Quantum computation

Abstract

A quantum computing system comprises a quantum processing unit comprising a plurality of quantum devices and a compiling system wherein the compiling system receives a quantum circuit specification and identifies a set of operations that satisfies a predetermined circuit pattern. The system performs a postselection measurement on a first set of the quantum devices (e.g. qubits), determines an updated operation acting on a second set of quantum devices, generates an updated quantum circuit specification by replacing the operations with the updated operations, then performs the operations from the updated circuit specification on the quantum devices. The measurement may need to meet a success criterion, if the criterion is not met the system may repeat the first set of operations, and only performs a new / updated second operation until the success criterion is met.

Description

Field of the invention The present invention relates to quantum computation. Background Quantum computers have the potential to perform computations that would be intractable on even the most powerful classical computers. Instead of representing information using classical bits, quantum computers generally use qubits that can be in a simultaneous superposition of multiple quantum states. Existing quantum computers have very limited qubit numbers, and the qubits in existing quantum computers generally have relatively short coherence times, which means they can only maintain accurate quantum states for relatively short durations. This means that there is a need for techniques that can be used to reduce the number of qubits and / or reduce the time (i.e. the number of operations) required to perform quantum computations. Summary of the invention According to a first aspect of the invention, there is provided a quantum computing system comprising: a quantum processing unit comprising a plurality of quantum devices; and a compiling system, wherein the compiling system is configured to: receive a quantum circuit specification comprising a plurality of operations to be performed on the plurality of quantum devices; identify a set of operations in the quantum circuit specification that satisfies a predefined circuit pattern, the predefined circuit pattern involving a preparation operation on a first set of quantum devices, a unitary operation on the first set of quantum devices and a second set of quantum devices, and a postselection measurement operation on the first set of quantum devices; determine an updated operation acting on the second set of quantum devices; and generate an updated quantum circuit specification by replacing the set of operations in the quantum circuit specification with the updated operation; and wherein the quantum processing unit is configured to: receive the updated quantum circuit specification; and perform operations from the updated quantum circuit specification on the plurality of quantum devices. The quantum computing system of the first aspect can advantageously be used to reduce the number of quantum devices required to perform quantum computations by replacing the set of operations with the updated operation. A quantum processing unit is a device (such as a chip) with one or more quantum devices (such as qubits) that are controlled by a control system (e.g. the control system may transmit microwave pulses for performing operations and readout on the quantum devices). A circuit specification is a data structure that defines sequences of operations (e.g. quantum logic gates) to be performed on quantum devices. The compiling system is a classical processing system that processes a circuit specification to generate an updated circuit specification for use by the control system. The compiling system may optionally receive a high-level circuit specification and output a low level (e.g. machine code or pulse specification) updated circuit specification. Alternatively, the updated circuit specification may be a high-level specification that is converted into low level control signals by the control system. Operations that can be performed on quantum devices include logic gates (e.g. CNOT gates, Hadamard gates, phase gates etc.), readout / measurement operations etc. The unitary operation may be formed of other operations / suboperations (i.e. it may be a compound operation). A circuit pattern is a collection / set of operations that occur in a certain sequence and / or act on certain quantum devices. A postselection measurement operation is a measurement operation that requires the observation of one or more predefined measurement outcomes (e.g. particular measurement value(s) or quantum state(s)). For example, a postselection measurement operation may require that one or more quantum devices are observed to be in a particular state (e.g. the zero state) or equivalently, that measurement of the one or more quantum devices results in a particular measurement value (e.g. a zero value) in order for the quantum computation to be successful. In general, at least part of the quantum computation will be repeated if the postselection measurement operation does not yield the correct outcome. Many quantum computations are probabilistic, meaning that they are only successful with some arbitrary probability that may or may not be known in advance of the computation. Postselection is used to identify successful computation events. The compiling system may be further configured to determine a suboperation representing action of the set of operations on the second set of quantum devices. The suboperation is an operation that acts only on the second set of quantum devices and has the same effect on the second set of quantum devices as the set of operations when the postselection is successful (i.e. the correct postselection measurement outcome / value / state is detected). The compiling system may be further configured to determine whether the suboperation is rank one or proportional to a unitary operation and to determine the updated operation in response to determining that the suboperation is proportional to the unitary operation or is rank one. A rank one matrix is a matrix having rank one (i.e. having one independent column or row), and a unitary matrix is a matrix for which its inverse equals it conjugate transpose. The compiling system may be configured, responsive to determining that the suboperation is proportional to the unitary operation, to determine that the updated operation comprises the suboperation. The compiling system may additionally / alternatively be configured, responsive to determining that the suboperation is rank one, to determine that the updated operation comprises another postselection measurement operation on the second set of quantum devices followed by a state preparation operation on the second set of quantum devices. Determining the updated operation may comprise performing a singular value decomposition to determine first and second (normalised) quantum states, wherein the other postselection measurement is based on the first (normalised) quantum state (i.e. observing the quantum devices in the first (normalised) quantum state) and the state preparation is based on the second (normalised) quantum state (i.e. preparing the quantum devices in the second (normalised) quantum state). As will be known to one skilled in the art, singular value decomposition is a technique that is used to split an arbitrary matrix (such as a matrix representing a unitary operation or set of unitary operations) into a product of a unitary matrix, a non-unitary matrix with singular values on its diagonal, and a second unitary matrix. The second set of quantum devices may exclude quantum devices in the first set of quantum devices. The quantum devices may be qubits. Alternatively, the quantum devices may be other devices capable of storing quantum information, such as qudits or qutrits. According to a second aspect of the invention, there is provided a quantum computing system comprising: a control system; and a plurality of quantum devices communicatively coupled to the control system, wherein the control system is configured to: perform a first quantum operation on the plurality of quantum devices, the first quantum operation associated with a first projected unitary encoding of a first non-unitary operation; subsequent to performing the first quantum operation, perform a first measurement operation on a first subset of the plurality of quantum devices to obtain a first measurement outcome; determine whether the first measurement outcome satisfies a first success criterion; responsive to determining that the first measurement outcome does not satisfy the first success criterion, repeat the first quantum operation and the first measurement operation until the first measurement outcome satisfies the first success criterion; and responsive to determining that the first measurement outcome satisfies the first success criterion, perform a second quantum operation on the plurality of quantum devices, the second quantum operation associated with a second projected unitary encoding of a second non-unitary operation. The quantum computing system of the second aspect advantageously reduces qubit requirements compared to existing approaches, and it also allows for early termination and restart of the quantum computation in the event of an unfavourable postselection outcome (i.e. where the first measurement outcome does not satisfy the first success criterion). In contrast, existing approaches perform further quantum operations subsequent to the first quantum operation before performing postselection operations, thereby requiring the entire computation be repeated in the event of an unfavourable postselection outcome (i.e. existing approaches require that the first operation and all subsequent operations be repeated, whereas the second aspect of the invention does not require repetition of subsequent operations because they are not performed until the first measurement outcome satisfies the first success criterion). The success criterion may be a predefined measurement value (e.g. a zero or one value) or a predefined quantum state (e.g. a |0) state). A quantum operation being associated with a projected unitary encoding means that the action of the quantum operation upon the quantum devices is to perform the projected unitary encoding on the quantum devices. In other words, if the projected unitary encoding is represented by a matrix operation, the quantum operation associated with that projected unitary encoding will apply that matrix operation to the quantum state of the quantum devices. The quantum computing system may be further configured to, subsequent to performing the second quantum operation, perform a second measurement operation on a second subset of the plurality of quantum devices to obtain a second measurement outcome; determine whether the second measurement outcome satisfies a second success criterion; responsive to determining that the second measurement outcome does not satisfy the second success criterion, repeat the first quantum operation, the first measurement operation, the second quantum operation and the second measurement operation until the first measurement outcome satisfies the first success criterion and the second measurement operation satisfies the second measurement outcome. The second subset may share one or more quantum devices with the first subset. The projected unitary encoding of the first non-unitary operation and the projected unitary encoding of the second non-unitary operation may be block encodings. A projected unitary encoding encodes a general matrix (which may be non-unitary) inside a (larger) unitary matrix, and can be extracted with projectors associated with the projected unitary encoding. A block encoding is a special case of a projected unitary encoding, where the general matrix is encoded in a block (e.g. the top-left block) of a (larger) unitary matrix. Further information regarding projected unitary encodings and block encodings can be found in arXiv:1806.01838v1 [quant-ph], which is hereby incorporated by reference, and further information about block encodings can be found in arXiv:2206.03505v1 [quant-ph] and arXiv:2302.10949v1 [quant-ph], both of which are hereby incorporated by reference. The quantum devices may be qubits. Alternatively, the quantum devices may be other devices capable of storing quantum information, such as qudits or qutrits. According to a third aspect of the invention, there is provided a computer-implemented method of performing a quantum computation operation on a quantum computing system comprising a quantum processing unit and a compiling system, the quantum processing unit comprising a plurality of quantum devices, the method comprising: receiving, at the compiling system, a quantum circuit specification comprising a plurality of operations to be performed on the plurality of quantum devices; identifying, at the compiling system, a set of operations in the quantum circuit specification that satisfies a predefined circuit pattern, the predefined circuit pattern involving a preparation operation on a first set of quantum devices, a unitary operation on the first set of quantum devices and a second set of quantum devices, and a postselection measurement operation on the first set of quantum devices; determining, at the compiling system, an updated operation acting on the second set of quantum devices; generating, at the compiling system, an updated quantum circuit specification by replacing the set of operations in the quantum circuit specification with the updated operation; receiving, at the quantum processing unit from the compiling system, the updated circuit specification; and performing, at the quantum processing unit, operations from the updated quantum circuit specification on the plurality of quantum devices. The third aspect of the invention provides the same benefits as the first aspect of the invention. The method may further comprise determining, at the compiling system, a suboperation representing action of the set of operations on the second set of quantum devices. The method may further comprise determining, at the compiling system, whether the suboperation is rank one or proportional to a unitary operation, wherein the updated operation is determined in response to determining that the suboperation is proportional to the unitary operation or is rank one. The method may further comprise, responsive to determining that the suboperation is proportional to the unitary operation, determining, by the compiling system, that the updated operation comprises the suboperation. The method may further comprise, responsive to determining that the suboperation is rank one, determining, by the compiling system, that the updated operation comprises another postselection measurement operation on the second set of quantum devices followed by a state preparation operation on the second set of quantum devices. Determining the updated operation may comprise performing a singular value decomposition to determine first and second (normalised) quantum states, wherein the other postselection measurement is based on the first (normalised) quantum state and the state preparation is based on the second (normalised) quantum state. The second set of quantum devices may exclude quantum devices in the first set of quantum devices. The quantum devices may be qubits. Alternatively, the quantum devices may be other devices capable of storing quantum information, such as qudits or qutrits. According to a fourth aspect of the invention, there is provided a computer implemented method performed by a quantum computing system comprising a control system and a plurality of qubits communicatively coupled to the control system, the method comprising: performing a first quantum operation on the plurality of quantum devices, the first quantum operation associated with a first projected unitary encoding of a first non-unitary operation; performing a first measurement operation on a first subset of the plurality of quantum devices to obtain a first measurement outcome; determining whether the first measurement outcome satisfies a first success criterion; responsive to determining that the first measurement outcome does not satisfy the first success criterion, repeating the first quantum operation and the first measurement operation until the first measurement outcome satisfies the first success criterion; and responsive to determining that the first measurement outcome satisfies the first success criterion, performing a second quantum operation on the plurality of quantum devices, the second quantum operation associated with a second projected unitary encoding of a second non-unitary operation. The fourth aspect of the invention provides the same benefits as the second aspect of the invention. The method may further comprise, subsequent to performing the second quantum operation, performing a second measurement operation on a second subset of the plurality of quantum devices to obtain a second measurement outcome; determining whether the second measurement outcome satisfies a second success criterion; responsive to determining that the second measurement outcome does not satisfy the second success criterion, repeating the first quantum operation, the first measurement operation, the second quantum operation and the second measurement operation until the first measurement outcome satisfies the first