{"id":7570,"date":"2025-09-04T14:51:01","date_gmt":"2025-09-04T12:51:01","guid":{"rendered":"https:\/\/www.qilimanjaro.tech\/?p=7570"},"modified":"2026-04-13T12:14:52","modified_gmt":"2026-04-13T10:14:52","slug":"fluxonium-qubits","status":"publish","type":"post","link":"https:\/\/qilimanjaro.tech\/ca\/fluxonium-qubits\/","title":{"rendered":"Fluxonium: The Qubit Behind Qilimanjaro\u2019s Quantum Computers"},"content":{"rendered":"
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At Qilimanjaro, we are a full-stack quantum computing company<\/span>. This means we work across every layer of the technology: from designing and calibrating the quantum chip, to building the software and control systems that connect the hardware with users, all the way to developing the theory and algorithms that run on our devices. At the core of this stack lies our Quantum Processing Unit (QPU)<\/span>.<\/p>

There are several ways to implement a QPU, with leading approaches based on superconducting circuits, trapped ions, neutral atoms,<\/strong> and photonics<\/strong>. Our focus is on superconducting circuits, and within this platform we specialize in a particularly powerful type of qubit: the fluxonium<\/strong>.<\/p>

In this blog post, we\u2019ll dive into the details of what makes the fluxonium qubit unique and why it sits at the heart of our technology.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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What is a Qubit?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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But first, what is a qubit? A quantum bit is our way to codify the information in a quantum computer. A qubit is a quantum system that can exist in these two states, usually denoted as |0\u27e9 and |1\u27e9. Unlike a classical bit, which can only be in one state at a time, a qubit can also be in a superposition of both states, meaning that it has some probability of being |0\u27e9 and some probability of being |1\u27e9. This allows a qubit to store more information than a classical bit.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
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Qubits have a certain probability \u03b1\u00b2 <\/span>to be in state |0\u232a<\/span>and a certain probability, \u03b2\u00b2<\/span> to be in state |1\u232a<\/span>This superposition of states is only realizable within quantum mechanics.\u00b2<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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However, in order to maintain this quantum superposition, we need to avoid the decoherence of the system. Decoherence is the process by which a qubit or a quantum system loses its quantum properties due to its interaction with the environment. Decoherence causes the qubit to collapse into one of the two states, |0\u27e9 or |1\u27e9, and lose its superposition and entanglement with other qubits.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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The interaction of this qubit with the environment makes the state collapse into |0\u232aor |1\u232a<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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How do we make a Qubit?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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To build a useful qubit, we need a system that behaves like a two-level atom<\/span>. Real atoms are good models because their energy levels are not equally spaced – the jump from |0\u27e9 \u2192 |1\u27e9 requires a different energy than the jump from |1\u27e9 \u2192 |2\u27e9 . This uneven spacing, called anharmonicity<\/span><\/strong>, allows us to isolate and control just the lowest two states, |0\u27e9 \u2192 |1\u27e9 , without unintentionally exciting higher states.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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In this diagram we show the typical state distribution of an atom. We can see that the energy separation between states is different, i.e. \u039501<\/span>, the energy that a particle needs to jump from state |0\u232aor |1\u232a, is different from \u039512<\/span>, the energy required for a particle to jump from state |1\u232aor |2\u232a<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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This property is what makes coherent control possible. By sending a microwave pulse with the right frequency, \u03c901, we can selectively drive the qubit from |0\u232a\u2192 |1\u232a<\/p>

Our next challenge is to recreate this behavior using circuits<\/strong>. Can we design an electrical system with energy levels distributed like those of an atom? In other words, can we build an electronic atom<\/em>?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t

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The LC Oscillator<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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The simplest circuit we can build from basic components is an LC oscillator<\/strong>, which consists of an inductor (L) and a capacitor (C) connected in parallel. The total energy of this circuit \u2014 or its Hamiltonian, in physics language \u2014 has two parts:<\/p>

  1. The first term comes from the charge stored in the capacitor.<\/li>
  2. The second term is related to the flux (\u03c6) through the inductor.<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
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    To see if this circuit could work as a qubit, we look at its energy spectrum<\/strong>, which tells us how the possible energy levels are arranged. After diagonalising the Hamiltonian, we find that the LC oscillator behaves like a harmonic oscillator:<\/strong> its energy levels are evenly spaced.<\/strong> This means that the transition frequency, \u03c901, is exactly the same for |0\u232a\u2192 |1\u232a, |1\u232a\u2192 |2\u232a, |2\u232a\u2192 |3\u232a and so on.<\/p>

    As a result, if we send a microwave pulse at frequency \u03c901, we can excite the qubit from |0\u232a\u2192 |1\u232a. But the same pulse also drives higher transitions – |1\u232a\u2192 |2\u232a, |2\u232a\u2192 |3\u232a etc. Instead of isolating a two-level system, we create a coherent state<\/strong>: a superposition involving many levels at once.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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    Energy spectrum of the LC oscillator. <\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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    This is why the LC oscillator cannot serve as a qubit. Unlike atoms, whose energy levels are non-uniformly spaced, <\/span>the LC oscillator is too symmetric. To make a real qubit, we need to introduce non-linearity<\/span> into the circuit so that only the two lowest states can be selectively controlled<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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    Circuit with non-linear inductance<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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    To break the uniform spacing of the LC oscillator, we need to introduce non-linearity<\/span><\/strong>. This is achieved with a Josephson Junction (JJ)<\/span><\/strong>. A Josephson Junction is essentially a superconductor\u2013insulator\u2013superconductor sandwich<\/span>: two superconducting wires separated by a very thin insulating barrier.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

