بررسی ظهور بیش از یک کیوبیت در یک زنجیره کوانتومی، شامل نواحی فرومغناطیس و پارامغناطیس، با استفاده از روش گروه بازبهنجارش ماتریس چگالی (DMRG) [پايان نامه فارسي]
محمدمهدی نصیری فاطمه ساری
| شناسگر رکورد: | ۲۰۳۱۲ |
| رشته تحصیلی: | مواد،انرژی و فناوری کوآنتومی |
| عنوان: | بررسی ظهور بیش از یک کیوبیت در یک زنجیره کوانتومی، شامل نواحی فرومغناطیس و پارامغناطیس، با استفاده از روش گروه بازبهنجارش ماتریس چگالی (DMRG) |
| نويسنده: | محمدمهدی نصیری فاطمه ساری |
| استاد راهنما : | دکتر سیدمحمدصادق واعظی |
| مقطع تحصیلی : | کارشناسی ارشد |
| دانشگاه : | خاتم |
| تاریخ دفاع : | ۱۴۰۱ |
| چکیده: | The study of systems with topological order is one of the hot topics in the field of condensed matter physics. Perhaps one of the most important reasons is the use of such systems in quantum computing. A quantum computer is able to perform some calculations (much faster) exponentially faster than a conventional computer. But building and designing such computers is very difficult. One of the main obstacles is decoherence in quantum systems. This means that the system state is lost due to measurement or any other malfunction. In topologically ordered systems, there are quasiparticle excitations called anyon. Non-abelian anyons can be used for error-resistant quantum computations. Majorana fermions are the simplest type of non-abelian anyons. Majorana fermions are zero-energy excitations (which commute with Hamiltonian), hence, they are referred to as zero mode. To peform quantum computing, we need systems in which Majorana fermions are created. Alexei Kitaev was one of the first who studied such systems in terms of their application in quantum computing. He proposed a model that is in fact a one-dimensional fermionic chain with Z۲ symmetry and showed that free fermions (zero edge mode) occur at the boundary of the system. Majorana fermions (γ) have γ_i^†=γ_(i ) and {γ_(i ),γ_(j ) }=۲δ_ij feature. We can show that anywhere in the system one electron is equivalent to two fermions of C_i=γ_(i-)-iγ_(i+) He showed that when |h||J| (Ferromagnetic phase) system has topological order. In this case, the zero modes are paired with each other and disappear, except for two modes, one at the beginning of the chain γ_(۱-) and one at the other end〖 γ〗_(L+). In this case the degeneracy of the ground state is equal ۲. With these two modes, a qubit can be made, and because they are spaced apart, no local measurement can eliminate the state of this qubit. This is exactly the feature we were looking for. When | J |<|h| (paramagnetic phase without topological order) all modes are paired and destroyed, and (no zero-edge mode remains) the ground state has no degeneracy. The case |J||h| there are still two zero modes at the beginning and the end of the system. Despite all these efforts, there are still many questions that need further investigation. For example, we know that we need more than one qubit to do quantum computing. Suppose we have two chains with a ferromagnetic phase (topological order). Since each has a pair of zero modes in itself, we might think that by putting these two chains together, we would have a chain with two pairs of zero modes (equivalent to two qubits). But we know that when zero modes are adjacent, they can combine and disappear. To solve this problem (as you will see in this thesis) we found that by placing paramagnetic regions (without topological order) between the ferromagnetic regions we can prevent the combination of zero modes. We were also able to find some kind of correlation length that depends on the problem variables. By engineering these variables, the amount of zero modes (required number of qubits) can be controlled. To verify this claim, in addition to theoretical tools, we have employed the state of art Density Matrix Renormalization Group (DMRG) method. As we will see the results are in agreement with our expectations. |
| شماره ثبت | جزء | نسخه | جلد | بخش | قسمت | مرجع | شماره بازیابی | در دست امانت | تاریخ بازگشت | ملاحظات | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 284044 | 1 | پایان نامه گروه رهیافت و به صورت لاتین تحویل کتابخانه گردید. |
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