success criterion and the second measurement operation satisfies the second measurement outcome. The projected unitary encoding of the first non-unitary operation and the projected unitary encoding of the second non-unitary operation may be block encodings. The quantum devices may be qubits. Alternatively, the quantum devices may be other devices capable of storing quantum information, such as qudits or qutrits. According to a fifth aspect of the invention, there is provided a non-transitory computer-readable medium comprising instructions which, when executed by a quantum computing system comprising a quantum processing unit and a compiling system, the quantum processing unit comprising a plurality of quantum devices, cause the quantum computing system to perform the method of the third aspect. According to a sixth aspect of the invention, there is provided a non-transitory computer-readable medium comprising instructions which, when executed by a quantum computing system comprising a control system and a plurality of qubits communicatively coupled to the control system, cause the quantum computing system to perform the method of the fourth aspect of the invention. Brief description of the drawings Examples of the present invention will now be described in detail with reference to the accompanying drawings, in which: Fig. 1 shows a quantum computing system; Fig. 2 shows a method of compiling a quantum circuit; Figs. 3a-c show quantum circuits; Fig. 4 shows a method of performing a multiplication operation on a quantum computer; Fig. 5 shows two equivalent quantum circuits; Fig. 6 shows two equivalent quantum circuits for multiplication operations; and Fig. 7 shows a quantum circuit. Detailed description A schematic of an exemplary quantum computing system 100 for performing the methods of the present disclosure is shown in Fig. 1. The quantum computing system 100 comprises a plurality of quantum devices 106, such as physical or logical qubits. The quantum devices 106 are controlled by a classical control system 104, and both the quantum devices 106 and control system 104 are part of a quantum processing unit (QPU) 108. The control system 104 transmits control signals to the quantum devices 106 for performing operations on the quantum devices 106 (including measurement operations) and receives measurement information from the quantum devices 106. The measurement information will generally be analogue data signals, although the analogue signals may alternatively be converted to digital signals before being transmitted to the control system 104 in some implementations (e.g. the quantum devices 106 may be provided with one or more analogue-to-digital converters). The control system 104 may receive high-level instructions and convert these high-level instructions (such as logic gates) into low-level qubit instructions (e.g. microwave pulses etc.), which may be in analogue format. The illustrated quantum computing system 100 additionally comprises a compiling system 102. The compiling system 102 is operable to receive quantum circuit specifications for sending to the control system 104. The compiling system 102 may process the circuit specifications to generate updated circuit specifications and / or translate high-level circuit specifications into low-level machine code or pulse specifications that the control system 104 can use to perform operations on the quantum devices 106. One skilled in the art will appreciate that the quantum computing system 100 may also comprise additional components, including intermediary components positioned between the illustrated components, and that the illustrated components may be connected in a different configuration. For example, the quantum computing system 100 may additionally comprise a decoding system used to perform quantum error correction. The quantum computing system 100 of Fig. 1 is used to compile quantum circuits requiring fewer quantum operations (i.e. that have shorter circuit depth) and fewer qubits compared to circuit specifications received by (input to) the quantum computing system 100. The steps performed by the quantum computing system 100 when compiling and performing quantum circuits are shown in Fig. 2. In a first step 201, the compiling system 102 receives a quantum circuit specification comprising a plurality of operations to be performed on the quantum devices 106. The quantum circuit specification may include quantum operations such as qubit quantum logic gates and may specify which quantum device(s) each operation acts upon. Examples of quantum logic gates include (among others) phase gates, Hadamard gates, control-NOT gates etc. In a second step 202, the compiling system 102 identifies a set of operations in the quantum circuit specification that satisfies a predefined circuit pattern. In particular, the compiling system 102 identifies a set of operations involving a preparation operation on a first set of quantum devices, followed by a unitary operation on the first set of quantum devices and a second set of quantum devices, followed by a postselection measurement operation on the first set of quantum devices. This circuit pattern is shown in Fig. 3a, in which a first set of qubits (represented by the topmost line of N qubits, wherein the forward slash on a qubit line indicates a register of one or more qubits) is prepared in a |0) state, a unitary operation U is performed on the first set of qubits (the top register of N qubits) and a second set of qubits (the bottom register of M qubits), and a postselection measurement operation (measurement of the state |0)) is performed on the first set of qubits. In a next step 203, the compiling system 102 determines an updated operation acting upon the second set of quantum devices (the bottom register of qubits in Fig. 3a). Determining the updated