for an arbitrary number of times on the same set of qbits. We achieve this goal by adding an additional SWAP-gate and a bath contact to the algorithm. This way one qbit may repeatedly be cooled without adding additional qbits to the system. By using a product Liouville space to model the bath contact we calculate the density matrix of the system after a given number of applications of the algorithm.PACS numbers: 03.67.Lx, Algorithmic cooling is a method to obtain highly polarized spins in a spin system without cooling down the environment. It may for example be used for medical magnetic resonance imaging to improve the resolution by cooling down a subset of nuclear spins of a patient without cooling of the patient himself, or for the preparation of the ground state of a quantum computer by means of the computer itself, that means that no external cooling mechanism would have to be attached to the system [1,2].The spin to be cooled down (a nuclear spin for example) has to couple weakly to the environment. In addition one uses some rapid relaxing spins to transport energy out of the system. The transportation of energy from the cooled spin to the others is achieved in a strictly non classical way by applying a quantum algorithm to the system, therefore the spins are further referred to as qbits.Recently, Boykin et al. [3] have developed a quantum algorithm to cool down a single qbit with the aid of two auxiliary qbits. Initially the system is prepared in an equilibrium state with all spins at the same inverse temperature β(0). (Note that we label all quantities belonging to the n th application of the algorithm by (n), so the initial state and the temperature of the bath, introduced later on, are labeled (0).) By applying several quantum gate operations one spin is cooled down by transferring energy to the others. The algorithm itself consists of a controlled NOT (CNOT) gate and a controlled swap gate (CSWAP) [4]. The CSWAP is a 3 qbit gate which swaps qbit 1 with qbit 3 if qbit 2 is |0 , otherwise it does nothing. This leads to an increase of the inverse temperature β(1) of qbit 1 to approximately 3/2 β(0) (cf. [3,5]). Having applied the algorithm once, the initial state is recovered by two further applications of the algorithm. However, by cooling down two other qbits by applying the same algorithm as described above to two additional sets of 3 qbits allows a second application of * Electronic address: Florian.Rempp@itp1.uni-stuttgart.de 00 00 11 11

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Introduction to Quantum Algorithms for Physics and Chemistry

Yung¹,

Whitfield²,

Boixo³

et al. 2014

Advances in Chemical Physics

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An enormous number of model chemistries are used in computational chemistry to solve or approximately solve the Schrödinger equation; each with their own drawbacks. One key limitation is that the hardware used in computational chemistry is based on classical physics, and is often not well suited for simulating models in quantum physics. In this review, we focus on applications of quantum computation to chemical physics problems. We describe the algorithms that have been proposed for the electronicstructure problem, the simulation of chemical dynamics, thermal state preparation, density functional theory and adiabatic quantum simulation.

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Algorithmic cooling and scalable NMR quantum computers

Cited by 170 publications

References 12 publications

Maximizing the purity of a qubit evolving in an anisotropic environment

Maximizing the purity of a qubit evolving in an anisotropic environment

Cyclic cooling algorithm

Introduction to Quantum Algorithms for Physics and Chemistry

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