Optimal Algorithmic Cooling of Spins

Elias, Yuval; Fernandez, José M.; Mor, Tal; Weinstein, Yossi

doi:10.1560/ijc_46_4_371

Cited by 20 publications

(60 citation statements)

References 34 publications

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“…This idea was improved by adding contact with a heat-bath to extract entropy from the system [5], a process known as Heat-Bath Algorithmic Cooling (HBAC). Based on this work, many cooling algorithms have been designed [6][7][8][9][10][11]. HBAC is not only of theoretical interest, experiments have already demonstrated an improvement in polarization using this protocol with a few qubits [12][13][14][15][16][17][18], where a few rounds of HBAC were reached; and some studies have even included the impact of noise [19].…”

Section: Introductionmentioning

confidence: 99%

Achievable Polarization for Heat-Bath Algorithmic Cooling

Rodríguez-Briones

Laflamme

2016

Phys. Rev. Lett.

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Pure quantum states play a central role in applications of quantum information, both as initial states for quantum algorithms and as resources for quantum error correction. Preparation of highly pure states that satisfy the threshold for quantum error correction remains a challenge, not only for ensemble implementations like NMR or ESR but also for other technologies. Heat-Bath Algorithmic Cooling is a method to increase the purity of a set of qubits coupled to a bath. We investigated the achievable polarization by analysing the limit when no more entropy can be extracted from the system. In particular we give an analytic form for the maximum polarization achievable for the case when the initial state of the qubits is totally mixed, and the corresponding steady state of the whole system. It is however possible to reach higher polarization while starting with certain states, thus our result provides an achievable bound. We also give the number of steps needed to get a specific required polarization.PACS numbers: 03.67.Pp INTRODUCTIONPurification of quantum states is essential for applications of quantum information science, not only for many quantum algorithms but also as a resource for quantum error correction. The need to find a scalable way to reach approximate pure states is a challenge for many quantum computation modalities, especially the ones that relies on ensembles such as NMR or ESR [1].A potential solution is algorithmic cooling (AC), a protocol which purifies qubits by removing entropy of a subset of them, at the expense of increasing the entropy of others [2, 3]. An explicit way to implement this idea in ensemble quantum computers was given by Schulman et al. [4]. They showed that it is possible to reach polarization of order unity using only a number of qubits which is polynomial in the initial polarization. This idea was improved by adding contact with a heat-bath to extract entropy from the system [5], a process known as Heat-Bath Algorithmic Cooling (HBAC). Based on this work, many cooling algorithms have been designed [6][7][8][9][10][11]. HBAC is not only of theoretical interest, experiments have already demonstrated an improvement in polarization using this protocol with a few qubits [12][13][14][15][16][17][18], where a few rounds of HBAC were reached; and some studies have even included the impact of noise [19].Through numerical simulations, Moussa [7] and Schulman et al. [8] observed that if the polarization of the bath ( b ) is much smaller than 2 −n , where n is the number of qubits used, the asymptotic polarization reached will be ∼ 2 n−2 b ; but when b is greater than 2 −n , a polarization of order one can be reached. Inspired also by the work of Patange [20], who investigated the use of algorithmic cooling on spins bigger than 1 2 (using NV center where the defect has an effective spin 1), we investigate the case of cooling a qubit using a general spin l, and extra qubits which get contact with a bath. We found the asymptotic limit by solving the evolution equation with the results su...

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Section: Introductionmentioning

confidence: 99%

Achievable Polarization for Heat-Bath Algorithmic Cooling

Rodríguez-Briones

Laflamme

2016

Phys. Rev. Lett.

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“…Based on this new idea, many practical cooling algorithms have been designed [11][12][13][14][15]. In short, HBAC purifies qubits by applying alternating rounds of entropy compression and pumping out entropy from the system of interest to a thermal bath.…”

Section: Theory Of Algorithmic Coolingmentioning

confidence: 99%

“…During the application of permutation gates, 1 H spins in the crystal were strongly decoupled from 13 C spins, and 'spinlocked' by a transverse, phase-matched RF field, which preserved the 1 H polarization and allowed the H m1 to re-equilibrate with the hydrogen bath through spin diffusion mediated by hydrogen-hydrogen dipolar couplings. In the beginning of the experiment, all 13 C spins were initialized in completely mixed states by rotating the thermal polarization to a transverse Bloch sphere axis and dephasing it. After first five steps of the experiment, ideally the polarization of all three 13 C spins should equal to the bath polarization .…”

Section: Ssnmr Algorithmic Cooling Experimentsmentioning

confidence: 99%

“…Instead of applying a multi-pulse sequence to realize the refreshing step, cross polarization (CP) [27] which was found to be better in preserving the heat bath polarization was used. The permutation gates applied on 13 C's were numerically optimized using the GRadient Ascent Pulse Engineering (GRAPE) algorithm [28]. The pulse design takes several error sources into considerations: distributions of the static magnetic field and the RF control field, and the finite bandwidth of the NMR probe resonant circuit.…”

Section: Ssnmr Algorithmic Cooling Experimentsmentioning

confidence: 99%

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Heat Bath Algorithmic Cooling with Spins: Review and Prospects

Park

Rodríguez-Briones

Feng

et al. 2016

Electron Spin Resonance (ESR) Based Quantum Computing

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“…Repeating the process while assuming infinite relaxation time ratios allows enhancing the polarization of one spin asymptotically to 2ε [27]. Algorithms applying these processes to n qubits ideally cool exponentially beyond the unitary cooling [5,6], and can be practicable or optimal, see [6,7,24,[28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Algorithmic cooling in liquid-state nuclear magnetic resonance

et al. 2016

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Algorithmic cooling is a method that employs thermalization to increase qubit purification level, namely it reduces the qubit-system's entropy. We utilized gradient ascent pulse engineering (GRAPE), an optimal control algorithm, to implement algorithmic cooling in liquid state nuclear magnetic resonance. Various cooling algorithms were applied onto the three qubits of 13 C2-trichloroethylene, cooling the system beyond Shannon's entropy bound in several different ways. In particular, in one experiment a carbon qubit was cooled by a factor of 4.61. This work is a step towards potentially integrating tools of NMR quantum computing into in vivo magnetic resonance spectroscopy.

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Optimal Algorithmic Cooling of Spins

Cited by 20 publications

References 34 publications

Achievable Polarization for Heat-Bath Algorithmic Cooling

Achievable Polarization for Heat-Bath Algorithmic Cooling

Heat Bath Algorithmic Cooling with Spins: Review and Prospects

Algorithmic cooling in liquid-state nuclear magnetic resonance

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