operation may involve determining a suboperation representing action of the set of operations on the subset of the second set of quantum devices. This suboperation may be logically equivalent to an M x M matrix u, where u = «o| ® n)t / (|O)® n) where the left hand side of the tensor products acts upon the first set of quantum devices and the right hand size of the tensor product acts upon the second set of quantum devices. This equation assumes preparation and postselection of the first set of qubits in the state 10), one skilled in the art will appreciate that this equation can be adjusted accordingly when using different preparation and postselection states (or alternatively, operations relating to preparation and postselection can be incorporated into 1 / ). For example, the suboperation can be obtained by reshaping the unitary operation U (which is a 2N+M x 2n+m matrix) into a 2N x 2N x 2M x 2M tensor Uijkl; then ukt = U00kt. Reshaping is a relatively low-resource operation, and if the initial and postselected state are computation basis states |i) and |j) then ukt = UiM. If the suboperation is proportional to a unitary operation (i.e. if u / c is unitary for some scale factor c e R+) then the updated operation comprises the suboperation acting on the second set of quantum devices (e.g. it may comprise the suboperation divided by c (i.e. normalised) to ensure that the updated operation is unitary). If the suboperation is not proportional to a unitary but is rank one (i.e. u is a matrix with rank equal to one), a singular value decomposition can be performed on u to yield a decomposition u = c|0)(0I with firstand second normalised states |0) and |0) respectively, where c is once again a scale factor. In this case, the updated operation comprises a postselecting the (normalised) measurement outcome |0) on the second set of quantum devices followed by preparation of the second set of quantum devices in the (normalised) state |0). Once the updated operation has been determined, the compiling system 102 proceeds to step 204 in which an updated quantum circuit specification is generated by replacing the set of operations in the quantum circuit specification with the updated operation. The updated quantum circuit specification is then sent to the QPU 108 by the compiling system 102. The QPU 108 receives the updated quantum circuit specification and performs operations from the updated quantum circuit specification on the plurality of quantum devices 106 in step 205. The method of Fig. 2 replaces the circuit shown in Fig. 3a with that shown on the right hand side of Fig. 3b (in the case that the suboperation u is proportional to a unitary operation) or that shown on the right hand side of Fig. 3c (in the case that the suboperation u is rank one). In both cases, it can be seen that the top register of qubits is no longer required, thereby reducing the number of qubits required in the quantum circuit. In addition, the circuit of Fig. 3b removes the need for postselection, thereby providing a deterministic circuit that does not need to be repeated (unlike postselected circuits, in which the circuit has to be repeated if the wrong measurement outcome is obtained) and preventing detrimental effects caused by measurement errors. Similarly, the circuit of Fig. 3c further improves performance by moving the postselection operation earlier in the circuit and reducing the number of operations required (the unitary U is no longer performed). Furthermore, when the scale factor c is less than one (c <1), the circuit transformation automatically includes a uniform amplitude amplification by an amplification factor 1 / c, which boosts the success probability of the postselection. The compilation speed may optionally be increased by using a database of common operations to generate the updated quantum circuit specification for certain operations U. While the method of Fig. 2 initialises and postselects the first set of qubits using the state |0), it should be appreciated that different initialisation and / or postselection states and / or bases may be used, in which case the operations required to map the |0) state into the chosen initialisation and / or postselection operations can effectively be defined as part of (i.e. absorbed into) the unitary operation U. In addition, SWAP gates can be used and absorbed into the unitary U such that the input and output qubits needn’t be aligned, and different size input and output registers can be used by absorbing surplus qubits into the bottom register of Fig. 3a. The method of Fig. 2 is particularly beneficial when used to perform matrix multiplication using projected unitary encodings (such as block matrices). An example of such a method, which may be performed by a quantum computing system 100 such as that shown in Fig. 1, is shown in Fig. 4. In a first step 401, a control system 104 performs a first quantum operation on a plurality of quantum devices 106, followed by a first measurement operation on a first subset of the plurality of quantum devices in step 402 to obtain a first measurement outcome. The first quantum operation may be associated with (i.e. a circuit representing) a projected unitary encoding of a first non-unitary operation. In step 403, the control system 104 determines whether the first measurement outcome satisfies a first success criterion, e.g. whether the measurement outcome is equal to a desired / predefined first measurement value. If the first measurement outcome does not satisfy the first success criterion, the method returns to step 401 and the first quantum operation and first measurement operation are repeated until the first measurement outcome satisfies the first success criterion. It should be understood that additional operations may be repeated in addition to the first quantum operation (e.g. operations