18 research outputs found
Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
One-dimensional multi-component Fermi or Bose systems with strong zero-range
interactions can be described in terms of local exchange coefficients and
mapping the problem into a spin model is thus possible. For arbitrary external
confining potentials the local exchanges are given by highly non-trivial
geometric factors that depend solely on the geometry of the confinement through
the single-particle eigenstates of the external potential. To obtain accurate
effective Hamiltonians to describe such systems one needs to be able to compute
these geometric factors with high precision which is difficult due to the
computational complexity of the high-dimensional integrals involved. An
approach using the local density approximation would therefore be a most
welcome approximation due to its simplicity. Here we assess the accuracy of the
local density approximation by going beyond the simple harmonic oscillator that
has been the focus of previous studies and consider some double-wells of
current experimental interest. We find that the local density approximation
works quite well as long as the potentials resemble harmonic wells but break
down for larger barriers. In order to explore the consequences of applying the
local density approximation in a concrete setup we consider quantum state
transfer in the effective spin models that one obtains. Here we find that even
minute deviations in the local exchange coefficients between the exact and the
local density approximation can induce large deviations in the fidelity of
state transfer for four, five, and six particles.Comment: 12 pages, 7 figures, 1 table, final versio
Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons
Quantum error correction with erasure qubits promises significant advantages
over standard error correction due to favorable thresholds for erasure errors.
To realize this advantage in practice requires a qubit for which nearly all
errors are such erasure errors, and the ability to check for erasure errors
without dephasing the qubit. We experimentally demonstrate that a "dual-rail
qubit" consisting of a pair of resonantly-coupled transmons can form a highly
coherent erasure qubit, where the erasure error rate is given by the transmon
but for which residual dephasing is strongly suppressed, leading to
millisecond-scale coherence within the qubit subspace. We show that
single-qubit gates are limited primarily by erasure errors, with erasure
probability per gate while the
residual errors are times lower. We further demonstrate mid-circuit
detection of erasure errors while introducing dephasing error per
check. Finally, we show that the suppression of transmon noise allows this
dual-rail qubit to preserve high coherence over a broad tunable operating
range, offering an improved capacity to avoid frequency collisions. This work
establishes transmon-based dual-rail qubits as an attractive building block for
hardware-efficient quantum error correction.Comment: 8+12 pages, 16 figure
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Demonstrating a Long-Coherence Dual-Rail Erasure Qubit Using Tunable Transmons
Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a “dual-rail qubit” consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability erasure per gate while the residual errors are times lower. We further demonstrate midcircuit detection of erasure errors while introducing dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction