As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily v
erified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information for a single QC. On the other hand, a comparison between different QCs on the same arbitrary circuit provides a lower-bound for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform fidelities.
Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is
represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the pure phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the mixed or coding phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge.
We study variants of Shors code that are adept at handling single-axis correlated idling errors, which are commonly observed in many quantum systems. By using the repetition code structure of the Shors code basis states, we calculate the logical chan
nel applied to the encoded information when subjected to coherent and correlated single qubit idling errors, followed by stabilizer measurement. Changing the signs of the stabilizer generators allows us to change how the coherent errors interfere, leading to a quantum error correcting code which performs as well as a classical repetition code of equivalent distance against these errors. We demonstrate a factor of 4 improvement of the logical memory in a distance-3 logical qubit implemented on a trapped-ion quantum computer. Even-distan
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the encoded logic
al qubit. Fault-tolerant circuits contain the spread of errors while operating the logical qubit, and are essential for realizing error suppression in practice. While fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. In this work, we experimentally demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a Bacon-Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6% and a Clifford gate error of 0.3% after error correction. Additionally, we prepare magic states with fidelities exceeding the distillation threshold, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant operation. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved.
We probe electric-field noise near the metal surface of an ion trap chip in a previously unexplored high-temperature regime. We observe a non-trivial temperature dependence with the noise amplitude at 1-MHz frequency saturating around 500~K. Measurem
ents of the noise spectrum reveal a $1/f^{alphaapprox1}$-dependence and a small decrease in $alpha$ between low and high temperatures. This behavior can be explained by considering noise from a distribution of thermally-activated two-level fluctuators with activation energies between 0.35~eV and 0.65~eV. Processes in this energy range may be relevant to understanding electric-field noise in ion traps; for example defect motion in the solid state and surface adsorbate binding energies. Studying these processes may aid in identifying the origin of excess electric-field noise in ion traps -- a major source of ion motional decoherence limiting the performance of surface traps as quantum devices.
Spontaneous symmetry breaking is a universal concept throughout science. For instance, the Landau-Ginzburg paradigm of translational symmetry breaking underlies the classification of nearly all quantum phases of matter and explains the emergence of c
rystals, insulators, and superconductors. Usually, the consequences of translational invariance are studied in large systems to suppress edge effects which cause undesired symmetry breaking. While this approach works for investigating global properties, studies of local observables and their correlations require access and control of the individual constituents. Periodic boundary conditions, on the other hand, could allow for translational symmetry in small systems where single particle control is achievable. Here, we crystallize up to fifteen 40Ca+ ions in a microscopic ring with inherent periodic boundary conditions. We show the rings translational symmetry is preserved at millikelvin temperatures by delocalizing the Doppler laser cooled ions. This establishes an upper bound for undesired symmetry breaking at a level where quantum control becomes feasible. These findings pave the way towards studying quantum many-body physics with translational symmetry at the single particle level in a variety of disciplines from simulation of Hawking radiation to exploration of quantum phase transitions.
We present a design of an r.f. trap using planar electrodes with the goal to trap on the order of 100 ions in a small ring structure of diameters ranging between 100 $mu$m and 200 $mu$m. In order to minimize the influence of trap electrode imperfecti
ons due to the fabrication, we aim at trapping the ions around 400 $mu$m above the trap electrodes. In view of experiments to create freely rotating crystals near the ground state, we numerically study factors breaking the rotational symmetry such as external stray electric fields, local charging of the trap electrodes, and fabrication imperfections. We conclude that these imperfections can be controlled sufficiently well under state-of-the-art experimental conditions to allow for freely rotating ion rings even at energies comparable to the ground state energy of the rotational degree-of-freedom.