preceding the first quantum operation in a quantum operation and / or operations to prepare quantum device states). Once the first success criterion is satisfied in step 403, the control system 104 performs a second quantum operation on the plurality of quantum devices 106 in step 404, the second quantum operation being associated with a second projected unitary encoding of a second non-unitary operation. At this point, the result of a multiplication between the first and second non-unitary operations is encoded in a second subset of the plurality of quantum devices. This second subset of quantum devices can be fed into a further quantum computation, or alternatively the method may proceed to step 405 in which the control system 104 performs a second measurement operation on the second subset of quantum devices 106 to obtain a second measurement outcome. In step 406, the control system 104 determines whether this second measurement outcome satisfies a second success criterion (e.g. whether the second measurement outcome is equal to a desired / predefined second measurement value). If the second measurement outcome does not satisfy the second success criterion, the method returns to step 401 and is repeated from the start. However, if the second measurement outcome does satisfy the second success criterion, the result of a multiplication between the first and second non-unitary operations can be inferred e.g. by measuring the quantum devices 106 in the second subset of quantum devices. In essence, the multiplication method of Fig. 4 applies the compilation method of Fig. 2 to the circuit shown on the left hand side of Fig. 5 to produce the circuit on the right hand side of Fig. 5. In this case, the set of operations includes those within the dashed box, i.e. a variant of a controlled-not gate (acting on the top qubit, controlled by all qubits in the bottom register being in the |0) state) followed by an X gate acting on the top qubit and postselection of the top qubit in the |0) state. As shown in Fig. 5, the method of Fig. 2 produces the equivalent circuit on the right hand side of Fig. 5, in which the top qubit is no longer required, and the set of operations is replaced by a postselection of the bottom register of qubits in the |0) state followed by initialisation of the bottom register of qubits in the |0) state. The circuit identity in Fig. 5 can be applied to the operations in the dashed box on the circuit on the left hand side of Fig. 6 (which is a multiplication circuit that multiplies first and second non-unitary operations encoded in first and second projected unitary encodings U2 and U1 and encodes the multiplication result in the bottom register of qubits) to provide the circuit on the right hand side of Fig. 6 (where the dashed box on the right of Fig. 6 represents operations equivalent to those in the dashed box on the left hand side of Fig. 6). The circuit on the right hand side of Fig. 6 has two advantages over the equivalent circuit on the left hand side: firstly, it requires fewer qubits (the topmost qubit from the left hand side of Fig. 6 is no longer required). Secondly, by performing on of the postselection measurement before performing the second projected unitary encoding Ult the circuit can be terminated and restarted earlier if the measurement outcome does not satisfy the first success criterion (i.e. observation of the state |0)). This early termination and restart avoids the need to perform (and then repeat) the second projected unitary encoding U1 in scenarios where the computation is destined to fail, thereby reducing the average number of total operations required to obtain a successful outcome (in conventional approaches, the postselection occurs at the end of the circuit and the entire computation must be repeated if the outcome does not satisfy the success criterion, whereas the approach disclosed herein effectively detects unfavourable postselection measurement outcomes at an early stage, such that only part of the computation needs to be repeated). While the method of Fig. 2 is particularly beneficial when used to perform matrix multiplication as in Fig. 4, it can also be applied to other circuits. For example, the circuit on the left hand side of Fig. 7 can be simplified by using the method of Fig. 2 to obtain the circuit shown on the right hand side of Fig. 7 with u / c = X. The term “set” used herein should be understood to refer to a collection of one or more entities / concepts (e.g. quantum devices). Likewise, a “subset” should be understood to refer to one or more entities / concepts (e.g. quantum devices) selected from a set. It should be understood that any method of the present disclosure could include additional steps, and any device could include additional components. In addition, unless indicated otherwise or technically infeasible, the method steps disclosed herein may be performed in alternative orders, and any order described herein should be considered as exemplary rather than limiting. The illustrated steps and components could be split into multiple sub-steps / subcomponents. Furthermore, one skilled in the art will appreciate that any computation that can be performed by a classical processing device can also be performed by a quantum computing device. Accordingly, any methods or described herein that is performed on a classical computing device (such as a CPU) can also be performed by a quantum processing device, such as a quantum processing unit (QPU) comprising a plurality of qubits. While the above examples use qubits as the quantum devices, it should be understood that these examples could alternatively be implemented with other types of quantum devices, 5 such as qutrits or qudits, and that the invention disclosed herein is applicable to both qubits and other types of quantum devices.

