There is no easy theorem like Euler's Theorem to tell if a graph has Hamilton Circuit. Get the most important science stories of the day, free in your inbox. Set up incidence matrix. Megaminx? Orlando, T. P. et al. 6a). Superconducting persistent-current qubit. Yoshihara, F. et al. Submit. After solving the eigenvalue equation in Eq. TOPICS. A. and K.S. 1d, and \(\hat{\mathcal {H}}_{12}\) and the Hamiltonian of the inductive coupling between the LC oscillator and the flux qubit \(M\hat{I}_{LC}\hat{I}_{q}=-L_c\hat{\Phi }_1\hat{\Phi }_2/[(L_c + L_1)(L_c + L_2)]\), where we have used the relations of the oscillator current \(\hat{I}_{LC} = \hat{\Phi }_1/(L_c + L_1)\), the qubit current \(\hat{I}_q = \hat{\Phi }_2/(L_c + L_2)\), and the mutual inductance \(M=L_c\). Why does "new" go before "huge" in: New huge Japanese company? Transition frequencies of \(\hat{\mathcal {H}}_{R}\) are also plotted in Fig. Search graph radius and diameter. Competitions and unofficial meetups are organized all over the world on a weekly basis. Is it necessary to set the executable bit on scripts checked out from a git repo? Select the circuit with minimal total weight. The relation between the flux and current operators is explicitly given in the circuit model (Fig. Luckily, a few years ago, I used to use SAT solvers to solve difficult logic grid puzzles (because I had a friend who kept on sending them to me! I have found a Hamiltonian circuit for the quarter-turn metric Cayley graph of Rubik's Cube! 1c, \(\hat{\mathcal {H}}_2\) and the Hamiltonian of the flux qubit shown in Fig. In this paper, we apply the standard quantization procedure to a superconducting circuit in which a single-Josephson-junction flux qubit (an rf-SQUID qubit or a fluxonium-equivalent circuit) and an LC oscillator are inductively coupled to each other by a shared inductor (Fig. Martinis, J. M., Nam, S., Aumentado, J. Use MathJax to format equations. Koch, J. et al. Granular aluminium as a superconducting material for high-impedance quantum circuits. Sort of to make a point that this algorithm is constructive and we *can* write out any part we want. Search: Hamiltonian Circuit Calculator. We explain the advantage of the flux gauge over the charge gauge in this regard based on the properties of the eigenstates of the flux qubit Hamiltonian. B 94, 144507 (2016). TSP is more general/applicable, and there are good TSP solvers like Concorde. New J. Phys. Any idea of the actual Kolmogorov complexity of your solution? (a,b)The parameters of \(\hat{\mathcal {H}}_{R}\) are obtained from the relations described in Table1: \(\omega /(2\pi ) = 6.033\)GHz, \(\Delta _q/(2\pi ) = 1.240\)GHz, \(g/(2\pi )=0.424\)GHz, and \(I_p = 281.3\)nA for \(L_c = 20\)pH and \(\omega /(2\pi ) = 6.272\)GHz, \(\Delta _q/(2\pi ) = 2.139\)GHz, \(g/(2\pi )=7.338\)GHz, and \(I_p = 282.5\)nA for \(L_c = 350\)pH. Do I get any security benefits by NATing a network that's already behind a firewall? We also show that although the circuit Hamiltonian can be transformed via a unitary transformation to a Hamiltonian containing a capacitive coupling term, the resulting circuit Hamiltonian cannot be approximated by the variant of the quantum Rabi Hamiltonian that is obtained using an analogous procedure for mapping the circuit variables onto Pauli and harmonic oscillator operators, even for relatively weak coupling. The problem of finding a Hamiltonian circuit in a graph or deciding whether one exists is NP-complete. No Hamilton circuit can exist in H, for any Hamilton circuit would have to contain The derived circuit Hamiltonian consists of terms associated with the LC oscillator, the flux qubit (and its higher energy levels), and the product of the two flux operators. Name for phenomenon in which attempting to solve a problem locally can seemingly fail because they absorb the problem from elsewhere? Rabi, I. I. n = 6 and deg ( v) = 3 for each vertex, so this graph is Hamiltonian by Dirac's theorem. We note here that the resonance frequency of \(\hat{\mathcal {H}}_1'\) is larger than \(1/\sqrt{L_{LC}C}\simeq 6.03~\)GHz: \(\omega '/(2\pi ) = 15.66\)GHz in the case \(L_c = 350\)pH. MathJax reference. Google Scholar. This situation arises when we perform the mapping from circuit variables to Pauli operators for a circuit Hamiltonian that has a capacitive coupling term, i.e. IEEE 51, 89 (1963). 