Semioptimal practicable algorithmic cooling

Elias, Yuval; Mor, Tal; Weinstein, Yossi

doi:10.1103/physreva.83.042340

Cited by 25 publications

(41 citation statements)

References 26 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%

“…This provides 10 protons that are hyperfine coupled to the electron and are spectrally distinguishable through ENDOR. Nitrogen can be isotopically labelled as 15 N to provide an additional strongly coupled nuclear spin. This spin system therefore affords the possibility of implementing HBAC with up to 12 qubits [39].…”

Section: Prospects: Exploiting Larger Hilbert Spaces and The High Fiementioning

confidence: 99%

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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“…Here, the reset qubits periodically release their excess entropy to a heat-bath so that higher cooling of the computation qubit can be achieved by constructive iterations of AC. Since then, several HBAC algorithms have been proposed [10][11][12][13][14] and numerous experimental studies have also been reported [15][16][17][18][19][20][21] which use three or five qubit entropy compression circuits as the building block for AC. More recently asymptotic bounds for HBAC algorithms have been estimated numerically by Raeisi et * mahesh.ts@iiserpune.ac.in al.…”

Section: Introductionmentioning

confidence: 99%

Strong algorithmic cooling in large star-topology quantum registers

2017

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Cooling the qubit into a pure initial state is crucial for realizing fault-tolerant quantum information processing. Here we envisage a star-topology arrangement of reset and computation qubits for this purpose. The reset qubits cool or purify the computation qubit by transferring its entropy to a heat-bath with the help of a heat-bath algorithmic cooling procedure. By combining standard NMR methods with powerful quantum control techniques, we cool central qubits of two large startopology systems, with 13 and 37 spins respectively. We obtain polarization enhancements by a factor of over 24, and an associated reduction in the spin temperature from 298 K down to 12 K. Exploiting the enhanced polarization of computation qubit, we prepare combination-coherences of orders up to 15. By benchmarking the decay of these coherences we investigate the underlying noise process. Further, we also cool a pair of computation qubits and subsequently prepare them in an effective pure-state.

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Semioptimal practicable algorithmic cooling

Cited by 25 publications

References 26 publications

Achievable Polarization for Heat-Bath Algorithmic Cooling

Achievable Polarization for Heat-Bath Algorithmic Cooling

Heat Bath Algorithmic Cooling with Spins: Review and Prospects

Strong algorithmic cooling in large star-topology quantum registers

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