# US 12,182,663 B2 · Quantum circuits with reduced T gate count

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- Number: US 12,182,663 B2
- Document ID: US12182663B2
- Status: Granted
- Kind: B2
- Application number: 18/229,457
- Filed: 2023-08-02
- Published: 2024-04-25
- Granted: 2024-12-31
- Earliest claimed: 2017-09-08
- Assignees: Google Inc.
- Applicants: Google LLC
- Inventors: Craig Gidney
- Web page: https://patentgrep.com/patent/US12182663B2

## CPC

- G06N 10/20: Models of quantum computing, e.g. quantum circuits or universal quantum computers
- G06N 10/70: Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation
- H03K 19/195: using superconductive devices
- H03K 19/20: characterised by logic function, e.g. AND, OR, NOR, NOT circuits (H03K19/003 - H03K19/01 take precedence)
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- H03K: PULSE TECHNIQUE (measuring pulse characteristics G01R; modulating sinusoidal oscillations with pulses H03C; transmission of digital information H04L; discriminator circuits detecting phase difference between two signals by counting or integrating cycles of oscillation H03D3/04; automatic control, starting, synchronisation or stabilisation of generators of electronic oscillations or pulses where the type of generator is irrelevant or unspecified H03L; coding, decoding or code conversion, in general H03M)

## Abstract

Methods, systems and apparatus for producing quantum circuits with low T gate counts. In one aspect, a method for performing a temporary logical AND operation on two control qubits includes the actions of obtaining an ancilla qubit in an A-state; computing a logical-AND of the two control qubits and storing the computed logical-AND in the state of the ancilla qubit, comprising replacing the A-state of the ancilla qubit with the logical-AND of the two control qubits; maintaining the ancilla qubit storing the logical-AND of the two controls until a first condition is satisfied; and erasing the ancilla qubit when the first condition is satisfied.

## Claims

### Claim 1

A method for performing a temporary Toffoli quantum logic gate on two control qubits and a target qubit, the method comprising:
storing a computed logical-AND of two control qubits in a state of an ancilla qubit prepared in an A-state;
applying a CNOT quantum logic gate between (i) the ancilla qubit storing the logical-AND of the two control qubits, and (ii) the target qubit, the ancilla qubit acting as a control qubit for the CNOT quantum logic gate;
providing the ancilla qubit storing the logical-AND of the two control qubits as a resource for one or more additional operations; and
replacing the state of the ancilla qubit storing the computed logical-AND of the two control qubits with an A-state.

### Claim 2 (depends on 1)

The method of claim 1, further comprising providing the ancilla qubit in the A-state as a resource for one or more additional operations.

### Claim 3 (depends on 2)

The method of claim 2, wherein providing the ancilla qubit in the A-state as a resource for one or more additional operations comprises providing the ancilla qubit in the A-state to perform a T gate.

### Claim 4 (depends on 2)

The method of claim 2, wherein the method is used to perform a first temporary Toffoli quantum logic gate on two control qubits and a target qubit, and wherein providing the ancilla qubit in the A-state as a resource for one or more additional operations comprises providing the ancilla qubit in the A-state to perform a second temporary Toffoli quantum logic gate on two control qubits and a target qubit.

### Claim 5 (depends on 1)

The method of claim 1, wherein storing the computed logical-AND of the two control qubits in the state of the ancilla qubit prepared in the A-state comprises:
applying a CNOT gate between the ancilla qubit in the A-state and a first control qubit;
applying a Hermitian conjugate of a T gate to the ancilla qubit;
applying a CNOT gate between the ancilla qubit and a second control qubit;
applying a T gate to the ancilla qubit;
applying a CNOT gate between the ancilla qubit and the first control qubit;
applying the Hermitian conjugate of a T gate to the ancilla qubit; and
applying a Hadamard gate to the ancilla qubit to store the logical AND of the two control qubits in the state of the ancilla qubit.

### Claim 6 (depends on 5)

The method of claim 5, further comprising applying an uncontrolled-S gate to the ancilla qubit storing the logical-AND of the two control qubits.