Claims

1. A quantum computing system comprising:a quantum processing unit comprising a plurality of quantum devices; anda compiling system,wherein the compiling system is configured to:receive a quantum circuit specification comprising a plurality of operations to be performed on the plurality of quantum devices;identify a set of operations in the quantum circuit specification that satisfies a predefined circuit pattern, the predefined circuit pattern involving:a preparation operation on a first set of quantum devices,a unitary operation on the first set of quantum devices and a second set of quantum devices, anda postselection measurement operation on the first set of quantum devices;determine an updated operation acting on the second set of quantum devices; and generate an updated quantum circuit specification by replacing the set of operations in the quantum circuit specification with the updated operation; andwherein the quantum processing unit is configured to:receive the updated quantum circuit specification; andperform operations from the updated quantum circuit specification on the plurality of quantum devices.

2. The quantum computing system of claim 1, wherein the compiling system is further configured to determine a suboperation representing action of the set of operations on the second set of quantum devices.

3. The quantum computing system of claim 2, wherein the compiling system is further configured to determine whether the suboperation is rank one or proportional to a unitary operation, and wherein the compiling system is configured to determine the updated operation in response to determining that the suboperation is proportional to the unitary operation or is rank one.

4. The quantum computing system of claim 3, wherein, responsive to determining that the suboperation is proportional to the unitary operation, the compiling system is configured to determine that the updated operation comprises the suboperation.

5. The quantum computing system of claim 3, wherein, responsive to determining that the suboperation is rank one, the compiling system is configured to determine that the 14updated operation comprises another postselection measurement operation on the second set of quantum devices followed by a state preparation operation on the second set of quantum devices.

6. The quantum computing system of claim 5, wherein determining the updated operation comprises performing a singular value decomposition to determine first and second quantum states, wherein the other postselection measurement is based on the first quantum state and the state preparation is based on the second quantum state.

7. The quantum computing system of any preceding claim, wherein the second set of quantum devices excludes quantum devices in the first set of quantum devices.

8. The quantum computing system of any preceding claim, wherein the quantum devices are qubits.

9. A quantum computing system comprising:a control system; anda plurality of quantum devices communicatively coupled to the control system,wherein the control system is configured to:perform a first quantum operation on the plurality of quantum devices, the first quantum operation associated with a first projected unitary encoding of a first non-unitary operation;subsequent to performing the first quantum operation, perform a first measurement operation on a first subset of the plurality of quantum devices to obtain a first measurement outcome;determine whether the first measurement outcome satisfies a first success criterion;responsive to determining that the first measurement outcome does not satisfy the first success criterion, repeat the first quantum operation and the first measurement operation until the first measurement outcome satisfies the first success criterion; andresponsive to determining that the first measurement outcome satisfies the first success criterion, perform a second quantum operation on the plurality of quantum devices, the second quantum operation associated with a second projected unitary encoding of a second non-unitary operation.

10. The quantum computing system of claim 9, wherein the control system is further configured to:subsequent to performing the second quantum operation, perform a second measurement operation on a second subset of the plurality of quantum devices to obtain a second measurement outcome;determine whether the second measurement outcome satisfies a second success criterion;responsive to determining that the second measurement outcome does not satisfy the second success criterion, repeat the first quantum operation, the first measurement operation, the second quantum operation and the second measurement operation until the first measurement outcome satisfies the first success criterion and the second measurement operation satisfies the second measurement outcome.

11. The quantum computing system of claim 9 or claim 10, wherein the projected unitary encoding of the first non-unitary operation and / or the projected unitary encoding of the second non-unitary operation are block encodings.

12. The quantum computing system of any of claims 9 to 11, wherein the quantum devices are qubits.

13. A computer-implemented method of performing a quantum computation operation on a quantum computing system comprising a quantum processing unit and a compiling system, the quantum processing unit comprising a plurality of quantum devices, the method comprising:receiving, at the compiling system, a quantum circuit specification comprising a plurality of operations to be performed on the plurality of quantum devices;identifying, at the compiling system, a set of operations in the quantum circuit specification that satisfies a predefined circuit pattern, the predefined circuit pattern involving:a preparation operation on a first set of quantum devices,a unitary operation on the first set of quantum devices and a second set of quantum devices, anda postselection measurement operation on the first set of quantum devices;determining, at the compiling system, an updated operation acting on the second set of quantum devices;generating, at the compiling system, an updated quantum circuit specification by replacing the set of operations in the quantum circuit specification with the updated operation;receiving, at the quantum processing unit from the compiling system, the updated circuit specification; andperforming, at the quantum processing unit, operations from the updated quantum circuit specification on the plurality of quantum devices.

14. The method of claim 13, further comprising determining, at the compiling system, a suboperation representing action of the set of operations on the second set of quantum devices.

