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US-20260127479-A1 - THREE QUBIT ENTANGLING GATE THROUGH TWO-LOCAL HAMILTONIAN CONTROL

US20260127479A1US 20260127479 A1US20260127479 A1US 20260127479A1US-20260127479-A1

Abstract

Methods, systems and apparatus for implementing a quantum gate on a quantum system comprising a second qubit coupled to a first qubit and a third qubit. In one aspect, a method includes evolving a state of the quantum system for a predetermined time, wherein during evolving: the ground and first excited state of the second qubit are separated by a first energy gap ω; the first and second excited state of the second qubit are separated by a second energy gap equal to a first multiple of ω minus qubit anharmoniticity η; the ground and first excited state of the first qubit and third qubit are separated by a third energy gap equal to ω-η; and the first and second excited state of the first qubit and third qubit are separated by a fourth energy gap equal to the first multiple of the ω minus a second multiple of η.

Inventors

  • Yuezhen Niu
  • Vadim Smelyanskly
  • Sergio Boixo Castrillo

Assignees

  • GOOGLE LLC

Dates

Publication Date
20260507
Application Date
20241119

Claims (20)

  1. 1 . A method for implementing a three-qubit quantum gate on a quantum system comprising a first qubit, second qubit and third qubit, wherein the second qubit is coupled to the first qubit and to the third qubit, the method comprising: evolving a state of the quantum system under a Hamiltonian describing the quantum system for a predetermined time, wherein the Hamiltonian comprises a diagonal part and an off-diagonal part and wherein during the evolving: operating frequencies of the first qubit, second qubit, and third qubit are parked such that basis states in a two-excitation subspace of the quantum system and basis states in a three-excitation subspace of the quantum system are degenerate under the diagonal part of the Hamiltonian
  2. 2 . The method of claim 1 , wherein the method further comprises applying multiple Pauli Z rotations to the evolved state of the quantum system to cancel additional phase accumulated in the computational basis during evolution of the state of the quantum system.
  3. 3 . The method of claim 2 , wherein applying multiple Pauli Z rotations comprises applying the operator e - i ⁡ ( ω - η ) ⁢ Δ ⁢ t 2 ⁢ σ 1 z ⁢ e - i ⁡ ( ω ) ⁢ Δ ⁢ t 2 ⁢ σ 2 z ⁢ e - i ⁡ ( ω - η ) ⁢ Δ ⁢ t 2 ⁢ σ 3 z to the evolved state of the quantum system, wherein ω represents an energy gap that separates the ground and first excited state of the second qubit, η represents qubit anharmoniticity, σ z i is a Pauli-z operator acting on the ith qubit and Δt is the predetermined time.
  4. 4 . The method of claim 1 , wherein the coupling between the first and second qubit and between the second and third qubit is homogeneous.
  5. 5 . The method of claim 4 , wherein the predetermined time is equal to π/2 g, wherein g represents qubit coupling strength.
  6. 6 . The method of claim 4 , wherein the three-qubit gate implements a swap operation between the first qubit and the third qubit, the swap operation being conditioned on the second qubit being in an excited state and assigns a minus sign to swapped basis states.
  7. 7 . The method of claim 1 , wherein the coupling between qubits is inhomogeneous.
  8. 8 . The method of claim 7 , wherein the predetermined time is equal to π/2 g with g = g 1 2 + g 2 2 2 wherein g 1 represents coupling strength between the first qubit and second qubit and g 2 represents coupling strength between the second qubit and third qubit.
  9. 9 . The method of claim 7 , wherein the three-qubit gate implements a partial swap operation between the first qubit and the third qubit, the partial swap operation being conditioned on the second qubit being in an excited state and assigns a minus sign to swapped basis states.
  10. 10 . The method of claim 1 , wherein the Hamiltonian describing the quantum system is given by H ^ 3 = - η 2 ⁢ ∑ j = I 3 n ˆ j ( n ˆ j - 1 ) + ∑ j = 1 3 ω j ( t ) ⁢ n ˆ j + g 1 ( t ) ⁢ ( â 1 ⁢ â 2 † + â 1 † ⁢ â 2 ) + g 2 ( t ) ⁢ ( â 2 ⁢ â 3 † + â 2 † ⁢ â 3 ) where η represents qubit anharmonicity, ω j (t) represents qubit frequency, g(t) represents two-qubit coupling strength, and î j represents an occupation number of qubit i.
  11. 11 . The method of claim 10 , wherein the qubit anharmonicity is equal to 200 MHz.
  12. 12 . The method of claim 10 , wherein a strength of the coupling between the first and second qubit or between the second and third qubit takes values in the range [−5 MHz, 50 MHz].
  13. 13 . The method of claim 10 , wherein energy gaps that separate ground and excited states of the first, second, and third qubits take values in the range [4.0 GHz, 6.0 GHz].
  14. 14 . The method of claim 1 , wherein the first qubit, second qubit and third qubit comprise trapped atoms or photons.
  15. 15 . An apparatus comprising: a quantum system comprising a first qubit, second qubit and third qubit, wherein the second qubit is coupled to the first qubit and to the third qubit; control electronics comprising: one or more control devices; and one or more control lines coupled from the one or more control devices to the quantum system; wherein the control electronics are configured to perform operations for implementing a three-qubit quantum gate on the quantum system, the operations comprising: evolving a state of the quantum system under a Hamiltonian describing the quantum system for a predetermined time, wherein the Hamiltonian comprises a diagonal part and an off-diagonal part and wherein during the evolving: operating frequencies of the first qubit, second qubit, and third qubit are parked such that basis states in a two-excitation subspace of the quantum system and basis states in a three-excitation subspace of the quantum system are degenerate under the diagonal part of the Hamiltonian.
  16. 16 . The apparatus of claim 15 , wherein the first qubit, second qubit and third qubit comprise trapped atoms or photons.
  17. 17 . The apparatus of claim 15 , wherein the coupling between the first and second qubit and between the second and third qubit is homogeneous, and the predetermined time is equal to π/2 g, wherein g represents qubit coupling strength.
  18. 18 . The apparatus of claim 15 , wherein the coupling between qubits is inhomogeneous and the predetermined time is equal to π/2 g with g = g 1 2 + g 2 2 2 wherein g 1 represents coupling strength between the first qubit and second qubit and g 2 represents coupling strength between the second qubit and third qubit.
  19. 19 . The apparatus of claim 15 , wherein the operations further comprise applying multiple Pauli Z rotations to the evolved state of the quantum system to cancel additional phase accumulated in the computational basis during evolution of the state of the quantum system.
  20. 20 . The apparatus of claim 19 , wherein applying multiple Pauli Z rotations comprises applying the operator e - i ⁡ ( ω - η ) ⁢ Δ ⁢ t 2 ⁢ σ 1 z ⁢ e - i ⁡ ( ω ) ⁢ Δ ⁢ t 2 ⁢ σ 2 z ⁢ e - i ⁡ ( ω - η ) ⁢ Δ ⁢ t 2 ⁢ σ 3 z to the evolved state of the quantum system, wherein ω represents an energy gap that separates the ground and first excited state of the second qubit, η represents qubit anharmonicity, σ z i is a Pauli-z operator acting on the ith qubit and Δt is the predetermined time.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS This application is a continuation application of, and claims priority to, U.S. patent application Ser. No. 18/481,109, filed on Oct. 4, 2023, which is a continuation application of, and claims priority to, U.S. patent application Ser. No. 16/981,606, now U.S. Pat. No. 11,809,957, filed on Sep. 16, 2020, which application is a National Stage Application under 35 U.S.C. § 371 and claims the benefit of International Application No. PCT/US2019/016047, filed on Jan. 31, 2019, which claims priority to U.S. Application No. 62/769,398, filed on Nov. 19, 2018. The disclosures of the foregoing applications are incorporated herein by reference in their entirety for all purposes. BACKGROUND This specification relates to quantum computing. Classical computers have memories made up of bits, where each bit can represent either a zero or a one. Quantum computers maintain sequences of quantum bits, called qubits, where each quantum bit can represent a zero, one or any quantum superposition of zeros and ones. Quantum computers operate by setting qubits in an initial state and controlling the qubits, e.g., according to a sequence of quantum logic gates. SUMMARY This specification describes control strategies for implementing three-qubit entangling gates using two-local Hamiltonian control. In general, one innovative aspect of the subject matter described in this specification can be implemented in a method for implementing a three-qubit quantum gate on a quantum system comprising a first qubit, second qubit and third qubit, wherein the second qubit is coupled to the first qubit and to the third qubit, the method comprising: evolving a state of the quantum system under a Hamiltonian describing the quantum system for a predetermined time, wherein during the evolving: the ground and first excited state of the second qubit are separated by a first energy gap; the first and second excited state of the second qubit are separated by a second energy gap that is equal to a first multiple of the first energy gap minus qubit anharmoniticity; the ground and first excited state of the first qubit and ground and first excited state of the third qubit are separated by a third energy gap that is equal to the first energy gap minus the qubit anharmonicity; and the first and second excited state of the first qubit and first and second excited state of the third qubit are separated by a fourth energy gap that is equal to the first multiple of the first energy gap minus a second multiple of the qubit anharmonicity. Other implementations of these aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods. A system of one or more classical and/or quantum computers can be configured to perform particular operations or actions by virtue of having software, firmware, hardware, or a combination thereof installed on the system that in operation causes or cause the system to perform the actions. One or more computer programs can be configured to perform particular operations or actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions. The foregoing and other implementations can each optionally include one or more of the following features, alone or in combination. The first multiple of the first energy gap may be equal to twice the energy gap. The second multiple of the qubit anharmonicity may be equal to three times the qubit anharmonicity. The method may further comprise applying multiple Pauli Z rotations to the evolved state of the quantum system to cancel additional phase accumulated in the computational basis during evolution of the state of the quantum system. Applying multiple Pauli Z rotations may comprise applying the operator e-i⁡(ω-η)⁢Δ⁢t2⁢σ1z⁢e-i⁡(ω)⁢Δ⁢t2⁢σ2z⁢e-i⁡(ω-η)⁢Δ⁢t2⁢σ3z to the evolved state of the quantum system. The coupling between the first and second qubit and between the second and third qubit may be homogeneous. The predetermined time may be equal to π/2 g where g represents qubit coupling strength. Implementing the three-qubit gate may comprise: performing a swap operation between the first qubit and the third qubit, the swap operation being conditioned on the second qubit being in an excited stat, and assigning a minus sign to swapped basis states. The coupling between qubits may be inhomogeneous. The predetermined time may be equal to π/2 g with g=g12+g222 where g1 represents coupling strength between the first qubit and second qubit, and g2 represents coupling strength between the second qubit and third qubit. Implementing the three-qubit gate may comprise: performing a partial swap operation between the first qubit and the third qubit, the partial swap operation being conditioned on the second qubit being in an excited state, and assigning a minus sign to swapped basis states. The