Algorithmic Cooling of Spins: A Practicable Method for Increasing Polarization

Fernandez, José M.; Lloyd, Seth; Mor, Tal; Roychowdhury, Vwani P.

doi:10.1142/s0219749904000419

Cited by 76 publications

(145 citation statements)

References 14 publications

Supporting

Mentioning

145

Contrasting

Order By: Relevance

“…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.

View full text Add to dashboard Cite

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...

show abstract

Section: Introductionmentioning

confidence: 99%

Achievable Polarization for Heat-Bath Algorithmic Cooling

Rodríguez-Briones

Laflamme

2016

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…Algorithmic cooling, experimentally implemented in this work, is a method that might contribute to both scopes. On the one hand, it was originally suggested as a method for increasing the qubits' purification level [5][6][7][8][9][10], as qubits in a highly pure state are required both for initialization and for fault tolerant [11,12] quantum computing. On the other hand, the suggested novel usage of data compression may potentially be found useful for increasing the signal to noise ratio of liquid-state NMR and in vivo magnetic resonance spectroscopy [6,13,14].…”

Section: Introductionmentioning

confidence: 99%

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…If these heated qubits are then allowed to relax back to the heat-bath temperature, the total entropy of the qubit system has decreased. The cooling algorithm then consists of alternating rounds of cooling and compression [9,10,11,12]. Recently Schulman et al [13] have shown an optimal algorithm, the partner pairing algorithm (PPA), for the scenario of having one special purpose reset qubit.…”

mentioning

confidence: 99%

Spin Based Heat Engine: Demonstration of Multiple Rounds of Algorithmic Cooling

et al. 2008

View full text Add to dashboard Cite

We show experimental results demonstrating multiple rounds of heat-bath algorithmic cooling in a 3 qubit solid-state nuclear magnetic resonance quantum information processor. By dynamically pumping entropy out of the system of interest and into the heat-bath, we are able show purification of a single qubit to a polarization 1.69 times that of the heat-bath and thus go beyond the Shannon bound for closed system cooling. The cooling algorithm implemented requires both high fidelity coherent control and a deliberate controlled interaction with the environment. We discuss the improvements in control that allowed this demonstration. This experimental work shows that given this level of quantum control in systems with sufficiently large polarizations, nearly pure qubits should be achievable. Using quantum mechanics to process information promises the possibility to dramatically speed-up certain computations and simulations [1]. Many experimental paths are being pursued in the goal of coherently manipulating quantum systems [2]. The standard circuit based model has certain experimental criteria [3]: one of which is the ability to initialize pure fiducial quantum states. This is needed not only to create the initial state for many quantum algorithms, but it is also necessary to have pure qubits on demand throughout the computation in order to compute fault-tolerantly in the presence of errors [4]. However, many physical implementations are able to initialize only mixed states with a certain bias towards the desired state. In these cases it will almost certainly be necessary to run some protocol to purify the qubits. Aside from quantum information purposes, the ability to increase the bias of nuclear spins is fundamentally important in nuclear magnetic resonance (NMR) where small signal to noise ratios are usually overcome with signal averaging. A boost in the initial bias by a factor b would reduce the experiment time by b 2 .A potential solution is algorithmic, whereby a series of logic gates can lower the temperature of a subset of the qubits. If the relaxation rate back to thermal equilibrium (T 1 ) is sufficiently longer than the cooling operations, then it is possible to cool a subset far below their thermal equilibrium bias. This algorithmic cooling is essentially classical and is based on early work from von Neumann [5]. If the bits start with some bias ǫ, so the probability of being in the state 0 or spin up is P ↑ = 1+ǫ 2 and P ↓ = 1−ǫ 2 , then the application of a logic gate can compress the uncertainty into some fraction of the qubits and increase the bias on the rest. Using these ideas it was shown that by starting with a sufficient number of qubits, it is possible to initialize a small number of qubits to a fiducial state with near certainty [6,7]. However, for the starting biases typical of room temperature NMR, that sufficient number is an impractically large number e.g., to purify only one qubit requires ≈ 10 12 spins. In a closed system, the compression step is limited by the Shannon bound: the total en...

show abstract

Algorithmic Cooling of Spins: A Practicable Method for Increasing Polarization

Cited by 76 publications

References 14 publications

Achievable Polarization for Heat-Bath Algorithmic Cooling

Achievable Polarization for Heat-Bath Algorithmic Cooling

Algorithmic cooling in liquid-state nuclear magnetic resonance

Spin Based Heat Engine: Demonstration of Multiple Rounds of Algorithmic Cooling

Contact Info

Product

Resources

About