15. The method of claim 14, further comprising determining, at the compiling system, whether the suboperation is rank one or proportional to a unitary operation, wherein the updated operation is determined in response to determining that the suboperation is proportional to the unitary operation or is rank one.

16. The method of claim 15, wherein, responsive to determining that the suboperation is proportional to the unitary operation, the compiling system determines that the updated operation comprises the suboperation.

17. The method of claim 15, wherein, responsive to determining that the suboperation is rank one, the compiling system determines that the updated operation comprises another postselection measurement operation on the second set of quantum devices followed by a state preparation operation on the second set of quantum devices.

18. The method of claim 17, wherein determining the updated operation comprises performing a singular value decomposition to determine first and second quantum states, wherein the other postselection measurement is based on the first quantum state and the state preparation is based on the second quantum state.

19. The method of any of claims 13 to 18, wherein the second set of quantum devices excludes quantum devices in the first set of quantum devices.

20. The method of any of claims 13 to 19, wherein the quantum devices are qubits.

21. A computer implemented method performed by a quantum computing system comprising a control system and a plurality of qubits communicatively coupled to the control system, the method comprising:performing a first quantum operation on the plurality of quantum devices, the first quantum operation associated with a first projected unitary encoding of a first non-unitary operation;performing a first measurement operation on a first subset of the plurality of quantum devices to obtain a first measurement outcome;determining whether the first measurement outcome satisfies a first success criterion;responsive to determining that the first measurement outcome does not satisfy the first success criterion, repeating the first quantum operation and the first measurement operation until the first measurement outcome satisfies the first success criterion; andresponsive to determining that the first measurement outcome satisfies the first success criterion, performing a second quantum operation on the plurality of quantum devices, the second quantum operation associated with a second projected unitary encoding of a second non-unitary operation.

22. The method of claim 21, further comprising:subsequent to performing the second quantum operation, performing a second measurement operation on a second subset of the plurality of quantum devices to obtain a second measurement outcome;determining whether the second measurement outcome satisfies a second success criterion;responsive to determining that the second measurement outcome does not satisfy the second success criterion, repeating the first quantum operation, the first measurement operation, the second quantum operation and the second measurement operation until the first measurement outcome satisfies the first success criterion and the second measurement operation satisfies the second measurement outcome.

23. The method of claim 21 or claim 22, wherein the projected unitary encoding of the first non-unitary operation and the projected unitary encoding of the second non-unitary operation are block encodings.

24. The method of any of claims 21 to 23, wherein the quantum devices are qubits.

25. A non-transitory computer-readable medium comprising instructions which, when executed by a quantum computing system comprising a quantum processing unit and a compiling system, the quantum processing unit comprising a plurality of quantum devices, cause the quantum computing system to:receive, at the compiling system, a quantum circuit specification comprising a plurality of operations to be performed on the plurality of quantum devices;identify, at the compiling system, a set of operations in the quantum circuit specification that satisfies a predefined circuit pattern, the predefined circuit pattern involving:a preparation operation on a first set of quantum devices,a unitary operation on the first set of quantum devices and a second set of quantum devices, anda postselection measurement operation on the first set of quantum devices;determine, at the compiling system, an updated operation acting on the second set of quantum devices;generate, at the compiling system, an updated quantum circuit specification by replacing the set of operations in the quantum circuit specification with the updated operation;receive, at the quantum processing unit from the compiling system, the updated circuit specification; andperform, at the quantum processing unit, operations from the updated quantum circuit specification on the plurality of quantum devices.

26. A non-transitory computer-readable medium comprising instructions which, when executed by a quantum computing system comprising a control system and a plurality of qubits communicatively coupled to the control system, cause the quantum computing system to:perform a first quantum operation on the plurality of quantum devices, the first quantum operation associated with a first projected unitary encoding of a first non-unitary operation;perform a first measurement operation on a first subset of the plurality of quantum devices to obtain a first measurement outcome;determine whether the first measurement outcome satisfies a first success criterion;responsive to determining that the first measurement outcome does not satisfy the first success criterion, repeat the first quantum operation and the first measurement operation until the first measurement outcome satisfies the first success criterion; andresponsive to determining that the first measurement outcome satisfies the first success criterion, perform a second quantum operation on the plurality of quantum devices, the second quantum operation associated with a second projected unitary encoding of a second non-unitary operation.

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