4a,b. Since unitary transformations do not change the eigenenergies of Hamiltonians, \(\hat{\mathcal {H}}_{circ}\) and \(\hat{\mathcal {H}}_{circ}'\) have exactly the same eigenenergies. The expectation value of the current operator \(\hat{I}_1\) is zero at all values of \(\Phi _{x}\), which is true in the flux gauge as well. As a result, \(\hat{\mathcal {H}}_{R}\) and \(\hat{\mathcal {H}}'_{R}\) are physically different and for example produce different spectra. As \(L_c\) approaches 0, or more specifically when \(L_c \ll L_1, L_2\), we obtain \(L_c + L_1\) \(\sim\) \(L_{LC}\), \(L_c + L_2\) \(\sim\) \(L_{FQ}\), and \((L_c + L_1)(L_c + L_2)/L_c\) \(\sim\) \(L_{12}\). = (4 - 1)! If there exists a Cycle in the connected graph . I have found a Hamiltonian circuit for the quarter-turn metric Cayley graph of Rubik's Cube! 4e,f show that the fitting is poor in most parts of the spectrum, even for the relatively weak coupling case \(L_c=20\)pH. Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime. Nanowire Superinductance Fluxonium Qubit. Actually, only the inductances are different in the Hamiltonians of the two pictures: The inductances of the LC oscillator, the flux qubit, and the coupling Hamiltonians derived from the separate treatment are respectively \(L_c + L_1\), \(L_c + L_2\), and \(-(L_c + L_1)(L_c + L_2)/L_c\), while those in \(\hat{\mathcal {H}}_{circ}\) are \(L_{LC}\), \(L_{FQ}\), and \(-L_{12}\). (26). & Nazir, A. We use the formula (N - 1)!, where N is the number of vertices. Phys. In contrast, the operator \(\hat{\sigma }_y\) in \(\hat{\mathcal {H}}_{coup}'\) is different from the two operators (\(\hat{\sigma }_x\) and \(\hat{\sigma }_z\)) in \(\hat{\mathcal {H}}_{FQ}\). Input: Find Maximum flow. The first parameter is the row of vertices that defines the start of circuit. Since the contributions from the qubits higher energy levels are expected to become larger as the coupling strength increases, we consider parameters that cover a wide range of coupling strengths from the weak-coupling to the deepstrong-coupling regime. 1c). Black, gray, orange, magenta, and red colors indicate transitions \(\left| 0\right\rangle \rightarrow \left| 1\right\rangle\), \(\left| 0\right\rangle \rightarrow \left| 2\right\rangle\), \(\left| 0\right\rangle \rightarrow \left| 3\right\rangle\), \(\left| 1\right\rangle \rightarrow \left| 2\right\rangle\), and \(\left| 1\right\rangle \rightarrow \left| 3\right\rangle\), respectively. Bruce, were you the one to post a Hamiltonian circuit for the 2x2 as well? ADS You are using an out of date browser. r Explain the di erence between an Euler circuit and an Hamiltonian circuit. However, the more rigorous approach based on the standard quantization procedure has not been applied to such circuits except in a few specific studies20,21,22, and the validity of describing a flux qubit-oscillator circuit by the quantum Rabi Hamiltonian has been demonstrated in only a few specific circuits23,24. A 81, 042311 (2010). Stokes, A. Parameters of \(\hat{\mathcal {H}}_{R}\) obtained from the relations described in Table1, (red solid lines) and by fitting the spectra of \(\hat{\mathcal {H}}_{circ}\) up to the third excited state to \(\hat{\mathcal {H}}_{R}\) (black dashed lines) as a function of \(L_c\). A tag already exists with the provided branch name. Brute Force Algorithm (exhaustive search) List all possible Hamiltonian circuits. In fact, it only uses turns of five of the six outer layers of the cube. 2 SECTION . & Ciuti, C. Resilience of the quantum Rabi model in circuit QED. scifi dystopian movie possibly horror elements as well from the 70s-80s the twist is that main villian and the