Millisecond Coherence Time in a Tunable Molecular Electronic Spin Qubit

Abstract

Quantum information processing (QIP) could revolutionize areas ranging from chemical modeling to cryptography. One key figure of merit for the smallest unit for QIP, the qubit, is the coherence time (T 2), which establishes the lifetime for the qubit. Transition metal complexes offer tremendous potential as tunable qubits, yet their development is hampered by the absence of synthetic design principles to achieve a long T 2. We harnessed molecular design to create a series of qubits, (Ph4P)2[V(C8S8)3] (1), (Ph4P)2[V(β-C3S5)3] (2), (Ph4P)2[V(α-C3S5)3] (3), and (Ph4P)2[V(C3S4O)3] (4), with T 2s of 1-4 μs at 80 K in protiated and deuterated environments. Crucially, through chemical tuning of nuclear spin content in the vanadium(IV) environment we realized a T 2 of ∼1 ms for the species (d 20-Ph4P)2[V(C8S8)3] (1') in CS2, a value that surpasses the coordination complex record by an order of magnitude. This value even eclipses some prominent solid-state qubits. Electrochemical and continuous wave electron paramagnetic resonance (EPR) data reveal variation in the electronic influence of the ligands on the metal ion across 1-4. However, pulsed measurements indicate that the most important influence on decoherence is nuclear spins in the protiated and deuterated solvents utilized herein. Our results illuminate a path forward in synthetic design principles, which should unite CS2 solubility with nuclear spin free ligand fields to develop a new generation of molecular qubits.

Figure 1

Depiction of the immediate environment of [V(C₈S₈)₃]^2– in solution, which is high in nuclear spin content, which affects the lifetime of the superpositions of a dissolved electronic spin qubit. The inset denotes the investigated superposition of [V(C₈S₈)₃]^2– in this report.

Figure 2

Evaluation of the viability of [V(C₈S₈)₃]^2– as a qubit in protiated, deuterated, and nuclear spin-free solvents. (a) The Hahn echo decay curve for 1′ at 10 K in CS₂ indicates the time frame for the loss of quantum information from the spin qubit. The red line is a biexponential fit that quantifies the time constant for this decay, T₂, of 675(7) μs. The fast decay at 2τ < 0.1 ms is attributed to a small percentage of closely spaced [V(C₈S₈)₃]^2– moieties that occur due to the inability of CS₂ to form a frozen glass. (b) Logarithmic temperature dependence of T₂ for [V(C₈S₈)₃]^2– in protiated, deuterated, and nuclear spin-free solvents, which illustrates the enormous impact of eliminating nuclear spins on the magnitude of the coherence time.

Figure 3

Rabi oscillation for 1′ in CS₂ at 20 K which shows the ability of [V(C₈S₈)₃]^2– to assume any arbitrary superposition of the |±1/2,–1/2⟩ levels. The blue line is a guide for the eye, while spin orientations for specific nutation pulse lengths are depicted. Inset: Spin-flip operation time as a function of B₁ attenuation.

Figure 4

Evaluation of a series of VS₆ qubits. (a) Molecular structures of the complexes as they appear in the crystal structures of 1–4. Green, yellow, red, and gray spheres represent vanadium, sulfur, oxygen, and carbon atoms, respectively. (b) Nutations for 1–4 that verify quantum control in each member of the series. Data were recorded in 1:1 DMF/Tol at 20 K, and 14 dB attenuation of B₁. The spin-flip operation time of 52 ns is highlighted. (c) Temperature dependences of T₂ for 1–4 in 1:1 DMF/Tol are nearly indistinguishable.

Figure 5

Comparison of the highest T₂ values of [V(C₈S₈)₃]^2– with those of other notable molecular and solid state electronic spin qubits. Data were extracted from refs (−16), (−27), and (35). Conditions under which data were collected follow. {Fe₈}: single crystal, 240 GHz mw irradiation. {Cr₇Ni}: 0.1 mM d₈-Tol solution, X-band mw irradiation. CuPc: 0.1% cocrystallization with unmetalated ligand, X-band mw irradiation. (Ph₄P)₂[Cu(S₂C₄N₂)₂]: 1:500 Cu:Ni cocrystallization, X-band mw irradiation. NV center: defects in diamond, 240 GHz mw irradiation. N@C₆₀: <0.8 mM in 3:1 CS₂:S₂Cl₂, X-band mw irradiation.