Quantum computing on encrypted data

A quantum computing system comprising:

• an interface operable to:
• receive an encrypted state and a control message from a computing device;
• and
• send an encrypted output state and encryption-key-update information to the computing device;
• a quantum register operable to store the encrypted state;
• and
• quantum logic operable to apply a quantum circuit to the encrypted state to produce the encrypted output state, the quantum circuit comprising a sequence of operations that manipulates the quantum register, wherein the sequence of operations includes:
• a unitary operation parameterized by a control message from the computing device;
• and
• an operation that produces the encryption-key-update information
• wherein the sequence of operations uses an auxiliary quantum state as input, the auxiliary quantum state includes an auxiliary qubit, the quantum register includes a register qubit, and applying the sequence of operations includes:
• applying a first gate to the auxiliary qubit and the register qubit;
• after applying the first gate:
• measuring the register qubit to obtain the encryption-key-update information;
• and
• applying a second gate to the auxiliary qubit, wherein the second gate is parameterized by the control message.

A quantum computing method comprising:

• receiving an encrypted state from a correspondent;
• receiving a control message from the correspondent;
• storing the encrypted state in a quantum register;
• applying a quantum circuit to the encrypted state to produce an encrypted output state, the quantum circuit comprising a sequence of operations that manipulates the quantum register and uses an auxiliary quantum state selected from four specified states, and the sequence of operations includes:
• an operation parameterized by a control message from the correspondent;
• and
• an operation that produces encryption-key-update information
• wherein the auxiliary quantum state includes an auxiliary qubit, the quantum register includes a register qubit, and applying the sequence of operations includes:
• applying a first gate to the auxiliary qubit and the register qubit;
• after applying the first gate:
• measuring the register qubit to obtain the encryption-key-update information;
• and
• applying a second gate to the auxiliary qubit, wherein the second gate is parameterized by the control message;
• sending the encrypted output state to the correspondent;
• and
• sending the encryption-key-update information to the correspondent.

A quantum computing system comprising:

• an interface operable to:
• receive an encrypted state and a control message from a computing device;
• and
• send an encrypted output state and encryption-key-update information to the computing device;
• a quantum register operable to store the encrypted state;
• and
• quantum logic operable to apply a quantum circuit to the encrypted state to produce the encrypted output state, the quantum circuit comprising a sequence of operations that manipulates the quantum register, wherein the sequence of operations is configured to receive an auxiliary quantum state selected from four specified states, and the sequence of operations includes:
• an operation parameterized by a control message from the computing device;
• and
• an operation that produces encryption-key-update information
• wherein auxiliary quantum state includes an auxiliary qubit, the quantum register includes a register qubit, and applying the sequence of operations includes:
• applying a first gate to the auxiliary qubit and the register qubit;
• after applying the first gate:
• measuring the register qubit to obtain the encryption-key-update information;
• and
• applying a second gate to the auxiliary qubit, wherein the second gate is parameterized by the control message.

A method comprising:

• receiving an encrypted quantum input state from a correspondent;
• receiving a control message from the correspondent;
• storing the encrypted quantum input state in a quantum register that includes a register qubit;
• performing, by a quantum information processing apparatus, a quantum computation that generates an encrypted quantum output state from the encrypted quantum input state, wherein the quantum computation uses an auxiliary quantum state as input, the auxiliary quantum state includes an auxiliary qubit, and performing the quantum computation includes:
• applying a first gate to the auxiliary qubit and the register qubit;
• after applying the first gate:
• measuring the register qubit to obtain encryption-key-update information;
• and
• applying a second gate to the auxiliary qubit, wherein the second gate is parameterized by the control message;
• generating an encryption-key-update message based on the computation, wherein the encryption-key-update message includes the encryption-key-update information;
• sending the encrypted output state to the correspondent;
• and
• sending the encryption-key-update message to the correspondent.