Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit

Abstract

Quantum computation requires qubits that satisfy often-conflicting criteria, including scalable control and long-lasting coherence [1]. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits. Though such encoded qubits may be particularly susceptible to leakage out of their computational subspace, they can be insensitive to certain noise processes [2, 3] and can also allow logical control with a single type of entangling interaction [4] while maintaining favorable features of the underlying physical system. Here we demonstrate a qubit encoded in a subsystem of three coupled electron spins confined in gated, isotopically enhanced silicon quantum dots [4, 5]. Using a modified "blind" randomized benchmarking protocol that determines both computational and leakage errors [6, 7], we show that unitary operations have an average total error of 0.35%, with 0.17% of that coming from leakage driven by interactions with substrate nuclear spins. This demonstration utilizes only the voltage-controlled exchange interaction for qubit manipulation and highlights the operational benefits of encoded subsystems, heralding the realization of high-quality encoded multi-qubit operations [4, 8].Electrons trapped in silicon heterostructures have many attractive features, including very long coherence times in isotopically enriched material [9, 10] and compatibility with standard fabrication techniques. Singlespin qubits have recently demonstrated high-fidelity RFcontrolled single-qubit operations [10, 11] and two-qubit gates using the exchange interaction [12][13][14]. However, using RF signals for single-qubit control requires a large, stable magnetic field and introduces challenges with crosstalk. Fortunately, electron spins are particularly well-suited to forming encoded qubits. Two coupled electron spins can be operated at near-zero magnetic field as a "singlet-triplet" qubit [15,16]. That qubit is insensitive to uniform magnetic field fluctuations but still requires a magnetic field gradient for universal control. Three coupled electrons [17] can form a qubit with a tunable electric dipole moment, which could enhance RF selectivity, or the exchange-only qubit, which can be universally controlled using only the exchange interaction and does not require synchronization of gate operations with a local oscillator. Exchange is highly local and can be accurately controlled with a large on-off ratio using only fast voltage pulses. The combination of these features makes the exchange-only qubit especially attractive b X2

Approximate exchange-only entangling gates for the three-spin-1/2decoherence-free subsystem

“…In particular we have shown that an exchange-only CNOT gate can be implemented with a computational speed comparable to or better than previous solutions, with good fidelity, provided the exchange interactions can be performed in parallel. The fidelities for these constructions exceed 0.99, which is comparable to fidelities demonstrated for one logical qubit in three quantum dots [10], and for two-qubit gates with other quantum devices [37][38][39]. Fidelities exceeding the conservative requirements for faulttolerance [40][41][42] can be achieved with a slow down of about a factor of two.…”

“…The best-known application of the 3DFS is to quantum computing with quantum dots where evolution under the exchange interaction can be more accessible than universal one-quantum-dot evolutions [3]. Indeed the requisite control over three quantum dots has been proven feasible by many experimental demonstrations [4][5][6][7][8][9][10]. The application to quantum dots is further supported by the ability to implement entangling logical gates between two blocks of physical spins carrying 3DFSs with exchange interactions only [3], but these gates require many steps and are often difficult to construct and understand from first principles (with a possible exception being [11]).…”

Resonant exchange operation in triple-quantum-dot qubits for spin–photon transduction

“…Qubit dephasing is another important consideration. We assume the dominant TQD dephasing channel for spin-photon coupling is electrical charge noise; magnetic noise (typically due to hyperfine gradients in Si/SiGe devices [5]) also causes dephasing and leakage but is mostly suppressed at the high values of J needed for spin-photon coupling. In circuit QED, the qubit dephasing rate is often parameterized as γ, which is well-defined for white noise channels but timescale-dependent for colored noise.…”

“…Exchange can be used as the sole control mechanism for triple-quantum-dot (TQD) encoded qubits, which reside within a decoherence free subsystem (DFS) protected against global magnetic field fluctuations [2,3,4]. High-fidelity Si/SiGe TQD qubit operation has been shown experimentally [5], which is particularly relevant given the known physical (e.g., nuclearspin-free isotope) and technological (mature, scalable processing) advantages of silicon. However, transporting quantum information between distantly situated TQDs will require a mechanism different from exchange, due to the latter's intrinsically short-range nature.…”

“…This method has been used to demonstrate spin-photon strong coupling [12,13] and cavity-mediated spin-spin interactions [14] in silicon double-quantum-dots (DQDs). However, field gradients are undesirable for DFS TQDs since they induce qubit leakage [5]. Fortunately, the multiple control axes for TQDs allow for other ways to achieve strong coupling [15] such as the resonant exchange (RX) regime [16,17], which hosts spin-photon "sweet spots" where a vanishing longitudinal (DC) electric dipole suppresses charge noise and exists alongside a transverse (AC) dipole for MW coupling [18,19,20,21].…”