### Claim 7 (depends on 1)

The method of claim 1, wherein replacing the state of the ancilla qubit storing the computed logical-AND of the two control qubits with an A-state comprises:
applying a Hadamard gate to the ancilla qubit storing the logical-AND of the two control qubits;
applying a T gate to the ancilla qubit;
applying a CNOT gate between the ancilla qubit and a first control qubit;
applying a Hermitian conjugate of a T gate to the ancilla qubit;
applying a CNOT gate between the ancilla qubit and a second control qubit;
applying a T gate to the ancilla qubit; and
applying a CNOT gate between the ancilla qubit and the first control qubit to leave the ancilla qubit in an A-state.

### Claim 8 (depends on 7)

The method of claim 7, further comprising applying an uncontrolled-S gate to the ancilla qubit.

### Claim 9

A quantum computing device comprising:
a register of qubits comprising two control qubits, a target qubit, and an ancilla qubit prepared in an initial state;
a plurality of control lines coupled to the register of qubits;
a plurality of control circuits coupled to the plurality of control lines, the plurality of control circuits configured to perform operations comprising:
storing a computed logical-AND of two control qubits in a state of an ancilla qubit prepared in an A-state;
applying a CNOT quantum logic gate between (i) the ancilla qubit storing the logical-AND of the two control qubits, and (ii) the target qubit, the ancilla qubit acting as a control qubit for the CNOT quantum logic gate;
providing the ancilla qubit storing the logical-AND of the two control qubits as a resource for one or more additional operations; and
replacing the state of the ancilla qubit storing the computed logical-AND of the two control qubits with an A-state.

### Claim 10 (depends on 9)

The quantum computing device of claim 9, wherein the operations further comprise providing the ancilla qubit in the A-state as a resource for one or more additional operations.

### Claim 11 (depends on 10)

The quantum computing device of claim 10, wherein providing the ancilla qubit in the A-state as a resource for one or more additional operations comprises providing the ancilla qubit in the A-state to perform a T gate.

### Claim 12 (depends on 10)

The quantum computing device of claim 10, wherein the operations are used to perform a first temporary Toffoli quantum logic gate on the two control qubits and the target qubit, and wherein providing the ancilla qubit in the A-state as a resource for one or more additional operations comprises providing the ancilla qubit in the A-state to perform a second temporary Toffoli quantum logic gate on two control qubits and a target qubit.

### Claim 13 (depends on 9)

The quantum computing device of claim 9, wherein storing the computed logical-AND of the two control qubits in the state of the ancilla qubit prepared in the A-state comprises:
applying a CNOT gate between the ancilla qubit in the A-state and a first control qubit;
applying a Hermitian conjugate of a T gate to the ancilla qubit;
applying a CNOT gate between the ancilla qubit and a second control qubit;
applying a T gate to the ancilla qubit;
applying a CNOT gate between the ancilla qubit and the first control qubit;
applying the Hermitian conjugate of a T gate to the ancilla qubit; and
applying a Hadamard gate to the ancilla qubit to store the logical AND of the two control qubits in the state of the ancilla qubit.

### Claim 14 (depends on 13)

The quantum computing device of claim 13, wherein the operations further comprise applying an uncontrolled-S gate to the ancilla qubit storing the logical-AND of the two control qubits.

### Claim 15 (depends on 9)

The quantum computing device of claim 9, wherein replacing the state of the ancilla qubit storing the computed logical-AND of the two control qubits with an A-state comprises:
applying a Hadamard gate to the ancilla qubit storing the logical-AND of the two control qubits;
applying a T gate to the ancilla qubit;
applying a CNOT gate between the ancilla qubit and a first control qubit;
applying a Hermitian conjugate of a T gate to the ancilla qubit;
applying a CNOT gate between the ancilla qubit and a second control qubit;
applying a T gate to the ancilla qubit; and
applying a CNOT gate between the ancilla qubit and the first control qubit to leave the ancilla qubit in an A-state.

### Claim 16 (depends on 15)

The quantum computing device of claim 15, wherein the operations further comprise applying an uncontrolled-S gate to the ancilla qubit.