    \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
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    Schematic diagram of a Josephson Junction.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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    Even though the barrier is an insulator, current can still flow through it thanks to quantum tunneling <\/span><\/strong>\u2014 a purely quantum effect. Josephson showed that the current flowing through the junction relates to the magnetic flux \u03c6 in a sinusoidal way:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

    \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
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    where \u03990 is the critical current and \u03c60 is the flux quantum.<\/p>

    This relation tells us something important: the Josephson Junction behaves like an inductor<\/span>, but not a normal one. In a regular inductor, current and flux are related by a simple constant, 1\/L. In a JJ, the relation depends on the flux itself, making it non-linear<\/span><\/strong>. If we calculate the effective inductance by differentiating current with respect to flux, we find that it varies as:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

    \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
    \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Frame\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
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    Comparison of an inductance with a Josephson Junction.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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    Why is this important?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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    If we replace the inductor in our LC oscillator with a Josephson Junction, the energy potential of the system changes. Instead of the smooth parabolic potential of a harmonic oscillator, we now get a cosine-shaped potential<\/strong>.<\/p>

    What does this mean for the energy spectrum? In a parabolic potential, the energy levels are evenly spaced, which is why the LC oscillator fails as a qubit. But in a cosine potential, the wells are finite and periodic. According to quantum mechanics, when a particle is confined in such a potential, the energy levels must readjust<\/strong> \u2014 they are no longer uniformly separated.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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    The Transmon Qubit<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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    If we focus on one of these cosine wells, we find that the first few energy levels have different spacings. This gives exactly the property we want: an anharmonic spectrum<\/strong>. The lowest two states, |0\u232a\u2192 |1\u232aare isolated enough that we can selectively drive transitions between them with microwaves, without easily leaking into higher levels.<\/p>

    The circuit formed by a capacitor and a Josephson Junction<\/strong> is known as the transmon qubit<\/strong>.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

    \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"transmon\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
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    Energy spectrum of the transmon qubit.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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    The Fluxonium Qubit<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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    The fluxonium qubit builds on the transmon by adding a large superinductance<\/span> (an inductor with very high inductance) in parallel with the Josephson junction.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

    \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
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    Arquitecture of the Fluxonium<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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    This inductive \u201cshunt\u201d modifies the potential: instead of a simple cosine well, we now have a cosine potential confined inside a parabolic potential<\/span>.<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

    \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
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    The result is the <\/span>fluxonium energy spectrum<\/span><\/strong>, shown in the figure below.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

    \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"fluxonium2\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
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    Energy spectrum of the fluxoniums.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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    <\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t
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    Why Fluxoniums?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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    In superconducting qubits, a major source of energy loss and dephasing is dielectric noise<\/strong>\u2014tiny fluctuating electric dipoles in materials and interfaces that absorb energy from the qubit\u2019s electric field. This loss typically grows with frequency<\/strong>. Fluxoniums usually have a |0\u232a\u2192 |1\u232a transition around 0.1\u20131 GHz<\/strong>, while transmons are typically 4\u20135 GHz<\/strong>. Operating at the lower fluxonium frequencies therefore reduces dielectric noise<\/strong> and helps preserve coherence.<\/p>

    Moreover, fluxoniums are more anaharmonic<\/strong> than the transmons: the gap between |0\u232a\u2192 |1\u232aand |1\u232a\u2192 |2\u232a is larger. That extra separation lets us apply shorter<\/strong> (stronger\/faster)<\/strong> control pulses without accidentally driving the qubit to the state |1\u232a\u2192 |2\u232a.<\/p>

    Put simply, shorter pulses spread over more frequencies<\/strong>. Because fluxonium\u2019s levels are farther apart, that spread stays clear of unwanted transitions, so leakage is much less likely\u2014even when we drive the qubit with rapid pulses!<\/p>

    And one more advantage: fluxoniums are a natural fit for analog quantum computing<\/strong>\u2014a story for another post!<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"

    At Qilimanjaro, we are a full-stack quantum computing company. This means we work across every layer of the technology: from designing and calibrating the quantum chip, to building the software and control systems that connect the hardware with users, all the way to developing the theory and algorithms that run on our devices. At the […]<\/p>\n","protected":false},"author":3,"featured_media":7710,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-7570","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-science"],"yoast_head":"\nRevolutionizing Smart Cities through Advanced Optimization<\/title>\n<meta name=\"description\" content=\"Explore how quantum computing is driving sustainable innovation and reducing energy consumption for future computing challenges.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/qilimanjaro.tech\/ca\/fluxonium-qubits\/\" \/>\n<meta property=\"og:locale\" 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