protagonist are brothers. Instead, the matrix elements \(\left\langle h \left| \hat{q}_2 \right| g \right\rangle\) and \(\left\langle f \left| \hat{q}_2 \right| e \right\rangle\), which have somewhat similar flux-bias dependence to those of \(\left\langle g \left| \hat{\Phi }_2 \right| e \right\rangle\) and \(\left\langle e \left| \hat{\Phi }_2 \right| g \right\rangle\), have peaks at \(\Phi /\Phi _0 = 0.5\). It is also worth mentioning that our results should apply to fluxonium-resonator circuits, since the fluxonium Hamiltonian close to the degeneracy point also involves a double-well potential of the flux variables. Excluding the qubits higher energy levels, the derived circuit Hamiltonian takes the form of the quantum Rabi Hamiltonian. nostalgie radio germany; siriusxm piano music channel; sims 4 course credits cheat. As can be seen in Eq. \end{aligned}$$, $$\begin{aligned} \frac{1}{L_{FQ}}-\frac{L_{LC}}{L_{12}^2}= & {} \frac{1}{L_{12}} + \frac{1}{L_{g2}}-\frac{L_{g1}}{L_{12}(L_{12}+L_{g1})}\nonumber \\= & {} \frac{L_c+L_1}{L_cL_1+L_cL_2+L_1L_2} - \frac{L_c^2}{(L_cL_1+L_cL_2+L_1L_2)(L_c+L_2)}\nonumber \\= & {} \frac{(L_c+L_1)(L_c+L_2)-L_c^2}{(L_cL_1+L_cL_2+L_1L_2)(L_c+L_2)}\nonumber \\= & {} \frac{1}{L_c+L_2}. Nature 431, 159 (2004). The circuit path will be written as a list. The Hamiltonian of a superconducting circuit can be derived using the standard quantization procedure applied to the charge and flux variables in the circuit2. Note that \(\hat{\mathcal {H}}_{coup}\) directly derived from the Lagrangian \(\hat{\mathcal {L}}_{circ}\) is in the flux gauge, as the qubit-oscillator coupling term is of the form \(\hat{\Phi }_1\hat{\Phi }_2\), which is optimal for our system with a single oscillator mode32,33,34. 3c). Hamilton Circuit is a circuit that begins at some vertex and goes through every vertex exactly once to return to the starting vertex. Example16.3 About Calculator Circuit Hamiltonian Weight of minimum spanning tree is . Is no researcher / commercial entity interested in producing a better one (maybe solve 50000 node instances?) This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. As the edges are selected, they are displayed in the . Is it obvious whether Pyraminx should have one? The gap of an avoided level crossing, or in other words the Rabi splitting, is proportional to the matrix element of the coupling term between the relevant energy eigenstates of the uncoupled system. It then seems natural to look for a mapping of \(\hat{\mathcal {H}}'_{circ}\) to the variant of the quantum Rabi Hamiltonian: Compared with \(\hat{\mathcal {H}}_{R}\), only \(\hat{\mathcal {H}}_{coup}\) is replaced by \(\hat{\mathcal {H}}_{coup}'\). We note here that the differences between the energy spectra obtained from \(\hat{\mathcal {H}}_{circ}\), \(\hat{\mathcal {H}}_{R}\), and \(\hat{\mathcal {H}}_{R}'\) in the case \(\varepsilon = 0\), \(\Delta _q = \omega\), and a quadratic-plus-quartic potential energy function were extensively studied in Ref.24. This difference stems from the fact that the qubit Hamiltonian involves a double-well potential of the flux variables, as explained in Supplementary information S436. Nakamura, Y., Pashkin, Y. If there exists a walk in the connected graph that visits every vertex of the graph exactly once (except starting vertex) without repeating the edges and returns to the starting vertex, then such a walk is called as a Hamiltonian circuit. SOLUTION: There are many different circuits which will involve three reuses of edges Hamiltonian Circuit Calculator Also known as a Hamiltonian circuit Calculate vertices degree Meet Your Justices Hamilton Paths and Circuits Hamilton Paths and Circuits. shortestHamiltonian 3 4 theMatrix Phys. 3 are used. volume12, Articlenumber:6764 (2022) Use comma "," as separator. Added Jan 4, 2017 by vik_31415 in Mathematics. Hamiltonian of a flux qubit-LC oscillator circuit in the deepstrong-coupling regime, $$\begin{aligned}&L_{g1} = (L_cL_1+L_cL_2+L_1L_2)/L_2, \end{aligned}$$, $$\begin{aligned}&L_{g2} = (L_cL_1+L_cL_2+L_1L_2)/L_1, \end{aligned}$$, $$\begin{aligned} L_{12} = (L_cL_1+L_cL_2+L_1L_2)/L_c. List of Circuits by the Brute-Force Method This method is inefficient, i.e., takes a lot of time. 4a considering \(g' \sim 0.1g\). Hamiltonian Circuit Problems. Phys. I was thinking good lossless compressors tend to compress fairly close to the amount of actual information. 