Jonathan A. Jones

NMR experiments require sequences of radio frequency (RF) pulses to manipulate nuclear spins. Signal is lost due to non-uniform excitation of nuclear spins resonating at different energies (chemical shifts) and inhomogeneity in the RF unavoidably generated by hardware over the sample volume. To overcome this, we present Seedless, a tool to calculate NMR pulses that compensate for these effects to enhance control of magnetisation and boost signal. As calculations take only a few seconds using an optimised GRadient Ascent Pulse Engineering (GRAPE) implementation, this now allows pulses to be generated in a few seconds, allowing them to be optimised for individual samples and spectrometers (“on-the-fly”). Each calculated pulse requires bands of chemical shift to be identified, over which one of 4 transforms will be performed, selected from a set that covers all commonly used applications. Using imaging experiments, we demonstrate our pulses effectively both increase the size of the coil volume and signal-to-noise in all experiments. We illustrate the approach by showing sensitivity gains in 1, 2 and 3D applications suitable for chemical and biological NMR. Seedless provides a means to enhance sensitivity in all pulse sequences in a manner that can be tailored to different samples and hardware being used.

All NMR experiments require sequences of RF ‘pulses’ to manipulate nuclear spins. Signal is lost due to non-uniform excitation of nuclear spins resonating at different energies (chemical shifts) and inhomogeneity in the RF actually generated by hardware over the sample volume. Here, we present Seedless, a tool to calculate NMR pulses that compensate for these effects to enhance control of magnetisation and boost signal. The calculations take only a few seconds using an optimised GRadient Ascent Pulse Engineering (GRAPE) implementation, allowing pulses to be generated ‘on-the-fly’, optimised for individual samples and spectrometers. Each calculated pulse requires bands of chemical shift to be identified, over which one of 4 transforms will be performed, selected from a set that covers all commonly used applications: a universal rotation (e.g. 90° about the x axis), including as a special case an identity operation (return spins in the same state as they started), state-to-state (e.g. Z->Y), an XYcite (Z->XY plane), or a novel type, a suppression, that leaves spins minimally perturbed at all times during the pulse. Using imaging experiments we demonstrate our pulses effectively increase the size of the coil volume and effectively increase signal-to-noise in all experiments. We illustrate the approach by devising ultra-broadband pulses (300 ppm excitation pulse for ¹⁹ F 1D spectra), a ¹⁵ N HSQC with 58% increased S/N (950 MHz spectrometer + cryoprobe), triple resonance biomolecular NMR experiments such as HNCACO with 55% increased S/N (600 MHz spectrometer + RT probe), and a highly efficient pulse sequence for water suppression. The 8 optimised pulse sequences presented required 54 bespoke pulses all calculated on-the-fly. Seedless provides a means to enhance sensitivity in all pulse sequences in a manner that can be tailored to all samples/hardware being used.

We consider the problem of efficiently computing the Uhlmann fidelity in the case when explicit density matrix descriptions are available. We derive an alternative formula which is simpler to evaluate numerically, saving a factor of 10 in time for large matrices.

We consider the problem of efficiently computing the Uhlmann fidelity in the case when explicit density matrix descriptions are available. We derive an alternative formula which is simpler to evaluate numerically, saving a factor of 10 in time for large matrices.

Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers, which naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to classical simulation Here, we present a cross-verification technique that exploits the principles of measurement-based quantum computation to link quantum circuits of different input size, depth, and structure. Our technique enables consistency checks of quantum computations between independent devices, as well as within a single device. We showcase our protocol by applying it to five state-of-the-art quantum processors, based on four distinct physical architectures: nuclear magnetic resonance, superconducting circuits, trapped ions, and photonics, with up to six qubits and up to 200 distinct circuits.

The universal quantum homogenizer can transform a qubit from any state to any other state with arbitrary accuracy, using only unitary transformations to perform this task. Here we present an implementation of a finite quantum homogenizer using nuclear magnetic resonance (NMR), with a four-qubit system. We compare the homogenization of a mixed state to a pure state and the reverse process. After accounting for the effects of decoherence in the system, we find the experimental results to be consistent with the theoretical symmetry in how the qubit states evolve in the two cases. We analyze the implications of this symmetry by interpreting the homogenizer as a physical implementation of pure state preparation and information scrambling.

We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local not gates. This methodology is well known in nuclear magnetic resonance implementations, but previous approaches do not scale efficiently for the general fully connected Hamiltonian, where the complexity of finding time-optimal solutions makes them only practical up to a few tens of qubits. Given the rapid growth in the number of qubits in cutting-edge quantum processors, it is of interest to investigate the applicability of this control scheme to much larger-scale systems with realistic restrictions on connectivity. Here we present an efficient scheme to find near time-optimal solutions that can be applied to engineered qubit arrays with local connectivity for any number of qubits, indicating the potential for practical quantum computing in such systems.

We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local NOT gates. This methodology is well-known in NMR implementations, but previous approaches do not scale efficiently for the general fully-connected Hamiltonian, where the complexity of finding time-optimal solutions makes them only practical up to a few tens of qubits. Given the rapid growth in the number of qubits in cutting-edge quantum processors, it is of interest to investigate the applicability of this control scheme to much larger scale systems with realistic restrictions on connectivity. Here we present an efficient scheme to find near time-optimal solutions that can be applied to engineered qubit arrays with local connectivity for any number of qubits, indicating the potential for practical quantum computing in such systems.