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Register a new userBroad-band spectroscopy of a vanadyl porphyrin: a model electronuclear spin qudit
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We explore how to encode more than a qubit in vanadyl porphyrin molecules hosting a electronic spin 1/2 coupled to a nuclear spin 7/2. The spin Hamiltonian and its parameters, as well as the spin dynamics, have been determined via a combination of electron paramagnetic resonance, heat capacity, magnetization and on-chip magnetic spectroscopy experiments performed on single crystals. We find low temperature spin coherence times of micro-seconds and spin relaxation times longer than a second. For sufficiently strong magnetic fields (B larger than 0.1 T, corresponding to resonance frequencies of 9 to 10 GHz) these properties make vanadyl porphyrin molecules suitable qubit realizations. The presence of multiple equispaced nuclear spin levels then merely provides 8 alternatives to define the 0 and 1 basis states. For lower magnetic fields (below 0.1 T), and lower frequencies (smaller than 2 GHz), we find spectroscopic signatures of a sizeable electronuclear entanglement. This effect generates a larger set of allowed transitions between different electronuclear spin states and removes their degeneracies. Under these conditions, we show that each molecule fulfills the conditions to act as a universal 4-qubit processor or, equivalently, as a d = 16 qudit. These findings widen the catalogue of chemically designed systems able to implement non-trivial quantum functionalities, such as quantum simulations and, especially, quantum error correction at the molecular level.
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Quantum bit or qubit is a two-level system, which builds the foundation for quantum computation, simulation, communication and sensing. Quantum states of higher dimension, i.e., qutrits (D = 3) and especially qudits (D = 4 or higher), offer significant advantages. Particularly, they can provide noise-resistant quantum cryptography, simplify quantum logic and improve quantum metrology. Flying and solid-state qudits have been implemented on the basis of photonic chips and superconducting circuits, respectively. However, there is still a lack of room-temperature qudits with long coherence time and high spectral resolution. The silicon vacancy centers in silicon carbide (SiC) with spin S = 3/2 are quite promising in this respect, but until now they were treated as a canonical qubit system. Here, we apply a two-frequency protocol to excite and image multiple qudit modes in a SiC spin ensemble under ambient conditions. Strikingly, their spectral width is about one order of magnitude narrower than the inhomogeneous broadening of the corresponding spin resonance. By applying Ramsey interferometry to these spin qudits, we achieve a spectral selectivity of 600 kHz and a spectral resolution of 30 kHz. As a practical consequence, we demonstrate absolute DC magnetometry insensitive to thermal noise and strain fluctuations.
We consider the task of performing quantum state tomography on a $d$-state spin qudit, using only measurements of spin projection onto different quantization axes. By an exact mapping onto the classical problem of signal recovery on the sphere, we prove that full reconstruction of arbitrary qudit states requires a minimal number of measurement axes, $r_d^{mathrm{min}}$, that is bounded by $2d-1le r_d^{mathrm{min}}le d^2$. We conjecture that $r_d^{mathrm{min}}=2d-1$, which we verify numerically for all $dle200$. We then provide algorithms with $O(rd^3)$ serial runtime, parallelizable down to $O(rd^2)$, for (i) computing a priori upper bounds on the expected error with which spin projection measurements along $r$ given axes can reconstruct an unknown qudit state, and (ii) estimating a posteriori the statistical error in a reconstructed state. Our algorithms motivate a simple randomized tomography protocol, for which we find that using more measurement axes can yield substantial benefits that plateau after $rapprox3d$.
The spectrum of relativistic electron bunches with large energy dispersion is hardly obtainable with conventional magnetic spectrometers. We present a novel spectroscopic concept, based on the analysis of the photons generated by Thomson Scattering of a probe laser pulse inpinging with arbitrary incidence angle onto the electron bunch. The feasibility of a single-pulse spectrometer, using an energy-calibrated CCD device as detector, is investigated. Numerical simulations performed in conditions typical of a real experiment show the effectiveness and accuracy of the new method.
Recent advances in qubit fidelity and hardware availability have driven efforts to simulate molecular systems of increasing complexity in a quantum computer and motivated us to to design quantum algorithms for solving the electronic structure of periodic crystalline solids. To this effect, we present a hybrid quantum-classical algorithm based on Variational Quantum Deflation [Higgott et al., Quantum, 2019, 3, 156] and Quantum Phase Estimation [Dobv{s}iv{c}ek et al., Phys. Rev. A, 2007, 76, 030306(R)] to solve the band structure of any periodic system described by an adequate tight-binding model. We showcase our algorithm by computing the band structure of a simple-cubic crystal with one $s$ and three $p$ orbitals per site (a simple model for Polonium) using simulators with increasingly realistic levels of noise and culminating with calculations on IBM quantum computers. Our results show that the algorithm is reliable in a low-noise device, functional with low precision on present-day noisy quantum computers, and displays a complexity that scales as $Omega(M^3)$ with the number $M$ of tight-binding orbitals per unit-cell, similarly to its classical counterparts. Our simulations offer a new insight into the quantum mindset applied to solid state systems and suggest avenues to explore the potential of quantum computing in materials science.
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