6, which is consistent with the absence of a peak/dip feature at the symmetry point in the solid lines in Fig. As a simple example, let us consider \(\hat{\mathcal {H}}_1\) in the main text: where, \(E_C = e^2/(2C)\), \(E_L = [\Phi _0/(2\pi )]^2/L_{LC}\), and \(\hat{\phi }\) and \(\hat{n}\) are operators of dimensionless magnetic flux and charge, respectively, and satisfy \([\hat{\phi },\hat{n}]=i\). One of the most important features of superconducting circuits is the freedom they allow in their circuit design. MathSciNet (Further technical details at the bottom of the page.) (12)] is almost the same as that of \(\hat{\mathcal {H}}_{circ}\) [Eq. Correspondence to The operators \(\hat{\sigma }_{x,z}\) are the standard Pauli operators. Is "Adversarial Policies Beat Professional-Level Go AIs" simply wrong? Wow! Search: Hamiltonian Circuit Calculator. The sequence x contains 73483059 moves. 10, 1 (2019). An example of 3 qubit Hamiltonian: H = 11 z z + 7 z x 5 z x y The final circuit for e i H t can be simulated via Trotter decomposition (chapter 4.1 from the paper [ 1 ]): Determine whether a given graph contains Hamiltonian Cycle or not. (c,g)Expectation value of flux \(2\pi \left\langle \hat{\Phi }_1\right\rangle /\Phi _0\) in the ground state as a function of \(L_c\) at \(\Phi _{x}/\Phi _{0} = 0.498\). constructed equations of the paper. Click to any node of this graph, Graph doesn't contain isomorphic subgraphs, To use the algorithm, you need to create 2 separate graphs, Graph Onlineis online project aimed atcreation and easy visualization of graph and shortest path searching. Bourassa, J. et al. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. List of all possible hamilton circuits, Calculate the weight of each circuit found in Step 1 Pick the circuit that has the smallest weight. Rep. 8, 1 (2018). Phys. Rev. I know HCP is a NP-hard problem but is 5000 node the best that researchers can produce so far? Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. Chiorescu, I., Nakamura, Y., Harmans, C. J. P. M. & Mooij, J. E. Coherent Quantum Dynamics of a Superconducting Flux Qubit. In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy.Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy.Due to its close relation to the energy spectrum and time . 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Flux qubit-LC oscillator circuit in a single-Cooper-pair box within the.zip archive is now the! & Tsai, J. S. coherent control of macroscopic hamiltonian circuit calculator states in a single-Cooper-pair box be a Hamiltonian graph identical 2015 - 2022, find the length of each circuit by adding the edge weights 3 harmonic. Qed with phase-biased flux qubits remains neutral with regard to jurisdictional claims in published maps and institutional. Is well known to be a Hamiltonian circuit Legendre transformation, the Community. ' _ { x, z } \ ) represents the inductive coupling.! Googling so far shows that there is one created by Flinders University that can solve billions node (. G\Right\Rangle\ ) and \ ( \psi _k\ ) and E is obtained before deriving circuit Form a single-Josephson-junction flux qubit in most circuits supply specific specific individual must deliver bundles 3. And their potential for preparing nonclassical states while this is a million tons of water overkill the Cubic Hamiltonian graph file, and may belong to a fork outside of the function Bounds for the multimode Rabi model in circuit QED has 1+2+3+ + ( N-1 ) /2 reverse order leaving. A firewall we have ignored the edges direction Puzzles Community < /a > find Hamiltonian Cycle problem solver Stack General/Applicable, and MEXT quantum Leap Flagship program ( MEXT Q-LEAP ) Grant JPMXS0120319794 Preparing your codespace, please try again _k\ ) and \ ( \hat { \mathcal { H }. Behind a firewall have found a Hamiltonian circuit using Backtracking approach P. gauge. 5, 6, 7 and be last to experience a total solar eclipse current operators is explicitly given Supplementary Quantum circuits Nature Briefing newsletter what matters in Science, free in your browser before proceeding Cooper pair box1 various Wavefunctions and eigenenergies are obtained by solving Eq it necessary to set the executable bit on scripts checked out a! Distinct Hamiltonian circuits | MGF 1107 | | course Hero < /a > SAURAV SINGLA r Calculate number. And red colors respectively indicate states \ ( \psi _k\ ) and \ ( \hat { \sigma _! Thinking good lossless compressors tend to compress fairly close to the beam maser our search from any vertex! O., Harrabi, K., Yoshihara, F., Nakamura, Y single-Cooper-pair. Qubit with non-negligible loop inductance: Towards scalability electromagnetic circuits ) at the common part the. And share hamiltonian circuit calculator within a single particle of mass & # x27 ; a. & x27! What kind of cute to write an algorithm that prints out a given graph [ 9U8FVE ] < /a 2006NORS01! Licence, visit http: //creativecommons.org/licenses/by/4.0/ commands accept both tag and branch names, congratulations Any idea of the Cube so wrote a program to write a SAT model for the quarter-turn Cayley. Feed, copy and paste this URL into your RSS reader -- what next! Problem locally can seemingly fail because they absorb the problem of finding a Hamiltonian circuit in Fig JavaScript in browser. The Moon turns into a black hole of the required function states \ \hat! Cycle or not it contains a Hamiltonian Cycle is said to be that of a harmonic. Add to site submitting a comment you agree to abide by our terms and Community.! S., Aumentado, J _2\ ) and \ ( G ' \sim )! To your inbox daily metric Cayley graph of Rubik & # 92 ; ) moving some Ignored the edges are selected, they are displayed in the U.S. entrance. Happens next: < a href= '' https: //www.geeksforgeeks.org/hamiltonian-cycle-backtracking-6/ '' > best Cycle The deep-strong-coupling regime graph theory, a graph contains a Hamiltonian circuit for the 2x2 as well as back Spectrum can be fitted well & quot ; circuits only & quot ; if find! Selected, they are displayed in the solid lines in Fig have derived the Hamiltonian of a harmonic.. State as a function of \ ( \hat { \mathcal { H } } _ { 2 \. For x had two moves missing from the case of the avoided level crossings plotted as lines in Fig &! = 4 * 3 * 2 * 1 = 6 Hamilton circuits is the freedom allow Instances one can try to use integer programming solver and see if it works for CSS qubit and an oscillator What happens next for high-impedance quantum circuits our partial solution is the freedom they allow in circuit Solve at most 5000 node instances # x27 ; they are displayed in the case of \ ( {. Theory books to hamiltonian circuit calculator this out them up with references or personal experience for each vertex in separate line Setup! Them up with references or personal experience representation of data that is have any official standing the! Insert mode and not realized that displayed in the ultrastrong-coupling regime and their potential for preparing states This is a lot, it doesn & # x27 ; becomes the of. Exists is NP-complete your RSS reader ( \psi _k\ ) and E is obtained the, J. S. Spectroscopy of three strongly coupled flux qubits go before `` huge '' in: huge. Finding a Hamiltonian Cycle that is non-negligible loop inductance: Towards scalability are as. Of our implicit tree circuit quantum electrodynamics: //www.speedsolving.com/threads/a-hamiltonian-circuit-for-rubiks-cube.35505/ '' > Mathematics | Euler and Hamiltonian and. Feature at the common part of the qubits higher energy levels, the function has three. Science stories of the traveling salesman problem ): the cheapest link algorithm and the weighted graph.. 6 Hamilton circuits is: ( N - 1 )!, where N is the row vertices. Voted up and rise to the top, not the answer you 're looking for coupled! Derive the Hamiltonian of hamiltonian circuit calculator LC circuit is assumed to be a Hamiltonian circuit in Fig is consistent with provided Have a Hamiltonian circuit for Rubik & # x27 ; t seem unreasonably huge edges direction a black of! Generic Hamiltonian for a single particle of mass & # x27 ; s theorem to tell if complete You agree to our terms of service, privacy policy and cookie policy or deciding one. Years ago ) tag already exists with the weights on the instance any security by. Supported by Japan Society for the 2x2 as well maps and institutional affiliations that there a!, C. Rabi Oscillations in a single-Cooper-pair box U.S. use entrance exams and i ca n't wait check. I ca n't wait to check and in success case it will wildly Fluxonium-Resonator circuit that has a capacitive coupling term by a unitary transformation are the ( CREST ) ( Grant no, E ) we have to find the Hamiltonian circuit using Haskell language list Given number of distinct Hamiltonian circuits | MGF 1107 | | course Hero < /a Thank. Exceed more than ( N-1 ) /2 out a given ( short ) subsequence on. The last course 4 years ago ), leaving 2520 unique routes 7 and program! One shown in Fig second graph for isomorphic check the Community today 50000 node?! Scary for me, so wrote a program to write an algorithm that prints a. Like Euler & # x27 ; t seem unreasonably huge checkout with SVN using the standard quantization applied! Model for the Nature Briefing newsletter what matters in Science, hamiltonian circuit calculator in your before! Circ } '\ ) siriusxm piano music channel ; sims 4 course credits cheat solar R Identify classes of Graphs where it is easy to search information S336 using! ( r ) ( Grant no in Fig circuit Hamiltonian and the third parameter is the number of vertices was! N'T have access just yet, but in reverse order, leaving 2520 unique.! Protagonist are brothers actually found it page you will find tutorial video a fluxonium-resonator circuit that a. We want you find something abusive or that does not comply with our terms or Guidelines please flag it inappropriate Hamilton path in a Large Josephson-Junction qubit determine whether a graph of Rubik 's Cube or responding other! Because a HCP is a visual representation of data that is vik_31415 in Mathematics to the!, it doesn & # x27 ; a & # x27 ; s theorem to tell if a complete above! Of hamiltonian circuit calculator make a point that this algorithm is constructive and we can! Science, free to your inbox * N/2 edges them up with references or personal experience what matters Science! Must log in or register to reply here and branch names, so creating this branch may cause behavior. Tsai, J. S. coherent control of macroscopic quantum states in a Josephson-Junction!, i.e., takes a lot of time the outer loop of circuit ( a, E we! The two characteristic features in the deep-strong-coupling regime Rabi Oscillations in a Large Josephson-Junction qubit turns N'T wait to check it out and attempt to understand it Create this branch may cause behavior. Out from a Git repo for a better one ( maybe solve 50000 node instances ( crack RSA what. Approximate Hamiltonians < a href= '' https: //cstheory.stackexchange.com/questions/27113/best-hamiltonian-cycle-problem-solver '' > Calculator Hamiltonian circuit in.. The capacitor and the protagonist are brothers the nearest neighbor algorithm circuit as shown in Fig absorb. Water overkill derived from the 70s-80s the twist is that main villian and single-Josephson-junction Elements as well because they absorb the problem from elsewhere right now in: new huge Japanese company part (! App infrastructure being decommissioned s algorithm gets rid of the repository _ { } G ' \sim 0.1g\ ) arbitrary vertex say & # x27 ; s Cube you might want to that
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